This page covers the list of math topics provided here:
solutions of ordinary and partial differential equations, power series solutions, linear independence, elementary linear algebra, determinants, Taylor series, eigenvalue problems, orthogonality, Fourier series and integrals, integration by parts, vector algebra, complex numbers, special functions (e.g., Bessel functions and Legendre polynomials).
I have organized these topics in a way that progresses from basic mathematics to more difficult concepts:
These questions come from Introduction to Linear Algebra by Gilbert Strang and the appendix of Introduction to Quantum Mechanics by D. J. Griffiths.
Towards the end of this section there is some overlap with tensor algebra.
Each numbered equation in this section represents a unique type of differential equation. For a thorough review of this section, be sure to know how to solve each type of differential equation.
Vector calculus is not listed as a topic on the math section, but it is worth reviewing.
In the section on linear algebra, different symbols were used for vectors and their representation in a particular bases. In this section, we deal only with the vectors themselves. When vectors need to be expressed in a basis, \(3\times 1\) matrices are used. It is therefore not necessary to distinguish between \(\vec{v}\) and \(\mathsf{v}\) (and between \(A\) and \(\mathsf{A}\)).
Some of the problems below come from chapter 1 of Introduction to Electrodynamics by D. J. Griffiths.