Contents

Chapter #1: Mathematical Preliminaries

• Vectors, Derivatives and Extrema, Partial Derivatives, Integration

Chapter #2: Determinants and Matrices

• Determinants

Chapter #3: Vector Analysis

• Vectors in 3D Space, Vector Operators

Chapter #4: Tensor Analysis

• Tensor Properties

Chapter #5: Vector Spaces

• Vectors in Function Spaces, Operators

Chapter #6: Eigenvalue Problems

• Eigenvalue Equations

Chapter #7: ODEs

• First-Order Differential Equations

Chapter #19: Fourier Series

• Fourier Series

Chapter #20: Integral Transforms

• Fourier Transform

Primary Textbook:

• Arfken, G. B., Harris, F. E., & Weber, H.-J. (2012). Mathematical Methods for Physicists: A Comprehensive Guide. Elsevier.

Other References:

• Farina, D. (n.d.). Professor Dave Explains. YouTube. https://www.youtube.com/@ProfessorDaveExplains
• McMullen, C. (2023). Essential Calculus Skills Practice workbook with full solutions. Zishka Publishing.
• McMullen, C. (2022). Calculus with multiple variables essential skills workbook: Includes vector calculus and full solutions. Zishka Publishing.
• McMullen, C. (2022). Differential equations: Essential skills practice workbook with answers. Zishka Publishing.