Math 54 Spring 2021 Sections 109 and 111

Time: TuTh 12:10pm-1:00pm and 1:10pm-2pm (see Piazza for links)
Instructor: German Stefanich
Office hours: MW 11:10am-12pm
Email: gstefanich(at)berkeley(dot)edu

Discussion notes:

• January 20: 2x2 systems of linear equations.
• January 22: Row reduction.
• January 25: Row reduction (continued).
• January 27: Vectors, linear combinations, span. Exercises.
• January 29: Linear independence. Exercises.
• February 1: Linear independence (continued), parametric vector form. Exercises.
• February 3: Linear transformations. Exercises.
• February 5: One to one and onto linear transformations. Exercises.
• February 8: Composition and inverses. Exercises.
• February 10: Determinants. Exercises.
• February 12: Subspaces. Exercises.
• February 19: Solutions to some midterm problems
• February 24: Vector spaces, linear transformations. Exercises.
• February 26: Basis, coordinates. Exercises.
• March 1: Basis, coordinates (continued). Exercises.
• March 3: Matrix of a linear transformation. Exercises.
• March 5: Change of basis. Exercises.
• March 8: Change of basis (continued). Version 1.Version 2. (Courtesy of Patrick Lutz)
• March 10: Eigenvalues and eigenvectors. Exercises.
• March 12: Diagonalization. Exercises.
• March 15: Diagonalization (continued). Exercises.
• March 17: Diagonalizability for linear transformations, complex eigenvalues. Exercises.
• March 19: Orthogonality. Exercises.
• March 29: Complex eigenvalues and orthogonality, continued.
• March 31: Gram-Schmidt. Exercises.
• April 2: Least squares.
• April 5: Midterm 2 Q&A session. Version 1. Version 2.
• April 9: Spectral theorem. Version 1. Version 2. Exercises.
• April 12: Spectral theorem (continued). Singular values. Version 1. Version 2. Exercises.
• April 14: Singular value decomposition. Version 1. Version 2.
• April 16: Second order ODE. Version 1. Version 2.
• April 19: Second order ODE (continued). Exercises.
• April 21: Second order ODE (continued).
• April 23: Systems of ODE. Version 1. Version 2.
• April 26: Systems of ODE (continued). Version 1. Version 2.
• April 28: Inner product spaces. Version 1. Version 2.
• April 30: Fourier series. Version 1. Version 2.