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<title>Engineering Computation with Matlab</title>
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<div><nav class="navbar navbar-expand-lg fixed-top top-nav navbar-light bg-light"><a class="navbar-brand" href="#"><img src="build\Images\../Images/1371.png" width="30" height="30" class="d-inline-block align-top" alt=""> Engineering Computation Using MATLAB</a></nav></div>
<div class="nav-obj"><nav class="nav sidenav nav-scroll navbar-dark bg-dark"><ul class="navbar-nav"><li class="nav-item"><a class="nav-link" href="build\html\..\..\index.html">Home</a></li><li class="nav-item"><a class="nav-link" href="build\html\Preface.htm">Preface</a></li><li class="nav-item"><div class="nav-link"><a href="build\html\01_Introduction.htm#1">1 Introduction </a><span class="dropdown-toggle" data-target="#sec_1" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_1"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_1">1.1 Background</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_2">1.2 History of Computer Architectures </a><span class="dropdown-toggle" data-target="#sub_1_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_1_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_2_1">1.2.1 Babbage's Difference Engine</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_2_2">1.2.2 Colossus</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_2_3">1.2.3 The von Neumann Architecture</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_3">1.3 Modern Computer Software </a><span class="dropdown-toggle" data-target="#sub_1_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_1_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_3_1">1.3.1 Operating Systems</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_3_2">1.3.2 Software Tools</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_3_3">1.3.3 Programming Languages</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_3_4">1.3.4 Running a Computer Program</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_3_5">1.3.5 Running an Interpreted Program</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_4">1.4 Anticipated Outcomes </a><span class="dropdown-toggle" data-target="#sub_1_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_1_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_4_1">1.4.1 Introduction to MATLAB</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_4_2">1.4.2 Learning Programming Concepts</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\01_Introduction.htm#1_4_3">1.4.3 Problem-Solving Skills</a></div></li></ul></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\02_Basics.htm#2">2 Basics </a><span class="dropdown-toggle" data-target="#sec_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_2"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_1">2.1 Programming Language Background </a><span class="dropdown-toggle" data-target="#sub_2_1" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_2_1"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_1_1">2.1.1 Abstraction</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_1_2">2.1.2 Algorithms</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_1_3">2.1.3 Programming Paradigms</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_2">2.2 Basic Data Manipulation </a><span class="dropdown-toggle" data-target="#sub_2_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_2_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_2_1">2.2.1 Starting and Stopping MATLAB</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_2_2">2.2.2 Assigning Values to Variables</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_2_3">2.2.3 Data Typing</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_2_4">2.2.4 Classes and Objects</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_3">2.3 MATLAB User Interface </a><span class="dropdown-toggle" data-target="#sub_2_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_2_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_3_1">2.3.1 Command Window</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_3_2">2.3.2 Command History</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_3_3">2.3.3 Workspace Window</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_3_4">2.3.4 Current Folder Window</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_3_5">2.3.5 Variable Editor</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_3_6">2.3.6 Figure Window</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_3_7">2.3.7 Editor Window</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_4">2.4 Scripts </a><span class="dropdown-toggle" data-target="#sub_2_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_2_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_4_1">2.4.1 Text Files</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_4_2">2.4.2 Creating Scripts</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_4_3">2.4.3 The Current Directory</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_4_4">2.4.4 Running Scripts</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_4_5">2.4.5 Punctuating Scripts</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_4_6">2.4.6 Debugging Scripts</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\02_Basics.htm#2_5">2.5 Engineering Example - Spacecraft Launch</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\03_Functions.htm#3">3 Functions </a><span class="dropdown-toggle" data-target="#sec_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_3"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_1">3.1 Concepts: Abstraction and Encapsulation</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_2">3.2 Black Box View of a Function</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3">3.3 MATLAB Implementation </a><span class="dropdown-toggle" data-target="#sub_3_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_3_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3_1">3.3.1 General Template</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3_2">3.3.1 Function Definition</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3_3">3.3.3 Storing and Using Functions</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3_4">3.3.4 Calling Functions</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3_5">3.3.5 Variable Number of Parameters</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3_6">3.3.6 Returning Multiple Results</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3_7">3.3.7 Auxiliary Local Functions</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3_8">3.3.8 Encapsulation in MATLAB Functions</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_3_9">3.3.9 Global Variables</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\03_Functions.htm#3_4">3.4 Engineering Example: Measuring a Solid Object</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\04_Vectors.htm#4">4 Vectors </a><span class="dropdown-toggle" data-target="#sec_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_4"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_1">4.1 Concept: Data Collection </a><span class="dropdown-toggle" data-target="#sub_4_1" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_4_1"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_1_1">4.1.1 Data Abstraction</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_1_2">4.1.2 Homogeneous Collections</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_2">4.2 Vectors </a><span class="dropdown-toggle" data-target="#sub_4_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_4_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_2_1">4.2.2 Creating a Vector</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_2_2">4.2.2 Size of a Vector</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_2_3">4.2.3 Indexing a Vector</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_2_4">4.2.4 Shortening a Vector</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_2_5">4.2.5 Operating on Vectors</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_3">4.3 Engineering Example - Forces and Moments</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_4">4.4 Arrays </a><span class="dropdown-toggle" data-target="#sub_4_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_4_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_4_1">4.4.1 Properties of an Array</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_4_2">4.4.2 Creating an Array</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_4_3">4.4.3 Accessing Elements of an Array</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_4_4">4.4.4 Removing Elements of an Array</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_4_5">4.4.5 Operating on Arrays</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\04_Vectors.htm#4_5">4.5 Engineering Example - Computing Soil Volume</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\05_Execution.htm#5">5 Execution </a><span class="dropdown-toggle" data-target="#sec_5" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_5"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_1">5.1 Concept: Code Blocks</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_2">5.2 Conditional Execution in General</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_3">5.3 if Statements </a><span class="dropdown-toggle" data-target="#sub_5_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_5_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_3_1">5.3.1 General Template</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_3_2">5.3.2 MATLAB Implementation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_3_3">5.3.3 Important Ideas</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_4">5.4 switch Statements </a><span class="dropdown-toggle" data-target="#sub_5_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_5_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_4_1">5.4.1 General Template</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_4_2">5.4.2 MATLAB Implementation</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_5">5.5 Iteration in General</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_6">5.6 for Loops </a><span class="dropdown-toggle" data-target="#sub_5_6" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_5_6"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_6_1">5.6.1 General for Loop Template</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_6_2">5.6.2 MATLAB Implementation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_6_3">5.6.3 Indexing Implementation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_6_4">5.6.4 Breaking out of a for Loop</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_7">5.7 while Loops </a><span class="dropdown-toggle" data-target="#sub_5_7" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_5_7"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_7_1">5.7.1 General while Template</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_7_2">5.7.2 MATLAB while Loop Implementation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_7_3">5.7.3 Loop-and-a-Half Implementation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_7_4">5.7.4 Breaking a while Loop</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\05_Execution.htm#5_8">5.8 Engineering Example - Computing Liquid Levels</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\06_Strings.htm#6">6 Strings </a><span class="dropdown-toggle" data-target="#sec_6" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_6"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_1">6.1 Character String Concepts: Mapping, Casting, Tokens, and Delimiting</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_2">6.2 MATLAB Implementation </a><span class="dropdown-toggle" data-target="#sub_6_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_6_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_2_1">6.2.1 Slicing and Concatenating Strings</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_2_2">6.2.2 Arithmetic and Logical Operations</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_2_3">6.2.3 Useful Functions</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_3">6.3 Format Conversion Functions </a><span class="dropdown-toggle" data-target="#sub_6_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_6_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_3_1">6.3.1 Conversion from Numbers to Strings</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_3_2">6.3.2 Conversion from Strings to Numbers and Other Stuff</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_4">6.4 Character String Operations </a><span class="dropdown-toggle" data-target="#sub_6_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_6_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_4_1">6.4.1 Simple Data Output: The disp(...) Function</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_4_2">6.4.2 Complex Output</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_4_3">6.4.3 Comparing Strings</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_5">6.5 Arrays of Strings</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\06_Strings.htm#6_6">6.6 Engineering Example - Encryption</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\07_Structures.htm#7">7 Structures </a><span class="dropdown-toggle" data-target="#sec_7" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_7"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_1">7.1 Concept: Collecting Dissimilar Objects</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_2">7.2 Cell Arrays </a><span class="dropdown-toggle" data-target="#sub_7_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_7_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_2_1">7.2.1 Creating Cell Arrays</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_2_2">7.2.2 Accessing Cell Arrays</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_2_3">7.2.3 Using Cell Arrays</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_2_4">7.2.4 Processing Cell Arrays</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_3">7.3 Structures </a><span class="dropdown-toggle" data-target="#sub_7_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_7_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_3_1">7.3.1 Constructing and Accessing One Structure</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_3_2">7.3.2 Constructor Functions</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_4">7.4 Structure Arrays </a><span class="dropdown-toggle" data-target="#sub_7_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_7_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_4_1">7.4.1 Constructing Structure Arrays</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_4_2">7.4.2 Accessing Structure Arrays</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_4_3">7.4.3 Manipulating Structures</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_5">7.5 Comparing Cell Arrays to Structure Arrays</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\07_Structures.htm#7_6">7.6 Engineering Example: Assembling a Physical Structure</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8">8 File I O </a><span class="dropdown-toggle" data-target="#sec_8" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_8"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_1">8.1 Concept: Serial Input and Output (I/O)</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_2">8.2 Workspace I/O</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_3">8.3 High-Level I/O Functions </a><span class="dropdown-toggle" data-target="#sub_8_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_8_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_3_1">8.3.1 Exploration</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_3_2">8.3.2 Spreadsheets</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_3_3">8.3.3 Delimited Text Files</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_4">8.4 Lower-Level File I/O </a><span class="dropdown-toggle" data-target="#sub_8_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_8_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_4_1">8.4.1 Opening and Closing Files</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_4_2">8.4.2 Reading Text Files</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_4_3">8.4.3 Writing Text Files</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\08_File_I_O.htm#8_5">8.5 Engineering Example - Spreadsheet Data</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\09_Recursion.htm#9">9 Recursion </a><span class="dropdown-toggle" data-target="#sec_9" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_9"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_1">9.1 Concept: The Activation Stack </a><span class="dropdown-toggle" data-target="#sub_9_1" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_9_1"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_1_1">9.1.1 A Stack</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_1_2">9.1.2 Activation Stack</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_1_3">9.1.3 Function Instances</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_2">9.2 Recursion Defined</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_3">9.3 Implementing a Recursive Function</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_4">9.4 Exceptions </a><span class="dropdown-toggle" data-target="#sub_9_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_9_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_4_1">9.4.1 Historical Approaches</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_4_2">9.4.2 Generic Exception Implementation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_4_3">9.4.3 MATLAB Implementation</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_5">9.5 Wrapper Functions</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_6">9.6 Examples of Recursion </a><span class="dropdown-toggle" data-target="#sub_9_6" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_9_6"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_6_1">9.6.1 Detecting Palindromes</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_6_2">9.6.2 Fibonacci Series</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_6_3">9.6.3 Zeros of a Function</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\09_Recursion.htm#9_7">9.7 Engineering Example - Robot Arm Motion</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10">10 Problem Solving </a><span class="dropdown-toggle" data-target="#sec_10" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_10"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_1">10.1 Solving Simple Problems</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_2">10.2 Assembling Solution Steps</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3">10.3 Summary of Operations </a><span class="dropdown-toggle" data-target="#sub_10_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_10_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3_1">10.3.1 Basic Arithmetic Operations</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3_2">10.3.2 Inserting into a Collection</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3_3">10.3.3 Traversing a Collection</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3_4">10.3.4 Building a Collection</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3_5">10.3.5 Mapping a Collection</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3_6">10.3.6 Filtering a Collection</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3_7">10.3.7 Folding a Collection</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3_8">10.3.8 Searching a Collection</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_3_9">10.3.9 Sorting a Collection</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_4">10.4 Solving Larger Problems</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\10_Problem_Solving.htm#10_5">10.5 Engineering Example - Processing Geopolitical Data</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\11_Plotting.htm#11">11 Plotting </a><span class="dropdown-toggle" data-target="#sec_11" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_11"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_1">11.1 Plotting in General </a><span class="dropdown-toggle" data-target="#sub_11_1" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_11_1"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_1_1">11.1.1 A Figure - The Plot Container</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_1_2">11.1.2 Simple Functions for Enhancing Plots</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_1_3">11.1.3 Multiple Plots on One Figure - Subplots</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_1_4">11.1.4 Manually Editing Plots</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_2">11.2 2-D Plotting </a><span class="dropdown-toggle" data-target="#sub_11_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_11_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_2_1">11.2.1 Simple Plots</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_2_2">11.2.2 Plot Options</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_2_3">11.2.3 Parametric Plots</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_2_4">11.2.4 Other 2-D Plot Capabilities</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_3">11.3 3-D Plotting </a><span class="dropdown-toggle" data-target="#sub_11_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_11_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_3_1">11.3.1 Linear 3-D Plots</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_3_2">11.3.2 Linear Parametric 3-D Plots</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_3_3">11.3.3 Other 3-D Plot Capabilities</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_4">11.4 Surface Plots </a><span class="dropdown-toggle" data-target="#sub_11_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_11_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_4_1">11.4.1 Basic Capabilities</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_4_2">11.4.2 Simple Exercises</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_4_3">11.4.3 3-D Parametric Surfaces</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_4_4">11.4.4 Bodies of Rotation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_4_5">11.4.5 Other 3-D Surface Plot Capabilities</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_4_6">11.4.6 Assembling Compound Surfaces</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_5">11.5 Manipulating Plotted Data</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_6">11.6 Engineering Example - Visualizing Geographic Data </a><span class="dropdown-toggle" data-target="#sub_11_6" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_11_6"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_6_1">11.6.1 Analyzing the Data</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\11_Plotting.htm#11_6_2">11.6.2 Displaying the Data</a></div></li></ul></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\12_Matrices.htm#12">12 Matrices </a><span class="dropdown-toggle" data-target="#sec_12" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_12"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_1">12.1 Concept: Behavioral Abstraction</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_2">12.2 Matrix Operations </a><span class="dropdown-toggle" data-target="#sub_12_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_12_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_2_1">12.2.1 Matrix Multiplication</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_2_2">12.2.2 Matrix Division</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_2_3">12.2.3 Matrix Exponentiation</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_3">12.3 Implementation </a><span class="dropdown-toggle" data-target="#sub_12_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_12_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_3_1">12.3.1 Matrix Multiplication</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_3_2">12.3.2 Matrix Division</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_4">12.4 Rotating Coordinates </a><span class="dropdown-toggle" data-target="#sub_12_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_12_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_4_1">12.4.1 2-D Rotation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_4_2">12.4.2 3-D Rotation</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_5">12.5 Solving Simultaneous Linear Equations </a><span class="dropdown-toggle" data-target="#sub_12_5" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_12_5"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_5_1">12.5.1 Intersecting Lines</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_6">12.2 Engineering Examples </a><span class="dropdown-toggle" data-target="#sub_12_6" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_12_6"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_6_1">12.2.1 Ceramic Composition</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\12_Matrices.htm#12_6_2">12.2.2 Analyzing an Electrical Circuit</a></div></li></ul></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\13_Images.htm#13">13 Images </a><span class="dropdown-toggle" data-target="#sec_13" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_13"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_1">13.1 Nature of an Image</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_2">13.2 Image Types </a><span class="dropdown-toggle" data-target="#sub_13_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_13_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_2_1">13.2.1 True Color Images</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_2_2">13.2.2 Gray Scale Images</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_2_3">13.2.3 Color Mapped Images</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_2_4">13.2.4 Preferred Image Format</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_3">13.3 Reading, Displaying, and Writing Images</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_4">13.4 Operating on Images </a><span class="dropdown-toggle" data-target="#sub_13_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_13_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_4_1">13.4.1 Stretching or Shrinking Images</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_4_2">13.4.2 Color Masking</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_4_3">13.4.3 Creating a Kaleidoscope</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_4_4">13.4.4 Images on a Surface</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\13_Images.htm#13_5">13.5 Engineering Example - Detecting Edges</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\14_Sounds.htm#14">14 Sounds </a><span class="dropdown-toggle" data-target="#sec_14" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_14"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_1">14.1 The Physics of Sound</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_2">14.2 Recording and Playback</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_3">14.3 Implementation</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_4">14.4 Time Domain Operations </a><span class="dropdown-toggle" data-target="#sub_14_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_14_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_4_1">14.4.2 Slicing and Concatenating Sounds</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_4_2">14.4.2 Musical Background</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_4_3">14.4.3 Changing Sound Frequency</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_5">14.5 The Fast Fourier Transform </a><span class="dropdown-toggle" data-target="#sub_14_5" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_14_5"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_5_1">14.5.1 Background</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_5_2">14.5.2 Implementation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_5_3">14.5.3 Simple Spectral Analysis</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_6">14.6 Frequency Domain Operations </a><span class="dropdown-toggle" data-target="#sub_14_6" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_14_6"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_6_1">14.6.1 Details of the Spectral Data</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_6_2">14.6.2 Notes fading with time</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\14_Sounds.htm#14_7">14.7 Engineering Example - Music Synthesizer</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15">15 Numerical Methods </a><span class="dropdown-toggle" data-target="#sec_15" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_15"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_1">15.1 Interpolation </a><span class="dropdown-toggle" data-target="#sub_15_1" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_15_1"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_1_1">15.1.1 Linear Interpolation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_1_2">15.1.2 Cubic Spline Interpolation</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_1_3">15.1.3 Extrapolation</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_2">15.2 Curve Fitting </a><span class="dropdown-toggle" data-target="#sub_15_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_15_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_2_1">15.2.1 Linear Regression</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_2_2">15.2.2 Polynomial Regression</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_2_3">15.2.3 Practical Application</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_3">15.3 Numerical Integration </a><span class="dropdown-toggle" data-target="#sub_15_3" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_15_3"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_3_1">15.3.1 Determination of the Complete Integral</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_3_2">15.3.2 Continuous Integration Problems</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_4">15.4 Numerical Differentiation </a><span class="dropdown-toggle" data-target="#sub_15_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_15_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_4_1">15.4.1 Difference Expressions</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_5">15.5 Analytical Operations </a><span class="dropdown-toggle" data-target="#sub_15_5" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_15_5"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_5_1">15.5.1 Analytical Integration</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_5_2">15.5.2 Analytical Differentiation</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_6">15.6 Implementation</a></div></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\15_Numerical_Methods.htm#15_7">15.7 Engineering Example - Shaping the Synthesizer Notes</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\16_Sorting.htm#16">16 Sorting </a><span class="dropdown-toggle" data-target="#sec_16" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_16"><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_1">16.1 Measuring Algorithm Cost</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_2">16.2 Algorithms for Sorting Data </a><span class="dropdown-toggle" data-target="#sub_16_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_16_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_2_1">16.2.1 Insertion Sort</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_2_2">16.2.2 Bubble Sort</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_2_3">16.2.3 Quick Sort</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_2_4">16.2.4 Merge Sort</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_2_5">16.2.5 Radix Sort</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_3">16.3 Performance Analysis</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_4">16.4 Applications of Sorting Algorithms </a><span class="dropdown-toggle" data-target="#sub_16_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_16_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_4_1">16.4.1 Using sort(...)</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_4_2">16.4.2 Insertion Sort</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_4_3">16.4.3 Bubble Sort</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_4_4">16.4.4 Quick Sort</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_4_5">16.4.5 Merge Sort</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_4_6">16.4.6 Radix Sort</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\16_Sorting.htm#16_5">16.5 Engineering Example - A Selection of Countries</a></div></li></ul></li><li class="nav-item"><div class="nav-link"><a href="build\html\17_Graphs.htm#17">17 Graphs </a><span class="dropdown-toggle" data-target="#sec_17" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sec_17"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_1">17.1 Stacks </a><span class="dropdown-toggle" data-target="#sub_17_1" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_17_1"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_1_1">17.1.1 The Nature of a Stack</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_1_2">17.1.2 Implementing Stacks</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_2">17.2 Queues </a><span class="dropdown-toggle" data-target="#sub_17_2" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_17_2"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_2_1">17.2.1 The Nature of a Queue</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_2_2">17.2.2 Implementing Queues</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_2_3">17.2.3 Priority Queues</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#">17.3 Testing Stacks and Queues</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_4">17.4 Graphs </a><span class="dropdown-toggle" data-target="#sub_17_4" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_17_4"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_4_1">17.4.1 Graph Examples</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_4_2">17.4.2 Processing Graphs</a></div></li></ul></li><li class="nav-item secnav"><li class="nav-item secnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_5">17.5 Minimum Spanning Trees</a></div></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_6">17.6 Finding Paths through a Graph </a><span class="dropdown-toggle" data-target="#sub_17_6" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_17_6"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_6_1">17.6.1 Depth-First Search</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_6_2">17.6.2 Breadth-First Search</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_6_3">17.6.3 Dijkstras Algorithm</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_6_4">17.6.4 An Approximation Algorithm</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_6_5">17.6.5 Serious Path Finding Algorithms</a></div></li></ul></li><li class="nav-item secnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_7">17.7 Engineering Applications </a><span class="dropdown-toggle" data-target="#sub_17_7" data-toggle="collapse"></span></div><ul class="list-unstyled collapse" id="sub_17_7"><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_7_1">17.7.1 Simple Applications</a></div></li><li class="nav-item subnav"><div class="nav-link"><a href="build\html\17_Graphs.htm#17_7_2">17.7.2 Complex Extensions</a></div></li></ul></li></ul></li><li class="nav-item"><a class="nav-link" href="build\html\Appendix_A.htm">Appendix A</a></li><li class="nav-item"><a class="nav-link" href="build\html\Appendix_B.htm">Appendix B</a></li><li class="nav-item"><a class="nav-link" href="build\html\Appendix_C.htm">Appendix C</a></li><li class="nav-item"><a class="nav-link" href="build\html\Appendix_D.htm">Appendix D</a></li><li class="nav-item"><a class="nav-link" href="build\html\text_index.htm">Index</a></li></ul></nav></div>
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<br><br>
<h1>Engineering Computation with Matlab</h1>
<h2>Fourth Edition</h2>
<h3>by David M. Smith</h3>
<p>(c) Copyright 2019 David M. Smith</p>
<p>Previously published by Pearson Addison Wesley</p>
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<p><i>This book is dedicated to the<br>
glory of Almighty God</i></p>
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