Five Critical Textbooks for (Applied!) Math & Physics Students

In the course of working through my first year at grad school, I’ve come up with five favorites for the basics of an undergrad understanding of the essential topics for applied math and physics. Without ado and in the order I’d take them off my shelf:

• Mathematical Methods in the Physical Sciences - ML Boas. This is my favorite, because it contains almost every technique you need, and it has a ton and a half of problems(over 3400). It contains a good review of complex analysis, linear algebra, differential equations, and calculus, but also chapters on special functions, partial differential equations, probability, tensors, and the calculus of variations. – Hidden Gem: Chapter 4, Section 12: Differentiation of Integrals, RP Feynman’s favorite trick.
• Calculus - Greenspan. A great reference on calculus.
• Complex Variables and Applications - Brown & Churchill: The most readable book on complex analysis I’ve read. Not so hidden gem: Most of the solutions are given right alongside the problem–a great book for self-study. Also the material on conformal mapping and fluid flows.
• Linear Algebra And Its Applications - Strang. Nice book on linear algebra theory. – Hidden Gem: Chapter 7, Section 4: Iterative Methods for Ax=b and Gershgorin’s circle theorem.
• Elementary Differential Equations and Boundary Value Problems - Boyce & DiPrima. Powerhouse of differential equation knowledge. Strangely, it is the book ESAM recommended, but not the book they use for teaching their undergrads.

I’ve spent probably the most time with Boas' Mathematical Methods in the Physical Sciences–I’ve worked nearly 1000 problems out of the book to get ready for the preliminary exams my first year. It was completely worthwhile.