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Overview of Course Topics:

Week 1: Limits and Differentiation

- Rules for evaluating limits
- Rules for differentiation
- l'Hospital's rule

Week 2: Integrals

- Fundamental Theorem of Calculus
- Integration techniques
- Differentiating improper integrals

Week 3: Partial Derivatives

- Functions of Several Variables
- Higher order partial derivatives
- The Greeks

Week 4: Multiple Integrals

- Change of variables
- Polar coordinates

Week 5 Linear Algebra I

- Vectors
- Matrices
- Solving Ax = b

Week 6 Linear Algebra II

- Eigenvalues and eigenvectors
- Matrix factorizations

Week 7: Taylor Series and Lagrange Multipliers

- Optimal investment portfolios

Week 8: Numerical methods

- Finite difference approximation
- Newton's method
- Numerical integration