Schedule for Calculus and Linear Algebra
Math 25B, Harvey Mudd College
Profs. Dagan Karp and Michael Orrison
Week 1
- 1.1-1.2: Vectors and Vector Spaces
- Appendix B: Mathematical Induction
Week 2
- 2.1: Introduction to Systems of Linear Equations
- 2.2: Direct Methods for Solving Systems of Linear Equations
- 2.3: Spanning Sets and Linear Independence
Week 3
- 3.1-3.2: Matrix Operations and Matrix Algebra
- 3.3: The Inverse of a Matrix
- 3.3: The Inverse of a Matrix (cont.)
Week 4
- 3.5: Subspaces, Basis, Dimension, and Rank
- 3.5: Subspaces, Basis, Dimension, and Rank (cont.)
- In-class Quiz.
Week 5
- 4.1: Introduction to Eigenvalues and Eigenvectors
- 4.2: Determinants
- 4.3: Eigenvalues and Eigenvectors of n x n Matrices
Week 6
- 4.4: Similarity and Diagonalization
- Coordinates, Encodings, and Change of Basis Matrices
- Review [get take-home exam]
Week 7
- Discuss Exam [take-home exam due]
- Applications of Linear Algebra
- Applications of Linear Algebra
Week 8
- Limits of single and multivariable functions, Epsilon-Delta
- Continuity and Differentiability of single variable functions
Week 9
- Partial Derivatives, Planes and the Tangent Plane,
Differentiability of Scalar Valued Multivariable Functions
- Differentiability Implies Continuity for Scalar Valued
Multivariable Functions, Derivative Theorems for Single Variable
Functions: Sum, Product, Quotient, Power rules.
- The chain rule in single and multivariable settings
Week 10
- Mean Value Theorem
- Definition of Definite Integration
- FTOC
Week 11
- Natural Logarithm
- Exponential Functions
- Taylor Polynomials
Week 12
- Taylor Series
- Infinite Series and Convergence
- Take Home Exam Out: Due Mon Nov 22