1. A closer look at bases. Components and change of basis

2. Complex Linear Algebra and complex eigenvalues

3. Introduction to ODE's

4. Systems of linear ODE's with constant coefficients

5. More on linear ODE systems

6. Symmetric matrices

7. Quadratic forms

8. Quadratic form optimization, Rayleigh quotient, Least Squares

9. Shifting focus to ODE's

10. Forward Euler, Runge-Kutta and other explicit schemes

11. MATLAB projects:

a. Numerical prediction of solar eclipses

b. The driven pendulum and exploration of chaos

c. Evolution of spring-truss systems

12. Inverse Euler and other implicit schemes

13. Linear equations with variable coefficients such as the Bessel equation

14. Methods for linear ODE's with variable coefficients