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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)
  • Week 2
    • Some applications of systems. Matrix arithmetic (1.2, 1.3)
    • Matrix algebra. Inverses and transposes of matrices (1.4)
  • Week 3
    • Elementary matrices and inversion of matrices (1.4)
    • Determinants: calculation by cofactors and properties (2.1, 2.2)
  • Week 4
    • Vector spaces (3.1)
    • Subspaces, linear combinations, and spans (3.2)
  • Week 5
    • Basis and dimension (3.4)
      Exam #1
  • Week 6
    • Change of basis (3.5)
    • Row space and column space of a matrix. Rank-nullity theorem.
  • Week 7
    • Introduction to linear transformations. Matrix representation of transformations.
    • Matrix representations, continued. Similar matrices (4.2, 4.3)
  • Week 8
    • Eigenvalues and eigenvectors (6.1)
    • Diagonalization of matrices (6.3)
  • Week 9
    • Scalar product in Bn. General inner product spaces (5.1, 5.4)
    • Inner product spaces, continued. Orthonormal sets (5.4, 5.5)
  • Week 10
    • The Gram-Schmidt procedure (5.6)
    • Exam #2
  • 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)
  • Week 12
    • Fourier series, continued (chapter 2)
    • Application of Fourier series. Bessel functions (chapter 2, chapter 6)
  • Week 13
    • Bessel functions, continued (chapter 6)
    • Applications of Bessel functions (chapter 6)
  • Week 14
    • Review for final
    • Final exam

      Last modified Tues March 15, 2011 by AP