OMG. Math 54. Course outline.

Week 1
• June 26: Hill, Sections 1.1 & 1.2 - Solving systems of linear equations by Gaussian Elimination
• June 27: 1.3 - Matrix multiplication
• June 28: 1.4 - Elementary matrices and inverses
• June 29: 1.4 cont. - A great big theorem about invertibility
• June 30: 3.1 & 3.2 - Euclidean n-space: vectors, dot products, projections, etc.

Week 2
• July 3: 3.3 - Abstract vector spaces
• July 4: The Fourth of July
• July 5: 3.4 Subspaces, span and nullspace
• July 6: More on 3.4 & Review
• July 7: Exam 1 - Covering all topics through Section 3.4

Week 3
• July 10: 3.5 - Linear independence
• July 11: 3.6 - Basis and dimension
• July 12: 3.7 - Finding bases, row space and column space
• July 13: 3.7 cont. - The rank of a matrix
• July 14: 3.9 - Change of bases, transition matrices

Week 4
• July 17: 4.1 - Linear transformations, rotation matrices
• July 18: 4.2 - Inner products, the Cauchy-Schwarz Inequality
• July 19: 4.3 - The Least Squares Method
• July 20: Review
• July 21: Exam 2 - Covering all topics through Section 4.3

Week 5
• July 24: 4.4 - Orthogonality and the Gram-Schmidt Process
• July 25: 5.1 - Determinants
• July 26: 5.2 - Eigenvalues and eigenvectors
• July 27: 5.3 - Diagonalization
• July 28: 5.4 - Real symmetric matrices

Week 6
• July 31: The Fibonacci sequence; 1^st order linear differential equations, and...
      Boyce and DiPrima, Section 3.1 - Linear second-order homogeneous differential equations with constant coefficients
• August 1: Section 3.2 - Fundamental solutions
• August 2: Section 3.3 - Linear independence and the Wronskian
• August 3: Review
• August 4: Exam 3

Week 7
• August 7: 4.1 - Generalizing to higher order linear equations (& complex roots)
• August 8: 7.5 - Systems of linear equations
• August 9: 7.6 & 7.7 - Complex eigenvalues; the fundamental matrix
• August 10: 10.1 - Some boundary value problems
• August 11: 10.2 - Fourier series

Week 8
• August 14: 10.3 & 10.4 - Fourier Convergence Theorem; even and odd functions
• August 15: 10.5 - The heat equation
• August 16: Who knows?!
• August 17: Review
• August 18: Exam 4

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