Textbook: "Mathematical Method in the Physical Sciences" by Mary L. Boas, Third Edition 2006, Wiley, ISBN 13-978-0-471-19826-0.
Pre-requsite: Calulus II, Math 10560 or Math 10860.
Syllabus for Intro to Applied Mathematics/Mathematical Methods Topics 1 to 6 in first semester and 7 to 12 in second semester
1. Infinite series and power series
2. Complex Numbers
o basics, infinite and power series
o trig functions
o Euler formula
3. Rudiments of linear algebra
o linear equations
o row reduction
o matrix operations
o eigenvalues, eigenvectors, and diagonalization
4. Partial Derivatives
o total differential
o Taylor and Power Series in several variables
o Chain Rule
o Lagrange Multipliers
5. Multiple Integration and Vector Analysis
o multiple integrals
o the Jacobian and change of variables
o inner, cross, and triple products
o gradient and line integrals
o Green's theorem, the divergence theorem, and Stokes theorem
6. Fourier Series and Transforms
7. Ordinary Differential Equations I (Constant coefficient differential equations and the Laplace transform)
8. Variational Calculus (Euler equation, Lagrange's Equation, and some example problems)
9. Assorted Special Functions
o Gamma, Beta, and Error Functions
o Asymptotic Series and Stirling's Formula
10. Ordinary Differential Equations II
o Series solution of differential equations
o Orthogonal functions, Legendre polynomials, Bessel functions
o Other classes of orthogonal functions and their ODEs
11. Partial Differential Equations
o Basic types of PDEs
o model problems (heat flow, vibrating string, steady state temperature)
12. Complex Function Theory
o contour integrals and Cauchy's theorem
o Laurent series and the residue calculus
o conformal maps