Instructor: David A. Meyer
Office hours: AP&M 7256, M 1:00pm-2:00pm, W 12:00nn-1:00pm, or by appointment
Lecture: Center 115, MWF 11:00am-11:50am
Email: dmeyer "at" math "dot" ucsd "dot" edu
Teaching assistant: Christopher Chang
Office hours: AP&M 6436, TuTh 1:00pm-2:00pm, or by appointment
Section B01: AP&M 2301, Tu 2:00pm-2:50pm
Section B02: AP&M 2301, Tu 3:00pm-3:50pm
Email: chc007 "at" math "dot" ucsd "dot" edu
Teaching assistant: Jon Grice
Office hours: AP&M 5768, W 10:00am-11:00am & 2:00pm-3:00pm, or by appointment
Section B03: AP&M 2301, Tu 4:00pm-4:50pm
Section B04: AP&M 2301, Tu 5:00pm-5:50pm
Email: jgrice "at" math "dot" ucsd "dot" edu
Teaching assistant: Benjamin Cooper
Office hours: AP&M 6422, MW 3:00pm-4:00pm, or by appointment
Section B05: AP&M 2301, Tu 6:00pm-6:50pm
Section B06: AP&M 2301, Tu 7:00pm-7:50pm
Email: bjcooper "at" math "dot" ucsd "dot" edu
MATLAB sections meet on Thursdays in CLICS Northwest at the same time as Tuesday recitation sections.
This course is an introduction to ordinary differential equations (ODEs). Differential equations most often arise as mathematical models of real situations, which is why scientists and engineers, as well as mathematicians, study them. In this course we will learn how to solve first and second order linear ODEs, by multiple methods, and also learn how to solve systems of first order linear ODEs.
The prerequisite for this course is a thorough knowledge of calculus. The textbook is W. E. Boyce and R. C. DiPrima, Elementary Differential Equations, 8th ed., (Hoboken, NJ: John Wiley & Sons, Inc. 2005). We will cover chapters 1, 2, 3, 5, 6 and 7.
There will be weekly homework and MATLAB assignments, due in sections (or in the AP&M sixth floor drop box for this course before midnight) on Tuesdays. Students are allowed to discuss the homework assignments among themselves, but are expected to turn in their own work — copying someone else's is not acceptable. Homework scores will contribute 10% to the final grade; MATLAB assignment scores will also contribute 10% to the final grade.
There will be two midterms, in the fourth and eighth weeks of the quarter. The final is scheduled for 11:30am Monday 11 June. Scores on the two midterms and final will contribute 22.5%, 22.5% and 35% to the final grade, respectively. There will be no makeup tests.
| 24 Apr 07 |
Equal Pay Day What lies Behind the Pay Gap between men and women? |
| 24 Apr 07 |
Leonhard Euler 300th Birthday Celebration Joan B. Kroc Institute for Peace and Justice, 6:00pm-8:45pm |
| 16-20 Apr 07 |
UCSD Earth Week |
| 2 Apr 07 |
§1.1. Mathematical modeling; direction fields [1] §1.2. Solving first order linear constant coefficient ODEs §1.4. History [2] |
| 4 Apr 07 |
§1.3. Classification of differential equations §2.1. Solving first order linear ODEs using integrating factors HWK (due Tu 10 Apr 07). §1.1: 1,7,24; §1.2: 1a,2a,13; §1.3: 3,4,12,24; §2.1: 13,18,30 |
| 6 Apr 07 |
Differential operators [notes] §2.2. Separable equations |
| 9 Apr 07 |
§2.4. Differences between linear and nonlinear equations |
| 11 Apr 07 |
§2.3. Modeling with first order equations reaction time escape velocity black holes [3] HWK (due Tu 17 Apr 07). §2.2: 3,12,23,30; §2.3: 8,12,31,32; §2.4: 2,10,21,25,32 |
| 13 Apr 07 |
social security §2.5. Autonomous equations and population dynamics |
| 16 Apr 07 |
§2.6. Exact equations and integrating factors Read §2.7, §2.8, §2.9. |
| 18 Apr 07 |
Second order differential operators [notes] §3.1. Homogeneous equations with constant coefficients §3.5. Repeated roots §3.4. Complex roots of the characteristic equation HWK (due Tu 24 Apr 07). §2.5: 5,10,20; §2.6: 4,12,19; §3.1: 14,17,23; §3.4: 9,20,29; §3.5: 3,12 |
| 20 Apr 07 |
§3.2. Fundamental solutions of linear homogeneous equations |
| 23 Apr 07 |
§3.3. Linear independence and the Wronskian HWK (due Tu 1 May 07). §3.2: 4,9,16,17,25; §3.3: 2,5,13,17,25 |
| 23 Apr 07 |
Review session: 5:00pm-5:50pm in Peterson 110 sample midterm |
| 25 Apr 07 |
Midterm 1: sections B01, B02, B03 in Center 115; sections B04, B05, B06 in Center 105 (covering §1.1-1.3; §2.1-2.6; §3.1,3.4,3.5) solutions |
| 27 Apr 07 |
Midterm 1 solutions Inhomogeneous equations |
| 30 Apr 07 |
§3.6. Method of undetermined coefficients HWK (due Tu 8 May 07). §3.6: 1,7,11,17,33,35; §3.7: 1,5,11,13,22,23 Read §3.8, §3.9. |
| 2 May 07 |
§3.7. Variation of parameters |
| 4 May 07 |
§7.2. Review of matrices |
| 7 May 07 |
§7.1. Introduction to systems of first order equations §7.3. Systems of linear algebraic equations HWK (due Tu 15 May 07). §7.1: 3,5,7,22; §7.2: 2,3,6,8,10,12,23; §7.3: 3,7,12,17,21 |
| 9 May 07 |
§7.3. Linear independence §7.5. Homogeneous linear systems with constant coefficients |
| 11 May 07 |
§7.3. Eigenvalues and eigenvectors §7.5. Homogeneous linear systems with constant coefficients |
| 14 May 07 |
§7.4. Basic theory of systems of first order linear equations §7.6. Complex eigenvalues HWK (due Tu 22 May 07). §7.4: 2,4,6; §7.5: 9,11,15,24,25,26,27,29; §7.6: 9,21,28 |
| 16 May 07 |
§7.7. Fundamental matrices |
| 18 May 07 |
§7.8. Repeated eigenvalues |
| 21 May 07 |
§7.9. Inhomogeneous systems HWK (due Tu 29 May 07). §7.7: 3,11,17; §7.8: 1,5,19; §7.9: 4,8,14 |
| 21 May 07 |
Review session: 5:00pm-5:50pm in CSB 001 not exactly sample midterm; solution |
| 23 May 07 |
Midterm 2: sections B01, B02, B03 in Center 105; sections B04, B05, B06 in Center 115 (covering §3.2,3.3,3.6,3.7; §7.1-7.7) solutions |
| 25 May 07 |
Midterm 2 solutions §7.9. Inhomogeneous systems |
| 28 May 07 |
Memorial Day |
| 30 May 07 |
§5.1. Review of power series §5.2. Series solutions near an ordinary point HWK (due Tu 5 June 07). §5.1: 1,3,4,9,13,23; §5.2: 2,11,22; §5.3: 2,5,11,18 |
| 1 Jun 07 |
§5.3. Series solutions near an ordinary point |
| 4 Jun 07 |
§6.1. Definition of the Laplace transform §6.2. Solution of initial value problems suggested problems. §6.1: 1,2,5,7,15,22,23; §6.2: 7,11,24,27ab,28,29 |
| 6 Jun 07 |
§6.3. Step functions §6.4. Differential equations with discontinuous forcing functions suggested problems. §6.3: 1,5,7,14,17,27; §6.4: 1,6 |
| 8 Jun 07 |
§6.6. The convolution integral suggested problems. §6.6: 3,4,8,13,22 |
| 9 Jun 07 |
Review session: 4:00pm-5:50pm in Center 115 sample final; solutions |
| 11 Jun 07 |
Final: 11:30am-2:30pm; sections B01, B03, B05 in Center 105; sections B02, B04, B06 in Center 115 (all sections covered in chapters 1,2,3,5,6,7) solutions |
| [1] |
R. P. Feynman,
"Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character,
as told to R. Leighton, edited by E. Hutchings
(New York: Bantam Books 1986). This includes the story about MIT students' "fragile" understanding of derivatives. |
| [2] |
N. Stephenson,
The Baroque Cycle: Quicksilver, The Confusion, The System of the World
(New York: Harper Perennial 2004, 2005). Three long novels involving the founders of calculus, Newton and Leibniz, and some of their contemporaries. |
| [3] | P.-S. de Laplace, "Proof that the attractive power of a heavenly object can be so large that light cannot be emitted from it", translated from Allgemeine geographische Ephemeriden, Bd I (1799). |