Hour and topic  Assignment  Relevant reading  Due date  Solutions 

0. Vector and Matrix Basics  Problem Set 0  Basics of Vectors and Matrices  W 9/6  Solutions 
1. Introduction to Linear Systems  Problem Set 1  Bretscher 1.1, The Method of Elimination  F 9/8  Solutions 
Weekly Problems  
2. GaussJordan Elimination  Problem Set 2  Bretscher 1.2  M 9/11  Solutions 
3. Introduction to Linear Transformations  Problem Set 3  Introduction to Linear Transformations  W 9/13  Solutions 
4. How much data do you need to determine a linear transformation?  Problem Set 4  Linear Combinations and Linear Transformations  F 9/15  Solutions 
5. More Examples of Linear Transformations  Problem Set 5  Bretscher 2.2 (you may skip the formulas for projections and reflections involving dot products)  M 9/18  Solutions 
6. More on Bases of \(\mathbb{R}^n\), Matrix Products  Problem Set 6  Bretscher 2.3; you may skip the discussion of block matrices  W 9/20  Solutions 
7. Matrix Inverses  Problem Set 7  Bretscher 2.4; you may skip the part on block matrices  F 9/22  Solutions 
8. Coordinates  Problem Set 8  Coordinates  M 9/25  Solutions 
9. Image and Kernel of a Linear Transformation, Introduction to Linear Independence  Problem Set 9  Bretscher 3.1 but don't worry about the term "rank" yet; we'll talk about that next week  W 9/27  Solutions 
10. Subspaces of \(\mathbb{R}^n\), Bases and Linear Independence  Problem Set 10 If you'd like more guidance on writing arguments showing that a set is closed under addition or scalar multiplication, check out the worksheet solutions, especially #3. 
Bretscher 3.2  F 9/29  Solutions 
11. Dimension and the RankNullity Theorem  Problem Set 11  Bretscher 3.3  M 10/2  Solutions 
12. Orthogonal Projections and Orthonormal Bases  Problem Set 12  Bretscher 5.1  F 10/6  Solutions 
13. Determinants  No problem set! (This material is covered in Problem Set 15.)  Computing Determinants Using Minors; Bretscher 6.1 through Example 4; Bretscher 6.2: Theorem 6.2.1, Theorem 6.2.6, Theorem 6.2.8, Example 6  
14. The GramSchmidt Process, The Transpose of a Matrix  Problem Set 14  Bretscher 5.2 (skip QR factorization) and the following parts of Bretscher 5.3: from Definition 5.3.5 to Theorem 5.3.6, and Theorem 5.3.9  W 10/11  Solutions 
15. Least Squares and Data Fitting  Problem Set 15  Bretscher 5.4 through Theorem 5.4.5 only  F 10/13  Solutions 
16. Introduction to Discrete Dynamical Systems and Eigenanalysis  Problem Set 16  §7.1 from the 4th edition of Bretscher (if you have the 5th edition, we've posted a copy here); Complex Numbers (and solutions to the practice problems)  M 10/16  Solutions 
17. Finding the Eigenvalues and Eigenvectors of a Matrix  Problem Set 17  Bretscher 7.2 and 7.3, but skip Theorem 7.3.6 and Example 6 in the 4th edition / Theorem 7.3.5 and Example 5 in the 5th edition; Complex Numbers (see the Handouts page for solutions to the practice problems)  W 10/18  Solutions 
18. Diagonalization  Problem Set 18  Bretscher 7.4 through Example 5 and Bretscher 7.5 through Example 5 if you have the 4th edition, Bretscher 7.1 and Bretscher 7.5 through Example 5 if you have the 5th edition  F 10/20  Solutions 
19. Diagonalization, Continued  Problem Set 19  Bretscher 7.5  M 10/23  Solutions 
20. Orthogonal Matrices, Symmetric Matrices and the Spectral Theorem  Problem Set 20  Orthogonal Matrices, Symmetric Matrices and the Spectral Theorem  W 10/25  Solutions 
21. Introduction to Continuous Dynamical Systems  Problem Set 21  Modeling with Systems of Differential Equations and Bretscher 9.1  F 10/27  Solutions 
22. Linear Continuous Dynamical Systems and the Matrix Exponential  Problem Set 22  A Brief Introduction to the Matrix Exponential  M 10/30  Solutions 
23. Linear Continuous Dynamical Systems, Continued  Problem Set 23  Bretscher 9.2  W 11/1  Solutions 
24. Nonlinear Continuous Dynamical Systems  Problem Set 24  Bretscher "9.4" and Linearization from Differential Equations by Blanchard, Devaney, and Hall  F 11/3  Solutions 
25. Introduction to Linear Differential Equations  Problem Set 25 Reading for #5: Linear Spaces and our annotated copy of Bretscher §4.1 
the worksheet "Introduction to Linear Differential Equations", Modeling Springs with Differential Equations  M 11/6  Solutions 
26. Linear Spaces  Problem Set 26  Linear Spaces and our annotated copy of Bretscher §4.1  W 11/8  Solutions 
27. Linear Transformations  Problem Set 27  Bretscher 4.2 through Example 2 only  F 11/10  Solutions 
28. Linear Differential Equations  Problem Set 28  Bretscher 9.3 through Theorem 9.3.10 (you may skip the operator approach to solving linear diferential equations) or Linear Differential Equations  You may turn this in M 11/20 with PS 31 (PS 30 will be due F 11/17)  Solutions 
29. More Practice with Linear Spaces and Linear Transformations  No problem set!  
30. Inner Product Spaces  Problem Set 30  Bretscher 5.5 through Example 7  F 11/17  Solutions 
31. Trigonometric Polynomials and Fourier Analysis  Problem Set 31

Bretscher 5.5, starting right after Example 7  M 11/20 (remember to also turn in PS 28)  Solutions 
32. Fourier Series  Problem Set 32

Fourier Series  M 11/27  Solutions 
33. Introduction to Partial Differential Equations  Problem Set 33

The Heat Equation and the Wave Equation, §1 and 2  W 11/29  Solutions 
34. The Heat Equation  Problem Set 34  The Heat Equation and the Wave Equation, §3  F 12/1  Solutions 
35. The Wave Equation  Problem Set 35  The Heat Equation and the Wave Equation, §4  Due M 12/4 by 1 pm to your section's mailbox in the 2nd floor hallway near SC 221  Solutions 
Note: Solutions to inclass worksheets can all be found on the worksheets page.