## MATH 2700 (Azoff)  Elementary Differential Equations    Fall 2011

This website was last updated on December 18.

Letter grades have been reported to the registrar and exams are available for pickup.

Contents
• Course Objectives
• Daily Schedule
• Assignments
• Notes to Previous Assignments
• Exams
• Course Syllabus
• ### Course Objectives

• Model physical and biological processes with differential equations.
• Find general solutions to simple classes of differential equations.
• Get qualitative information and approximate solutions for differential equations whose general solutions cannot be found explicitly.

### Daily Schedule

 Date Topic/Activity Notes M 15 Aug Overview W 17 1.1 Modeling F 19 1.2 Separation of Variables -Theory and Computation M 22 1.2 Separation of Variables - Applications Assignment 1 Due W 24 1.3 Slope Fields F 26 1.4 Euler's Method M 29 1.4 Using Software Assignment 2 Due W 31 1.5 Existence and Uniqueness - Statements F 2 Sept 1.5 Existence and Uniqueness - Consequences W 7 1.6 Phase Plane Assignment 3 Due F 9 1.7 Bifurcations M 12 1.8 Linear Equations - Computational Techniques W 14 1.8 Linear Equations - Theory and Applications Assignment 4 Due F 16 Review M 19 Exam 1 Covers through Section 1.7 W 21 2.1 Modeling with Systems F 23 2.2 Geometry of Systems M 26 2.3 Damped Harmonic Oscillator Assignment 5 Due W 28 2.4 Special Systems F 30 2.5 Euler's Method for Systems M 3 Oct 2.5 Using Software W 5 2.6 Existence and Uniqueness for Systems Assignment 6 Due F 7 3.1 Linearity - Theory M 10 3.1 Linearity - Applications W 12 3.2 Straight-Line Solutions F 14 Review M 17 Exam 2 Covers Sections 1.8, 1.9, 2.1, 2.2, 2.3, 2.4, 2.5, and 3.1 W 19 3.3 Solving Systems with Two Real Eigenvalues Assignment 7 Due F 21 3.3 Systems with Two Real Eigenvalues M 24 3.4 Complex Eigenvalues W 26 3.4 Complex Eigenvalues Assignment 8 Due M 31 Linear Systems Table W 2 Nov 3.6 Second Order Equations F 4 3.7 Trace-Determinant Plane M 7 4.1 Forcing W 9 4.2 Sinusoidal Forcing F 11 4.3 Undamped Forcing and Resonance Assignment 9 Due M 14 Euler's formula and forcing W 16 Review Assignment 10 Due F 18 Exam 3 Focusing on Sections 3.3, 3.4, 3.6, 3.7, 4.1-4.3 M 28 6.1 Laplace Transforms W 30 6.3 Second Order Initial Value Functions Test 3 and Assigns 7, 8 returned F 2 Dec 6.2 Discontinuous Functions M 5 6.4 Impulse Forcing Assignment 11 Due Tu 6 Review Last Day of Class W 14 Dec Final Exam 8 - 11 AM

### Assignments

 Assign# Date Due Section to Read WebWork Text Problems Page(s) Pages Hand In Practice/Class Discussion Bonus 1 M 22 Aug 1.1 wwassign1 14-21 18 5,6,7,10,12,17,21 14 2 M 29 Aug 1.2 wwassign2 33-36 1,2,7,13,21,23,29,35,39,41,43 1.3 47-51 3,7,13,15,19,21 3 W 7 Sept 1.4 wwassign3 61-63 3,7,12,15 12 1.5 71-73 4,10 3,7,9,11,13 16 4 W 14 Sept 1.6 wwassign4, probs 1-8 89-94 1,5,9,13,17,21,23,31,37,39 wwassign4, probs 9-11 1.7 106-110 4,18 5,7,11,13,15,17,21 5 M 26 Sept 1.8 wwassign5 121-124 5,11,13,17,19,21,25,29,30,31,33 1.9 133-135 5,9,15,19,21,23,24-27 6 W 5 Oct 2.1 None 161-166 4, 10 3,6,9,13,16,20,22,25 2.2 178-183 14 5,9,13,19 2.3 187-188 2, 8 1,5,7 7 W Oct 19 3.1 None 258-264 5, 11, 17, 27 6, 8, 10, 13, 14, 16, 18, 24, 26, 28 8 W 26 Oct 3.2 None 277-280 10, 14, 22 1, 6, 11, 20, 21 9 F 11 Nov 3.3 wwassign9 293-296 1, 4, 9, 13, 19ab, 21abc, 23 3.4 310-314 1, 3, 7, 9, 13, 15, 17, 23abc 3.6 342-346 1, 3, 9, 15, 19abcd, 27ab, 29 10 W 16 Nov 3.7 wwassign10 358-360 1, 3, 7, 9, 11 4.1 399-402 7, 11, 15, 21, 23, 27, 35, 39 4.2 412-414 3, 9, 11, 17, 19 4.3 424-427 3, 11, 13, 17, 19, 21 11 M 4 Dec 6.1 wwassign11 577-578 1, 3, 9, 11, 17,21 6.2 585-586 1, 5, 9 6.3 599-601 7, 9, 11, 15, 17, 23, 27, 29,31 6.4 608-609 3, 5 6.5 616-618 3, 5

### Notes to Previous Assignments

These are maintained at http://www.math.uga.edu/~azoff/courses/2700notes.pdf.  Text problems from Sections 1..1, 1.5, and 1.7, 2.1, 2.2, 2.3, 3.1, and 3.2 are currently included.

### Exams

The comprehensive final exam was held from 8 to 11 AM on Wednesday December 14 in our usual classroom.  The median score was 82%.

The following links were provided to help study for the exam.
The third hour exam was held Friday November 18.  It concentrated on Sections 3.3, 3.4, 3.6, 3.7, 4.1, 4.2, and 4.3.  The median score was 82.
A review session was held.  Class discussion problems in boldface type for Assignments 9 and 10 could be brought up at the review session and could help study for the test.

The second hour test was held Monday, October 17.  It covered Sections 1.8, 1.9, 2.1, 2.2, 2.3, 2.4, 2.5, and 3.1.  The median score was 74.

An additional review tool, courtesy of Dr. Krashen, is online at http://www.math.uga.edu/~dkrashen/courses/2700Fall2011/practice_exam2.pdf.
There was also a review session.

Here is a more detailed list of topics/study guide.
• Definition of linear first order differential equation
• Linearity principles for solutions of homogeneous and non-homogeneous linear differential equations
• Methods for solving linear first order differential equations with constant coefficients
1. Guessing
2. Separation of variables
3. Applying linearity (particular + general homogeneous)
4. Integrating factor
• Systems of differential equations
1. Modeling predator-prey and related situations
2. Construction from individual second order equations
3. Harmonic oscillators
4. Vector and direction fields, equilibria, phase portraits and solution curves, plotting individual dependent variables versus time
5. Solving completely and partially decoupled systems and initial value problems
6. Euler's method
7. Matrix notation and the linearity principle
8. Linear algebra topics including determinants, linear combinations, and independence
9. Application of (8) to equilbria, general solutions of systems, and solution of initial value problems
The first hour test, covering through Section 1.7 of the text, was held on Monday, September 19.  Electrical circuits on Pages 44-47 and neutron spiking appearing in some of the exercises were  excluded. The median score on the test was 79.

Study suggestions included looking over previous homeworks, class notes, the text, and chapter review problems on Pages 136-143 (excluding Problems 7,14, 15, 16, 45, 51, 52, and ignoring references to linearity in Problems 21-39)..

MATH 2700 (Azoff)
Elementary Differential Equations
Fall 2011 Course Syllabus

 Web Page http://www.math.uga.edu/~azoff/courses/2700.html Call Number 52-266 Prerequisite Integral Calculus (MATH 2260 or 2310H or 2410 or 2410H or 2210) Time & Place 10:10 - 11:00 AM  MWF 322 Boyd Objective Model physical and biological processes with differential equations. Find general solutions to simple classes of differential equations. Get qualitative information and approximate solutions for differential equations whose general solutions cannot be found explicitly. Text Differential Equations (with CD),  4th Edition, by Paul Banchard, Robert L. Devaney, and Glen R. Hall, Brooks/Cole Publishing Co., CENGAGE Learning, 2011 ISBN10: 1-133-10903-9;  ISBN13: 978-1-133-10903-7 Topics Modeling and classification Separation of variables and mixing Geometry and approximation Theory and equilibria Linear equations and systems Solution methods and applications for systems Laplace transforms 1 week 1 week 1 week 1 week 3 weeks  4 weeks  2 weeks Grading Homework/Quizzes Hour Tests (3 @ 100 pts)  Final Exam 100 points  300 points  200 points Homework will be collected once or twice a week;  no late work will be accepted.   See note below. Instructor E. Azoff e-mail     Phone     Office azoff@math.uga.edu 542-2608  443 Boyd Office   Hours MTuW:  3:30 - 4:30 Th:         2:00 - 3:00 F:           8:30 - 9:30 No Office Hours on Sept 29, 30, Oct 13, 14, 20, or 21

First Homework Assignment Due Monday August 22

 Section to Read WebWork Text Problems Page(s) Hand In Practice/Class Discussion Bonus 1.1 wwassign1 14-21 18 5,6,7,10,12,17,21 14

Note on Homework.