Mathematical Methods and Physical Insights

An Integrated Approach

Alec J. Schramm

• Publisher: Cambridge University Press
• Year: 2022
• Print ISBN: 9781107156418
• eBook ISBN: 9781009293426
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

Mathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions ('By the Ways') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, many taking advantage of Mathematica, to test and deepen comprehension.

Table of contents

• Cover
• Half-title
• Title page
• Copyright information
• Dedication
• Contents
• List of BTWs
• Preface
• Part I Things You Just Gotta' Know
• Part II The Calculus of Vector Fields
• Part III Calculus in the Complex Plane
• Part IV Linear Algebra
• Entr'acte: Tensors
• Part V Orthogonal Functions
• Part VI Differential Equations
• Appendix A Curvilinear Coordinates
• Appendix B Rotations in [mathbb(R)][sup(3)]
• Appendix C The Bessel Family of Functions
• References
• Index