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- If you want a deeper look at basic math (calculus, linear algebra, and differential equations), look here.
- To learn a little about applied physics, look here.
- If you’re a grad student considering working with me on numerical partial differential equations, look here.
Beyond the basics of calculus, linear algebra, and diff eq
Calculus
- Michael Spivak, Calculus
- Marsden and Tromba, Vector Calculus
- Shifrin, Multivariable Mathematics
- Hubbard and Hubbard, Vector Calculus, Linear Algebra, and Differential Forms
Linear Algebra
- Lax, Linear Algebra and its Applications
- Garcia and Horn, A Second Course in Linear Algebra
Differential Equations
- Gockenbach, Partial Differential Equations
- Strogatz, Nonlinear Dynamics and Chaos
- Hirsch and Smale, Differential Equations, Dynamical Systems, and an Introduction to Chaos
Applied Physics
Fluid and Solid Mechanics
- Faber, Fluid Dynamics for Physicists
- Lautrup, Physics of Continuous Matter
- Blandford and Thorne, Elasticity and Fluid Dynamics
Materials
- Jones, Soft Condensed Matter
- Chaikin and Lubensky, Principles of Condensed Matter Physics
Biophysics
- Keener and Sneyd, Mathematical Physiology
- Murray, Mathematical Biology
- Britton, Essential Mathematical Biology
Numerical Solution of Differential Equations
Basics
- Iserles, A First Course in the Numerical Analysis of Differential Equations
- Trefethen and Bau, Numerical Linear Algebra
- Atkinson and Han, Theoretical Numerical Analysis: A Functional Analysis Framework
Depth
- Hairer, Nørsett, and Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems
- Hairer and Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems
- Saad, Iterative Methods for Sparse Linear Systems
- Ciaramella and Gander, Iterative Methods and Preconditioners for Systems of Linear Equations
