Math21b Class material

Week 1

• Where is linear algebra used? (PDF)
• To the boat trip question in HW1
• Gauss Jordan elimination game
• To HW 2: splines -> Ceres discovery

Week 2

• Which trafos are linear?
• Dancing Dodecahedron.
• Solving Linear equations
• Linear transformations in the plane
• The Lorentz boost (PDF)

Week 3

• Three examples, where linear maps appear (PDF)
• To the coding example p.144-145 (PDF)
• How to solve
• Trickier problems (PDF)

Week 4

• Which sets are linear spaces? (PDF)
• On the history of linear algebra
• The basis in a nutshell (PDF)
• Orthogonality (PDF)

Week 5

• Gram-Schmidt orthogonalisation (PDF)
• Orthogonal transformations (PDF)

Week 6

• Data fitting (HTML animation)
• Least squares (PDF)
• Dow jones index data fitting (HTML)
• Determinant I (PDF)
• Determinant II (PDF)

Week 7

• Determinant III (PDF)
• Eigenvalues I (PDF) Plotting orbits
• Eigenvalues II (PDF)

Spring break

Week 8

• Eigenvalues III (PDF)
• Complex Numbers (PDF)
• Stability (PDF)

Week 9

• Some review for midterm 2 (PDF)
• Some True/False questions (PDF)
• Coordinate change (PDF)
• Symmetric Matrices (PDF)

Week 10

• Continuous dynamical systems (PDF)
• Continuous dynamical systems II (PDF)
• Nonlinear systems (PDF)

Week 11

• Linear spaces (PDF)
• Periodic system of elements
• Linear differential equations (PDF)
• Motivation for Fourier theory (HTML animation)

Week 12 (last week)

• Fourier series (PDF)
• Fourier approximation (HTML animation)
• Heat equation (PDF)
• Dirichlet problem (PDF)
• Wrap up (PDF)