# Math 54 Summer 2017

 Instructor: Patrick Lutz Email: Reverse of ude.yelekreb “at” ztulgp Office: 840 Evans Office Hours: MWF 9-10, TuTh 3-4 Final Week Office Hours: M 9-10, WF 9-11, TuTh 12-1 and 3-4

## Schedule

 Date Topics Readings Homework Problems Quiz Worksheet 1 6/19 Intro, review of complex numbers Handout, Appendix B (complex numbers) HW 1 No quiz today No worksheet today 2 6/20 Linear Equations and Gaussian Elimination 1.1, 1.2 1.1: 3, 11, 15, 23, 24 1.2: 5, 7, 11, 15, 16, 17, 18, 23, 26, 30 Quiz, Solutions Worksheet 3 6/21 Vectors 1.3 1.3: 1, 5, 9, 11, 14, 15, 22, 23 Quiz, Solutions Worksheet 4 6/22 Linear Independence, Matrices 1.7, 1.4 1.7: 1, 11, 17, 21, 22, 23, 33, 36 1.4: 1, 5, 7, 9, 11, 17, 18, 24 Quiz, Solutions Worksheet 5 6/23 Linear Transformations 1.8, 1.9 1.8: 1, 3, 7, 9, 13, 14, 17, 22, 30, 32 1.9: 1, 5, 9, 17, 22, 25, 35 Quiz, Solutions Worksheet 6 6/26 Geometry of solution sets, Review 1.5, 1.9 1.5: 5, 11, 24, 26, 38, 39 Supplementary exercises: 14, 18 Quiz, Solutions Worksheet 7 6/27 Matrix Algebra 2.1 2.1: 1, 2, 3, 7, 10, 12, 18, 19, 22, 23 Quiz, Solutions Worksheet 8 6/28 Inverses 2.2, 2.3 2.2: 1, 5, 9, 10, 12, 13, 16, 20, 31, 38 2.3: 1, 3, 5, 12, 13, 21, 36 Quiz, Solutions Worksheet 9 6/29 Subspaces, Bases 2.6 2.6: 2, 3, 5, 11, 13, 17, 18, 27, 28 Quiz, Solutions Worksheet 10 6/30 Bases, Dimension 2.7, 4.2 2.6: 22, 23 2.7: 9, 16, 21, 23, 24 4.2: 1, 3, 5 4.3: 13, 21, 23, 25 Quiz, Solutions Worksheet 11 7/03 Vector Spaces 4.1, 4.2, 4.3 4.1: 1, 5, 6, 7, 8, 9, 21, 22, 25, 26, 32 Quiz, Solutions Worksheet 7/04 Fireworks 12 7/05 Coordinates 2.7, 4.4 4.4: 1, 5, 13, 18, 20, 23, 24, 26, 27, 28, 31, 32 Quiz, Solutions Worksheet 13 7/06 More on Bases 4.5, 5.4 4.2: 31, 35 4.3: 31, 32 4.5: 21, 23, 25 5.4: 2, 6, 9 Quiz, Solutions Worksheet 14 7/07 Change of Basis 4.7 4.5: 26, 27, 30 4.7: 3, 9, 10, 20a Quiz, Solutions Worksheet 15 7/10 More Change of Basis 4.5, 4.7 2.3: 28, 30 4.5: 9, 11, 13 4.7: 13, 14 Quiz, Solutions Worksheet 16 7/11 Determinants 3.1, 3.2 3.1: 3, 15, 22 3.2: 7, 16, 19, 29, 33 4.6: 7, 9 Quiz, Solutions Worksheet 17 7/12 Eigenvalues 5.1, 5.2 5.1: 10, 11, 20, 21, 24, 26, 29, 31 5.2: 1, 2, 9, 17, 19 Quiz, Solutions Worksheet 18 7/13 Diagonalization 5.3, 5.4 5.1: 13, 15 5.2: 3, 5 5.3: 1, 4, 5, 9, 13, 21, 22, 23, 24 Quiz, Solutions Worksheet 19 7/14 More Diagonalization 5.3, 5.4 No homework No quiz today No worksheet today 7/17 Midterm 20 7/18 Review midterm, Complex Eigenvalues 5.5 5.5: 1, 2, 3, 4, 5, 6 Supplementary Exercises: 2, 3, 9 No quiz today Worksheet 21 7/19 Geometry of $$\mathbb{R}^n$$ 6.1 5.5: 7, 13 6.1: 1, 2, 3, 5, 7, 9, 13, 19, 28 Quiz, Solutions Worksheet 22 7/20 Orthogonal Basis 6.2 6.2: 7, 9, 17, 21, 23a-c, 26 Quiz, Solutions Worksheet 23 7/21 Projections, Gram-Schmidt 6.3, 6.4 6.3: 1, 3, 4, 9, 11, 21a-d, 23, 24 6.4: 9, 11, 22 Quiz, Solutions Worksheet 24 7/24 Least Squares 6.5 6.2: 24, 28 6.3: 22 6.5: 1, 3, 7, 13, 17, 18a-c, 20 Quiz, Solutions Worksheet 25 7/25 Inner product spaces 6.7 6.7: 1, 3, 5, 7, 14, 21, 23, 25, 26 Quiz, Solutions Worksheet 26 7/26 Symmetric matrices 7.1, 7.2 7.1: 1, 17, 26, 27, 29 Quiz, Solutions Worksheet 27 7/27 Intro to ODEs 4.2, 6.2 4.2: 3, 5, 10, 13, 15, 26 6.2: 1, 19 No quiz today Worksheet 28 7/28 Repeated and Complex roots 4.2, 4.3 4.2: 19, 37 4.3: 3, 13, 21, 22, 28, 36 6.2: 5, 9, 17 Quiz, Solutions Worksheet 29 7/31 Inhomogeneous ODEs 4.4, 4.5 4.4: 11, 12, 13, 21, 29 4.5: 2, 5, 17, 29 Quiz, Solutions Worksheet 30 8/01 Systems of ODEs 6.1, 9.1, 9.4 6.1: 7, 9 9.1: 3, 7, 11 9.4: 5, 26, 28 Optional: 6.1 34, 35 Quiz, Solutions Worksheet 31 8/02 More on Systems of ODEs 9.4, 9.5 9.4: 37 9.5: 11, 14, 17, 26, 31, 35 Quiz, Solutions Worksheet 32 8/03 Complex eigenvalues and pictures 9.5, 9.6 Optional (but cool): 9.8 9.5: 41, 49 9.6: 1, 3, 4, 23 Optional: 9.8 26, 27 Quiz, Solutions Worksheet 33 8/04 Intro to PDEs 10.1, 10.2, Notes HW 32 Quiz, Solutions Worksheet 34 8/07 Fourier Series 10.3, 10.4 (and Lay 6.8) NS&S 10.3: 9, 12, 14, 16 Lay 6.8: 13 Quiz, Solutions Worksheet 35 8/08 Fourier Series and the Heat Equation 10.4, 10.5 Optional: 10.4: 5, 7, 8, 10, 17, 19 Quiz, Solutions Worksheet 36 8/09 Other PDEs 10.6 No homework No quiz today No worksheet today 37 8/10 Review Everything No homework No quiz today No worksheet today 8/11 Final

## Course Mechanics

10% quizzes, 10% HW, 30% midterm, 50% final.

### Quizzes:

Every day at the beginning of class there will be a 10 minute, 4 point quiz on the previous day's material. It is my intention that if you understood the previous day's material then the quiz should not be tricky and should take less than 10 minutes. The lowest 7 scores will be dropped. There are no make-up quizzes.

### Homework:

Homework is assigned daily (and you should do it daily) and it is due Tuesdays and Fridays at the beginning of class. One problem per day will be graded for accuracy. The lowest 2 scores will be dropped.

When answering homework questions in this class, you are required to show your work or give an explanation of your answer. You don't have to write a lot, but you should write enough so that any of your classmates would be convinced that your answer is correct after reading your explanation. If you fail to do this, you will not receive full credit.

### Tests:

There will be a midterm on Monday, July 17 in class and a final on Friday, August 11 in class. Both will be 2 hours long and closed book. Your final score will replace your score in each other category (midterm, HW, and quizzes) if it helps.