### Homework for Calculus and Linear Algebra

Math 25B, Harvey Mudd College
Profs. Dagan Karp and Michael Orrison

Unless stated otherwise, all homework is due at the beginning of class. Also, the Focus Problems listed below are problems that you should sincerely attempt to solve. They are good problems with which to grapple because they will help you better understand important and useful ideas and techniques. You will not submit your Focus Problem solutions, but be aware that the ideas addressed in the Focus Problems may appear on quizzes and exams.
1. Due Fri. 9/3: Vectors and Vector Spaces

2. Due Wed. 9/8: Systems of Linear Equations
Reading — Section 2.1 and Appendix B (Mathematical Induction).
Focus Problems — (2.1) 8, 10, 12, 22, 38, 40.
Problems — (1.2) 74. (2.1) 14, 16, 24, 34, 36.

3. Due Fri. 9/10: Methods for Solving Linear Systems
Focus Problems — (2.2) 16, 19, 21, 23, 24, 40.
Problems — (2.2) 12, 14, 26, 28, 30, 42.

4. Due Wed. 9/15: Spanning Sets, Linear Independence, and Matrix Operations
Reading — Sections 2.3 and 3.1.
Focus Problems — (2.3) 4, 10, 22, 26, 44, 46.
Problems — (2.3) 8, 12, 24, 42. (3.1) 26, 38.

5. Due Fri. 9/17: Matrix Algebra and the Inverse of a Matrix
Reading — Sections 3.2 and 3.3.
Focus Problems — (3.1) 18, 24. (3.2) 26, 33. (3.3) 52, 54.
Problems — (3.2) 32, 36. (3.3) 18, 42, 44, 46.

6. Due Wed. 9/22: Subspaces, Basis, Dimension, and Rank
Focus Problems — (3.5) 60, 61, 62, 63, 64, 65.
Problems — (3.5) 12, 18, 20, 46, 48, 58.

7. Due Fri. 9/24: In-class Quiz
During class, you'll take a 45 minute quiz, which we will think of as "Homework 7." It will be worth 6 homework points, and most of the problems will be based on Focus Problems we have seen to date.

8. Due Wed. 9/29: Linear Transformations, Eigenvalues, and Eigenvectors
Reading — Sections 3.6 and 4.1.
Focus Problems — (3.6) 4, 6, 8, 10. (4.1) 24, 28.
Problems — (4.1) 26, 30, 35, 36, 37, 38.

9. Due Fri. 10/1: Determinants
Focus Problems — (4.2) 2, 4, 10, 40, 46, 56.
Problems — (4.2) 6, 8, 12, 14, 38, 54.

10. Due Wed. 10/6: Eigenvalues and Eigenvectors
Focus Problems — (4.3) 2, 4, 20, 26, 28, 40.
Problems — (4.3) 6, 8, 22, 24, 32, 34.

11. Due Fri. 10/8: Similarity and Diagonalization
Focus Problems — (4.4) 2, 4, 6, 24, 26, 28.
Problems — (4.4) 10, 12, 42, 44, 46, 48.

12. Due Tue. 10/12: Applications of Linear Algebra
Together with two other classmates, prepare a five minute presentation about an application of linear algebra that you find particularly interesting. Your presentation should be crafted so that your classmates can follow it using the knowledge they have gained as students in Math 25.

Your presentation should use 3-5 PDF slides that can be projected using a computer, and each member of your group should speak for roughly the same amount of time. Please email your slides to your instructor by 8:00 PM on Tuesday 10/12, and be prepared to speak on Wednesday or Friday.

13 = Calc. 1. Due Fri. 10/22: Epsilon-Delta Limits
14 = Calc. 2. Due Wed. 10/27: Continuity (single variable)
15 = Calc. 3. Due Fri. 10/29: Derivatives and Partial Derivatives
16 = Calc. 4. Due Wed. 11/3: (Multivariable) Chain Rule, Tangent Plane, MVT, IVT.
17 = Calc. 5. Due Fri. 11/5: More MVT, L'Hopital's Rule
18 = Calc. 6. Due Wed. 11/10: Integration: Definition and FTOC
19 = Calc. 7. Due Fri 11/12: Natural Logarithms and Exponentials
20 = Calc. 8. Due Wed 11/17: Taylor Polynomials
21 = Calc. 9. Due Fri 11/19: Taylor Series and Multivariable Approximations
22 = Calc. 10. Due Wed 12/1: Series Convergence
23 = Calc. 11. Due Wed 12/3: The Derivative Matrix and Multivariable Linear Approximations
24 = Calc. 12. Due Wed 12/8: Double Integration