Mathematics H54, Fall 2011

Honors Linear Algebra and Differential Equations

Lectures: Tuesdays and Thursdays, 8:10--9:30am, Room 740, Evans Hall.

Instructor: Michael VanValkenburgh, 895 Evans Hall.

Office Hours: on Monday and Wednesday, 4:15--5:15pm, on Friday, 3:15-4:15pm, and by appointment. These times are subject to change, depending on departmental seminars, etc., but I will give notice by email.

A description of the course: Math H54, Fall 2011 (pdf)

Announcements:

The office hour for Monday, December 5, is cancelled. All other office hours are the same as usual, including an office hour on Monday, December 12.
RRR Week: Optional reviews, held in the regular classroom at the regular time. (Tuesday and Thursday, 8:10--9:30am, Room 740, Evans Hall.) Please bring questions.
FINAL EXAM: Wednesday 12/14, 3-6pm, in a LARGER classroom:

Evans Room 60.

Homework:

Exams:

Practice Midterm 1
Read this only AFTER you take the practice midterm
Midterm 1
Solutions to Midterm 1
Practice Midterm 2
Solutions to Practice Midterm 2
Midterm 2
Solutions to Midterm 2
Practice Final 1
Comments on Practice Final 1
Practice Final 2
The Final
Solutions to the Final

Notes:

The Area of a Parallelogram via Linear Algebra.
Linear Dependence and the Zero Vector.
Math H54 Survey
Vector Spaces of Infinite Sequences.
Nullity equals Number of Free Variables.
Extend the Gram-Schmidt Process to Linearly Dependent Vectors?
Nonlinear Systems.

(Not this kind of matrix, or this kind of matrix, but this kind of matrix.)

Syllabus and Lecture Notes

Date	Topics	Book
1. Thurs 8/25	Systems of Linear Equations	§ 1.1, 1.2
2. Tues 8/30	e.r.o.s, r.r.e.f.s, vectors	§ 1.3, 1.4
3. Thurs 9/1	Homogeneous and Inhomogeneous Systems. Linear indep.	§ 1.5, 1.7
4. Tues 9/6	Linear Transformations, Intro to Matrices	§ 1.8, 1.9, 2.1
5. Thurs 9/8	Inverses of Matrices, Intro to Determinants	§ 2.2, 2.3, 3.1
6. Tues 9/13	Determinants	§ 3.1, 3.2
7. Thurs 9/15	Determinants and Q&A Session	§ 3.3
8. Tues 9/20	MIDTERM 1	Ch.1--3 (LA)
9. Thurs 9/22	Abstract Vector Spaces, Subspaces	§ 4.1, 4.2
10. Tues 9/27	Bases, Coordinate Systems	§ 4.3, 4.4
11. Thurs 9/29	Dimension, Rank	§ 4.5, 4.6
12. Tues 10/4	Change of Basis, Eigenvalues	§ 4.7, 5.1
13. Thurs 10/6	Characteristic Equation, Diagonalization	§ 5.2, 5.3
14. Tues 10/11	Diagonalization, Eigenvalues and Linear Transformations	§ 5.3, 5.4
15. Thurs 10/13	Eigenvalues and Linear Transformations, Dot Products	§ 5.4, 6.1
16. Tues 10/18	Orthogonality	§ 6.2, 6.3
17. Thurs 10/20	Gram-Schmidt, Least Squares	§ 6.4, 6.5
18. Tues 10/25	Least Squares, Inner Product Spaces	§ 6.5, 6.7
19. Thurs 10/27	MIDTERM 2	Ch. 4--6.7 (LA)
20. Tues 11/1	Homogeneous Linear Systems	§ 4.1, 4.2, 4.3
21. Thurs 11/3	Undetermined Coefficients, Variation of Parameters	§ 4.4, 4.5, 4.6
22. Tues 11/8	Higher-order Linear ODE, Matrix Methods	§ 4.6, 6.1, 6.2
23. Thurs 11/10	Matrix Methods for Linear Systems	§ 9.1, 9.4, 9.5, 9.6
24. Tues 11/15	The Matrix Exponential Function	§ 9.7, 9.8 and beyond
25. Thurs 11/17	More on Mtx Exp, Intro to PDE, Separation of Variables	§ 10.1, 10.2
26. Tues 11/22	Separation of Variables, Fourier Series	§ 10.2, 10.3
Thurs-Fri 11/24-25	NO CLASS (Thanksgiving)
27. Tues 11/29	Fourier Sine and Cosine Series, More Heat	§ 10.4, 10.5
28. Thurs 12/1	The Wave Equation, Laplace's Equation	§ 10.6, 10.7


RRR Week	Optional reviews, held in the regular classroom at the regular time.
Wednesday 12/14	FINAL EXAM, 3-6pm, in Evans Room 60.