Lecture Outlines (Linear Algebra for Engineers)

Bahman Gharesifard
Winter 2015


Course webpage: APSC 174

Lectures:

  • Lecture 1: (The language of sets)
  • Lecture 2: (Maps between sets)
  • Lecture 3: (Systems of linear equations)
  • Lecture 4: (Vector spaces)
  • Lecture 5: (Example of vector spaces)
  • Lecture 6: ("Proofs" using axioms: properties of vector spaces)
  • Lecture 7: (Vector subspaces I)
  • Lecture 8: (Vector subspaces II)
  • Lecture 9: (Linear combinations)
  • Lecture 10: (From linear combinations to linear equations)
  • Lecture 11: (Linear independence and dependence I)
  • Lecture 12: (Linear independence and dependence II)
  • Lecture 13: (From belonging to a span to existence of solutions to linear equations I)
  • Lecture 14: (From belonging to a span to existence of solutions to linear equations II)
  • Lecture 15: (From belonging to a span to existence of solutions to linear equations III)
  • Lecture 16: (Matrices and row operations I)
  • Lecture 17: (Matrices and row operations II)
  • Lecture 18: (Solving systems of linear equations)
  • Lecture 19: (Generating sets)
  • Lecture 20: (Bases and coordinates)
  • Lecture 21: (Dimension of a vector space)
  • Lecture 22: (Linear transformations)
  • Lecture 23: (Image of a linear transformation)
  • Lecture 24: (Kernel of linear transformation)
  • Lecture 25: (From linear transformations to matrices, and back)
  • Lecture 26: (Image and kernel of matrices)
  • Lecture 27: (The rank-nullity theorem)
  • Lecture 28: (From linear transformations to linear equations, and back)
  • Lecture 29: (Operations on matrices I)
  • Lecture 30: (Operations on matrices II)
  • Lecture 31: (Invertible linear transformations)
  • Lecture 32: (Determinants)
  • Lecture 33: (Eigenvalues and Eigenvectors I)
  • Lecture 34: (Eigenvalues and Eigenvectors II)
  • Lecture 35: (Eigenvalues and Eigenvectors III)

For questions, contact me with bahman at mast.queensu.ca or with 613-533-2441 (I prefer emails)