# MATH 309- Suggested Weekly Schedule

## Course: Linear Algebra for Differential Equations.

**Suggested Schedule**

- Week 1
- Systems of linear equations (Leon, 1.1)
- Solution of systems by Gaussiaan and Gauss-Jordan elimination. Row echelon form (1.1, 1.2)

- Systems of linear equations (Leon, 1.1)
- Week 2
- Some applications of systems. Matrix arithmetic (1.2, 1.3)
- Matrix algebra. Inverses and transposes of matrices (1.4)

- Some applications of systems. Matrix arithmetic (1.2, 1.3)
- Week 3
- Elementary matrices and inversion of matrices (1.4)
- Determinants: calculation by cofactors and properties (2.1, 2.2)

- Elementary matrices and inversion of matrices (1.4)
- Week 4
- Vector spaces (3.1)
- Subspaces, linear combinations, and spans (3.2)

- Vector spaces (3.1)
- Week 5
- Basis and dimension (3.4)

**Exam #1**

- Basis and dimension (3.4)
- Week 6
- Change of basis (3.5)
- Row space and column space of a matrix. Rank-nullity theorem.

- Change of basis (3.5)
- Week 7
- Introduction to linear transformations. Matrix representation of transformations.
- Matrix representations, continued. Similar matrices (4.2, 4.3)

- Introduction to linear transformations. Matrix representation of transformations.
- Week 8
- Eigenvalues and eigenvectors (6.1)
- Diagonalization of matrices (6.3)

- Eigenvalues and eigenvectors (6.1)
- Week 9
- Scalar product in
**B**n. General inner product spaces (5.1, 5.4) - Inner product spaces, continued. Orthonormal sets (5.4, 5.5)

- Scalar product in
- Week 10
- The Gram-Schmidt procedure (5.6)

**Exam #2**

- The Gram-Schmidt procedure (5.6)
- Week 11
- Introduction to partial differential equations. Superposition and separation of variables (Spiegel, chapter 1)

- Series solutions to PDEs. Fourier series (chapter 1, chapter 2)

- Introduction to partial differential equations. Superposition and separation of variables (Spiegel, chapter 1)
- Week 12
- Fourier series, continued (chapter 2)

- Application of Fourier series. Bessel functions (chapter 2, chapter 6)

- Fourier series, continued (chapter 2)
- Week 13
- Bessel functions, continued (chapter 6)
- Applications of Bessel functions (chapter 6)

- Bessel functions, continued (chapter 6)
- Week 14
- Review for final
**Final exam**

- Review for final

Last modified Tues March 15, 2011 by AP