## Math 54: Schedule and homework assignments

#### Michael Hutchings, Fall 2017

• The dates for the discussion sessions are the same as the dates for the lectures. Homework is due in discussion sessions on the dates listed. Quizzes take place in discussion sessions on the dates listed.
• Topics listed for a given lecture may be covered in the previous or subsequent lecture.
• The entry for each lecture lists the relevant sections of the book; it is best to read these before the lecture if possible. (For Part 1 and Part 2, the book is Lay; the Part 3, the book is Nagle et al.)
• Reading sections of the book that do not appear below is optional. Some of these (e.g. Lay 1.6) are not covered in the course, while others (e.g. Lay 2.6) discuss material which is redundant and covered elsewhere in the course.
• Quizzes will emphasize the sections listed but may review earlier material as needed.
• For extra practice, the supplementary exercises / review problems at the end of each chapter are highly recommended.

#### Part 1. Linear algebra, first half.

• Lecture Aug 23: Systems of linear equations, row reduction. 1.1, 1.2.
• Lecture Aug 25: Vectors and matrices. 1.3, 1.4, 1.5.
• Homework due Aug 28. 1.1: 1, 7, 9, 11, 15, 20, 28. 1.2: 3, 7, 11, 15, 23, 29, 30.
• Lecture Aug 28: Linear independence. 1.7.
• Homework due Aug 30. 1.3: 3, 5 11, 15, 25, 32. 1.4: 1, 5, 7, 11, 17, 18.
• Lecture Aug 30: Linear transformations. 1.8, 1.9.
• Homework due Sep 1. 1.5: 1, 5, 9, 13, 17, 29. 1.7: 1, 5, 11, 17, 21, 33-38.
• Quiz #1 Sep 1: covers 1.1-1.5, 1.7.
• Lecture Sep 1: Matrix operations. 2.1.
• Homework due Sep 6. 1.8: 1, 5, 9, 11, 17, 19, 23, 27, 30, 36. 1.9: 1, 6, 11, 15, 21, 23, 31.
• Lecture Sep 6: The inverse of a matrix. 2.2, 2.3.
• Homework due Sep 8. 2.1: 1, 5, 9, 10, 12, 15, 16, 17, 23.
• Quiz #2 Sep 8: covers 1.8, 1.9, 2.1.
• Lecture Sep 8: Introduction to determinants. 3.1, 3.2.
• Homework due Sep 11: 2.2: 1, 5, 8, 9, 10, 17, 19, 31. 2.3: 1, 3, 5, 7, 11, 18, 21, 22, 29.
• Lecture Sep 11: More about determinants. 3.3.
• Homework due Sep 13. 3.1: 1, 5, 13, 17, 38, 39, 40. 3.2: 5, 9, 19, 21, 27, 28, 29, 31.
• Lecture Sep 13: Vector spaces and subspaces. 4.1.
• Homework due Sep 15. 3.3: 1, 7, 11, 19, 23, 27, 29, 31, 32.
• Quiz #3 Sep 15: covers 2.2, 2.3, 3.1-3.3.
• Lecture Sep 15: Kernel and image of a linear transformation. 4.2.
• Homework due Sep 18. 4.1: 1, 2, 7, 8, 9, 12, 15, 17, 22, 29, 30, 32.
• Lecture Sep 18: Bases and coordinate systems. 4.3, 4.4
• Homework due Sep 20. 4.2: 3, 5, 7, 9, 15, 25, 26, 31, 33, 35.
• Lecture Sep 20: Dimension and rank. 4.5, 4.6.
• Homework due Sep 22. 4.3: 9, 11, 15, 19, 31, 33. 4.4: 1, 5, 7, 9, 11, 13, 17, 27.
• Quiz #4 Sep 22: covers 4.1-4.4.
• Lecture Sep 22. Change of basis. 4.7.

#### Part 2. Linear algebra, second half.

• Homework due Sep 25. 4.5: 1, 7, 11, 17, 19, 20, 23, 26, 29, 30, 31. 4.6: 5, 7, 17, 19.
• Lecture Sep 25: Eigenvectors and eigenvalues. 5.1
• Lecture Sep 27: Midterm #1, in class. Covers material up to and including 4.6.
• Homework due Sep 29. 4.7: 1, 3, 5, 7, 9, 11, 13.
• Lecture Sep 29: The characteristic equation. 5.2
• Homework due Oct 2. 5.1: 1, 5, 9, 15, 21, 22, 25, 26, 29, 31.
• Lecture Oct 2: Diagonalization. 5.3.
• Homework due Oct 4. 5.2: 1, 9, 15, 18, 21, 22, 23, 25.
• Lecture Oct 4: Eigenvectors and linear transformations. 5.4.
• Homework due Oct 6. 5.3: 1, 3, 5, 7, 11, 21, 22, 23, 24, 27.
• Quiz #5 Oct 6: covers 4.5-4.7, 5.1-5.3.
• Lecture Oct 6: Inner products. 6.1.
• Homework due Oct 9. 5.4: 1, 9, 11, 13, 17, 19, 21, 25, 29, 31.
• Lecture Oct 9: Orthogonal sets. 6.2.
• Homework due Oct 11. 6.1: 1, 9, 11, 13, 16, 19, 20, 24, 26, 29, 31.
• Lecture Oct 11: Orthogonal projections. 6.3, 6.4.
• Homework due Oct 13. 6.2: 1, 7, 11, 13, 15, 17, 23, 24, 27, 29, 34.
• Quiz #6 Oct 13: covers 5.4, 6.1, 6.2.
• Lecture Oct 13: Least-squares problems. 6.5.
• Homework due Oct 16. 6.3: 1, 5, 9, 15, 21, 22, 24. 6.4: 1, 9, 13, 17, 18, 19, 22.
• Lecture Oct 16: Inner product spaces. 6.7.
• Homework due Oct 18. 6.5: 1, 5, 7, 11, 13, 15, 17, 19, 20, 25.
• Lecture Oct 18: Diagonalization of symmetric matrices. 7.1
• Homework due Oct 20. 6.7: 1, 7, 9, 13, 16, 18, 21, 25.
• Quiz #7 Oct 20: covers 6.3-6.5, 6.7.
• Lecture Oct 20: Quadratic forms. 7.2
• Homework due Oct 23. 7.1: 7, 11, 13, 17, 24, 25, 26, 29, 35.
• Lecture Oct 23: Singular value decomposition. This is in Lay's book, but not in the Berkeley edition. Please see these notes.
• Homework due Oct 25. 7.2: 5, 7, 8, 11, 20, 21, 22, 25, 27.
• Lecture Oct 25: More about SVD; conclusion of linear algebra.
• Homework due Oct 27: Do all the exercises at the end of the notes on SVD.
• Quiz #8 Oct 27: covers 7.1, 7.2, SVD.

#### Part 3. Differential equations.

• Lecture Oct 27: Second order ODEs. 4.2.
• Lecture Oct 30: Midterm #2: Covers all of linear algebra, with emphasis on Part 2.
• Homework due Nov 1: 4.2 (the differential equations part), problems 5, 13, 17, 26, 36, 46.
• Lecture Nov 1: Complex roots. 4.3.
• Homework due Nov 3: None.
• Lecture Nov 3: Inhomogeneous equations. 4.4, 4.5.
• Homework due Nov 6: 4.3: 3, 9, 22, 25, 28, 31, 36, 38.
• Quiz #9 Nov 6: covers 4.2, 4.3.
• Lecture Nov 6: Variation of parameters. 4.6.
• Homework due Nov 8: 4.4: 9, 13, 17, 21, 25. 4.5: 1, 5, 17, 25, 43.
• Lecture Nov 8: Linear systems. 9.1, 9.4.
• Homework due Nov 13: 4.5: 46, 47. 4.6: 1, 3, 4, 9, 16.
• Quiz #10 Nov 13: covers 4.4, 4.5, 4.6.
• Lecture Nov 13: More linear systems. 9.5.
• Homework due Nov 15: 9.1: 1, 5, 8. 9.4: 1, 9, 16, 22, 31.
• Lecture Nov 15: Complex eigenvalues. 9.6.
• Homework due Nov 17: 9.5: 11, 13, 17, 25, 31, 35, 45.
• Lecture Nov 17: Inhomogeneous linear systems. 9.7.
• Homework due Nov 20: 9.6: 1, 3, 5, 13, 15, 19, 21.
• Quiz #11 Nov 20: covers 9.1, 9.4, 9.5, 9.6.
• Lecture Nov 20: Fourier series. 10.3.
• Homework due Nov 27: 9.7: 3, 11, 13, 15, 21, 28, 29.
• Lecture Nov 27: More Fourier series. 10.3, 10.4.
• Homework due Nov 29: 10.3: 7, 10, 11, 13, 16, 28.
• Lecture Nov 29: Even more Fourier series. 10.4.
• Homework due Dec 1: 10.4: 1, 3, 5, 7, 11, 17, 19.
• Quiz Dec 1: covers 10.3, 10.4.
• Lecture Dec 1: The heat equation. 10.5.
• Homework due Dec 4: 10.5: 3, 5, 7, 9.
• Lecture Dec 4: Optional review session.