Mathematical Methods and Physical Insights: An Integrated Approach (Hardcover)

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.

數學教學在物理情境下呈現時通常更有效。Schramm利用這一洞察力，引導學生通過研究高級物理所需的數學方法來發展他們的物理直覺。本書基於他在Occidental College多年來教授的本科數學方法課程，鼓勵物理學和數學之間的共生關係，物理學照亮數學，而數學則為物理學提供信息。本書適用於課堂教學和自學，首先回顧了一些有用的技巧，以確保學生對先備知識感到舒適。然後，它繼續涵蓋向量場、解析函數、線性代數、函數空間和微分方程。本書以輕鬆有趣的風格撰寫，還包括短小的補充插曲（'By the Ways'），作為可選的方框，展示可以進一步探索數學或物理學的方向。全書包含大量問題，其中許多利用Mathematica進行，以測試和加深理解。