# SYLLABUS

## Exam Dates

(Exams are held during class time, in Walker Gym: 50-340, Open Book)

• Exam 1 : October 3 (Tuesday)

• Exam 2: October 31 (Tuesday)

• Exam 3: December 5 (Tuesday)

## Part 1: Applied Linear Algebra

1. Four Special Matrices

2. Differences, Derivatives, and Boundary Conditions

3. Elimination Leads to K = LDLT

4. Inverses and Delta Functions

5. Eigenvalues and Eigenvectors

6. Positive Definite Matrices

7. Numerical Linear Algebra: LU, QR, SVD

## Part 2: A Framework for Applied Mathematics

1. Equilibrium and the Stiffness Matrix

2. Oscillation by Newton’s Law

3. Least Squares for Rectangular Matrices

4. Graph Models and Kirchhoff’s Laws

5. Networks and Transfer Functions

6. Nonlinear Problems

7. Structures in Equilibrium

## Part 3: Boundary Value Problems

1. Differential Equations of Equilibrium

2. Cubic Splines and Fourth Order Equations

4. Laplace’s Equation

5. Finite Differences and Fast Poisson Solvers

6. The Finite Element Method

7. Elasticity and Solid Mechanics

## Part 4: Fourier Series and Integrals

1. Fourier Series for Periodic Functions

2. Chebyshev, Legendre, and Bessel

3. The Discrete Fourier Transform and the FFT

4. Convolution and Signal Processing

5. Fourier Integrals

6. Deconvolution and Integral Equations

7. Wavelets and Signal Processing