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

    Return to Contents

    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


    Return to Contents

    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

    Return to Contents

    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.

    Return to Contents

     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.
    1. Guessing
    2. Separation of variables
    3. Applying linearity (particular + general homogeneous)
    4. Integrating factor
    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)..

    Return to Contents

    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.      Some assignments in this class will use a web-based homework system called WebWork.  The login link is https://webwork2.math.uga.edu/webwork2/Math2700_Azoff_F11/ . Your username is the first part of your uga email address, and your initial password is set to the first nine digits of your UGA MyID formatted as 810-xx-xxxx; your UGA password is not involved.

    Until an assignment is due, you can try the problems as many times as you like, and the system will tell you whether you have the right answer.  This lets you correct your work immediately.  Shortly after an assignment is due, answers will be posted.  You are welcome to work together on WebWork problems, but each student's problems will be slightly different, so copying others' answers will not work.

    See the webpage http://www.math.uga.edu/undergraduate/student_services.html  for an up-to-date list of possible free tutoring offered at UGA, including afternoon Study Hall sessions staffed by the Mathematics Department and facilites sponsored by Academic Services.

    Return to Contents