# Applied Math for Chemistry

## CHM 422 Course Topics

### Introduction

1. Transcendental Functions
A. Exponential Functions
B. Log Functions
C. Trigonometric Functions
D. Functions in Excel
2. Trigonometry and Geometry Applications
A. Dot Products
B. Spherical Polar Coordinates
C. Excel Methods
3. Complex Numbers
A. Imaginary Numbers and Complex Numbers
B. Complex Arithmetic
C. Complex Numbers in Excel
4. Power Series Expansions
A. Introduction
B. McLaurin Series
C. Taylor Series
D. Applications in Magnetic Resonance
E. Gaussian Function as a Power Series
5. Differential Equations
A. Introduction
B. Initial Value Problems
C. Separable Differential Equations
D. Linear 1st Order Differential Equations
E. Power Series Solutions
F. Linear Homogeneous Equations
6. Numerical Integration
A. Introduction
B. Functions Representable by a Power Series
C. Quadrature: Rectangle Rule, Midpoint Rule, Trapezoid Rule
D. Simpson's Rule
F. Digitized Data
7. Matrices
A. Introduction to Matrices and Matrix Notation
B. Matrix Algebra
C. Special Matrices
D. Matrix Operations
E. Determinants
F. Matrix Inversion
G. Rotation Matrices - Matrices as Operators
H. Matrix Operations in Excel
8. Eigenvalue/Eigenvector Problems
A. Linear Transformations
B. Diagonalization of Matrices
C. Solving for Eigenvectors
D. Physical Significance of Eigenvalues and Eigenvectors
E. Block Diagonal Matrices
F. Hermitian Matrices
G. Huckel MO Calculations
H. Pi Electron Density and Bond Order Calculations
9. Linear Algebra
A. Systems of Linear Equations
B. Method of Substitution
C. Cramer's Rule
D. Gauss Elimination and Gauss-Jordan Methods
E. Jacobi's Method
F. Excel Techniques
10. Curve Fitting
A. Linear Least Squares Method
B. Higher Order Least Squares Fits
C. Weighted Least Squares Fits
D. Application to Beer's Law Plots
11. Statistics
A. Review of Freshman Topics
B. Confidence Intervals
C. Chi-Squared Tests
D. Analysis of Variance Methods
E. Statistics in Excel