##
ACMS 20550 - 20750: Applied Mathematics Method I, II, Syllabus

** 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 7 in first semester 20550

- Chapter 1. Infinite series and power series
- Chapter 2. Complex Numbers
- basics, infinite and power series
- trig functions
- Euler formula

- Chapter 3. Rudiments of linear algebra
- linear equations
- row reduction
- matrix operations
- eigenvalues, eigenvectors, and diagonalization

- Chapter 4. Partial Derivatives
- total differential
- Taylor and Power Series in several variables
- Chain Rule
- Lagrange Multipliers

- Chapter 5. Multiple Integration
- multiple integrals
- the Jacobian and change of variables
- Surface integrals

- Chapter 6. Vector Analysis
- inner, cross, and triple products
- gradient and line integrals
- Green's theorem, the divergence theorem, and Stokes theorem

- Chapter 7. Fourier Series and Transforms
## Topics 8 to 13 in second semester 20750

- Chapter 8. Ordinary Differential Equations I (Constant coefficient differential equations and the Laplace transform)
- Chapter 9. Variational Calculus (Euler equation, Lagrange's Equation, and some example problems)
- Chapter 11. Assorted Special Functions
- Gamma, Beta, and Error Functions
- Asymptotic Series and Stirling's Formula

- Chapter 12. Ordinary Differential Equations II
- Series solution of differential equations
- Orthogonal functions, Legendre polynomials, Bessel functions
- Other classes of orthogonal functions and their ODEs

- Chapter 13. Partial Differential Equations
- Basic types of PDEs
- model problems (heat flow, vibrating string, steady state temperature)

- Chapter 14. Complex Function Theory
- contour integrals and Cauchy's theorem
- Laurent series and the residue calculus
- conformal maps