Notes and Recitations by Week

• Week 1: Matrices and Matrix Arithmetic

  The first step in your Linear Algebra journey!

• Week 2: Gaussian elimination, systems of equations and matrix inverses

  Matrices can be tricky… but here are the tools to demystify them!

• Week 3: Determinants, vector spaces and subspaces

  For every square matrix you need a determinant, and vector spaces are super helpful.

• Week 4: Linear independence, basis and dimension

  How we define vector spaces and their components

• Week 5: Change of basis, rank/nullity theorem, linear transformations

  Making some big conclusions and starting to transform linearly!

• Week 6: Eigenvalues and eigenvectors, diagonalization

  λ: The foundation for all linear algebra

• Week 7: More on eigenvalues and eigenvectors, Jordan Canonical Form, inner products

  Broadening diagonalization and going in a new (orthogonal) direction…

• Week 8: Interactions between linear transformations and inner products, symmetric matrices, Singular Value Decomposition

  Some interplays between symmetry, inner products, and matrices

• Week 9: Linear and constant-coefficient differential equations

  My personal favorite part of MATH2400: differential equations!

• Week 10: Physical applications and Cauchy-Euler equations

  The real reason why we teach linear algebra: real-world physical systems!

• Week 11: Systems of differential equations

  Making all these weeks come to a clash — linear algebra x diff eq collab

• Week 12: More complicated systems of differential equations

  Reconciling when systems of diff eq’s are tough

• Week 13: Geometry of systems of differential equations

  Seeing it all play out: sketching our diff eq systems by hand!