1: Introduction 2: Matrices and Gauss-Jordan Elimination 3: On the Solutions of Linear Systems 4: Linear Transformations 5: Visualizing Linear Transformations 6: Inverting Linear Transformations 7: Matrix Products 8: Kernel and Image 9: Subspace of R^n 10: Dimension 11: Rank-Nullity and Coordinates 12: Linear Spaces 13: Linear Transformations and Isomorphisms 14: Orthogonality and Least Squares 15: Review for Midterm 16: Finding an Orthonormal Basis 17: Orthogonal Transformations 18: Least Squares and Data Fitting 19: Data Fitting. Determinants 20: Determinants II 21: Volume and Cramer's Rule 22: Eigenvectors and Eigenvalues 23: Finding Eigenvalues and Eigenvectors 24: Finding Eigenvectors 25: Diagonalization 26: Complex Eigenvalues 27: (Missing) 28: Continuous Dynamical Systems 29: Continuous Dynamical Systems with Complex Eigenvalues 30: Nonlinear Systems 31: Midterm 2 review 32: Ordinary Differential Equations 33: Fourier Series