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.
Initial chapters review essential mathematical concepts and techniques that students need to know, helping students to fill gaps in their background knowledge and enabling instructors to focus on the main course material
Each Part has sections designed to highlight and apply the techniques and concepts within, so that physics motivates the math, which deepens understanding of physics
Boxed asides throughout the book called 'By the Ways' (BTWs) provide optional digressions into the math or physics, to help to lift motivated students to the next level
Flexible paths through the text allow it to be used for both one- and two-semester courses, depending on the course goals and instructor's preference
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