Math 20D (Introduction to Differential Equations)

Course Topics: Ordinary Differential Equations
Instructor: Prof. Michael Holst (5739 AP&M, mholst@math.ucsd.edu; Office Hours: MW 10:00am-11:00am)
Term: Fall 2004
Main Class Webpage: http://ccom.ucsd.edu/~mholst/teaching/ucsd/20d_f04/index.html
Computer Lab Webpage: http://www.math.ucsd.edu/~math20d/.
Textbook(s):

  • Stewart, Calculus: Early Transcendentals, 5th Edition, Brooks/Cole, 2003, Chapter 11;
  • Conrad, Differential Equations: A Systems Approach, 1st Edition, Prentice Hall, 2003, Chapters 1-7.
Other books: (Suggested reading if you find Conrad lacking.)
  • Boyce and Diprima, Elementary Differential Equations, 8th Edition, John Wiley and Sons, 2004, Chapters 1-9.
TA(s):
  • Matt Cecil (mcecil@math.ucsd.edu), APM 6402, Office Hours: Wed 10am-12pm. FINALS WEEK: Mon 1-3pm, Wed 3-5pm.
  • Ryan Tully-Doyle (rtullydo@math.ucsd.edu), APM 6402, Office Hours: Mon 11am-1pm. FINALS WEEK: By appointment.
  • Jake Wildstrom (dwildstr@math.ucsd.edu), APM 2250, Office Hours: Mon 3-4pm, Tue 12-1pm, Wed 1-2pm, Fri 12-1pm. FINALS WEEK: By appointment.
Lecture (A00): 9:00a-9:50a MWF, PCYNH/MULTI 106

Discussion Sections and Computer Labs: (DIS=WLH 2112; LAB1=APM B337/B349; LAB2=NW Mezzanine lab in CLICS)

  • 510270 (A01/A50): 08:00a-08:50a Tu (LAB1) - Thu (DIS); TA: Matt Cecil.
  • 510271 (A02/A51): 09:00a-09:50a Tu (LAB1) - Thu (DIS); TA: Matt Cecil.
  • 510272 (A03/A52): 10:00a-10:50a Tu (LAB2) - Thu (DIS); TA: Jake Wildstrom.
  • 510273 (A04/A53): 11:00a-11:50a Tu (LAB2) - Thu (DIS); TA: Jake Wildstrom.
  • 510274 (A05/A54): 12:00p-12:50p Tu (LAB2) - Thu (DIS); TA: Ryan Tully-Doyle.
  • 510275 (A06/A55): 01:00p-01:50p Tu (LAB2) - Thu (DIS); TA: Ryan Tully-Doyle.

CATALOG DESCRIPTION: 20D. Introduction to Differential Equations (4)
Infinite series.Ordinary differential equations:exact,separable, and linear; constant coefficients, undetermined coefficients, variations of parameters. Series solutions. Systems, Laplace transforms, technique for engineering sciences. Computing symbolic and graphical solutions using Matlab. Formerly numbered Math. 21D. May be taken as repeat credit for Math. 21D. Prerequisite: Math 20C (or Math 21C) with a grade of C- or better.
LECTURES, READING, HOMEWORKS: The list of lecture topics each week and the corresponding theory homeworks problems assigned each week will be posted on the Main Class Webpage that you are currently reading. You should read the relevant sections in the text before the lectures in order to get the most from the lectures. The lectures will highlight the important parts of the material, but there will not be time in lecture to cover all of the material in each section in detail. Therefore, having access to, and reading, the textbook is an important component of the course. Below is a list of the topics for each of the lectures during the quarter. (Sections numbered 11.* refer to the Stewart book, whereas the remaining sections refer to the Conrad book.)

Date Lecture Section(s) Topics Covered
WEEK 0
Fri 9/24 1 11.1   Sequences: Concepts, Squeeze Thm, Monotonic Seq Thm
WEEK 1
Mon 9/27 2 11.2-11.3   Geometric and Harmonic Series, Integral Test
Wed 9/29 3 11.4-11.5   Comparison and Alternating Series Tests
Fri 10/1 4 11.6   Absolute convergence, Ratio and Root Tests
WEEK 2
Mon 10/4 5 11.8-11.9   Power series, radius of convergence, examples
Wed 10/6 6 11.10   Taylor series and remainder estimate
Fri 10/8 7 11.12   Applications of Taylor series and remainder estimate
WEEK 3
Mon 10/11 8 1.1-1.2   Introduction to ODE and linear growth/decay models
Wed 10/13 9 1.3   Linear first-order ODE
Fri 10/15 10 2.1-2.2   Separable ODE, Exact form and integrating factors
WEEK 4
Mon 10/18 11 2.3   Graphical analysis of ODE
Wed 10/20 12 2.4 & Review   Initial Value Problems in ODE (IVP); REVIEW for Midterm 1
Fri 10/22 - Midterm 1   TOPICS COVERED: HW1-HW3 (Stewart 11.1-11.12, Conrad 1.1-1.2).
WEEK 5
Mon 10/25 13 2.5   Nonlinear growth models and asymptotic behavior
Wed 10/27 14 3.1-3.2   Systems of ODE and the phase plane
Fri 10/29 15 3.4-3.5   Autonomous systems; Interacting population models
WEEK 6
Mon 11/1 16 4.1   IVP for linear systems of ODE
Wed 11/3 17 4.2   Systems with constant coefficients
Fri 11/5 18 4.3   Systems wth oscillating solutions
WEEK 7
Mon 11/8 19 4.4   General solution of a linear system
Wed 11/10 20 4.4, 2.2   Examples from 4.1-4.4; second look at 2.2
Fri 11/12 21 5.1   IVP for 2nd-order ODEs
WEEK 8
Mon 11/15 22 5.2-5.3   Homogeneous equations, and the case of constant coefficients
Wed 11/17 23 5.5 & Review   Inhomogeneous equations (method of undetermined coefs); REVIEW for Midterm 2
Fri 11/19 - Midterm 2   TOPICS COVERED: HW4-HW7 (Conrad 1.3-4.4).
WEEK 9
Mon 11/22 24 5.8   Variation of constants/parameters
Wed 11/24 25 6.1, 6.3   Definition and properties of the Laplace transform
Fri 11/26 - Holiday   Thanksgiving
WEEK 10
Mon 11/29 26 6.4   Inverse transforms of rational functions
Wed 12/1 27 7.1-7.2   Series solutions of ODE at a regular point.
Fri 12/3 - Review   REVIEW for Final Exam
FINALS WEEK
Thu 12/9 - Final Exam   TOPICS COVERED: HW8-HW10 (Conrad 5.1-7.2) AND Commulative.

GRADES, EXAMS, DATES: Your scores on the theory and computer homeworks each count for 10% of your grade, making the combined homeworks count for 20% of your final grade. The remaining 80% of your grade will be calculated from your performance on two midterm exams and one final exam, to be given on the dates below.

EXAM DATES:

  • Midterm 1: Friday Oct 22, in class. Covers HW1-HW3 (Stewart 11.1-11.12, Conrad 1.1-1.2); 20% of grade.
  • Midterm 2: Friday Nov 19, in class. Covers HW4-HW7 (Conrad 1.3-4.4); 20% of grade.
  • Final: Thursday Dec 9, 8:00-11:00am, PCYNH/MULTI 106. Covers HW8-HW10 (Conrad 5.1-7.2) and Commulative; 40% of grade.
OTHER IMPORTANT DATES:
  • First lecture: Fri, Sep 24
  • Last lecture: Fri, Dec 3
  • Finals week: Mon-Sat, Dec 6-11
  • Holiday: Thu, Nov 11 (Veterans Day Holiday -- No discussion on Thu 11/11)
  • Holiday: Thu-Fri, Nov 25-26 (Thanksgiving Holiday -- No discussion on Thu 11/25, no lecture on Fri 11/26)
COMPUTER HOMEWORKS: Each week you will be assigned some computer problems that compliment the lectures and theory homeworks for that week. Your TA will explain exactly how to use the computers allocated to the class for this purpose, and will give you the laboratory time and location information for our particular class. The computer laboratory time is for your benefit; your TA will be available during that hour to help you with the computer problem sets each week. You should be able to complete the problem set for that week during the hour allocated. Some people have conflicts with other courses during the computer laboratory time; you do not have to attend the laboratory sessions, but you will have to make other arrangements to get access to a computer with MATLAB to complete the computer problem set each week. You should read the homework over before going to the lab each week, otherwise you will not be able to take advantage of the time you have in that hour with the TA. Your TA will explain exactly how to print out results to turn in each week. Complete information about the computer laboratories can be found at the computer homework website mentioned at the top of this page. Here is a list of topics for each of the laboraties during the quarter:
  1. Introduction to MATLAB Using Sequences and Series
  2. Taylor Series
  3. Modeling With ODEs
  4. Direction Fields with DFIELD
  5. The Phase Plane and Solution Curves for Systems of ODEs
  6. Solution of Linear Systems Using Eigenvalues and Eigenvectors
  7. Numerical Methods for ODEs and Systems of ODEs
  8. The Laplace Transform
WEEKLY THEORY HOMEWORK ASSIGNMENTS: The weekly homeworks assigned below are to be turned in to the TA by the deadlines posted below. The discussion sections are for your benefit; your TA will help you work the assigned homework problems, which is the best way to help you prepare for the midterms and final exams. I do not mind if you work with other students in the class on the homework problems each week (in fact, I encourage it), but everyone must write up and turn in a separate homework. If you can do the homework problems well, you will be well-prepared for the exams.

Below are the assigned homework problems for each week during the quarter. WARNING: I sometimes make minor changes to the problem sets (deleting or adding a problem here and there) to reflect how far we get in the lectures, so please check this page often for updated homework assignments.

  • HW1: Due 4pm Fri Oct 1: [Solutions are here]
    • 11.1 (Stewart): 1, 12, 19, 22, 56, 62, 68
    • 11.2 (Stewart): 2, 6, 19, 26, 37, 59, 61
    • 11.3 (Stewart): 3, 22, 28, 32
  • HW2: Due 4pm Fri October 8: [Solutions are here]
    • 11.4 (Stewart): 1, 2, 16, 30, 37, 46
    • 11.5 (Stewart): 8, 15, 24
    • 11.6 (Stewart): 7, 16, 33, 37
    • 11.8 (Stewart): 2, 12, 29, 36
    • 11.9 (Stewart): 7, 16, 26, 35
  • HW3: Due 4pm Fri October 15: [Solutions are here]
    • 11.10 (Stewart): 7, 19, 40, 42, 59, [Optional: 61]
    • 11.12 (Stewart): 2, 27, 35, [Optional: 37]
    • 1.1 (Conrad): 9, 12, 15, 17
    • 1.2 (Conrad): 8, 12, 16, 17

    ----- MIDTERM 1 (HW 1-3): Friday October 22 (Sample Midterm 1 and Score Histogram) -----

  • HW4: Due 4pm Fri October 22: [Solutions are here]
    • 1.3 (Conrad): 1, 5, 13, 24c, 24f
    • 2.1 (Conrad): 5, 8, 12, 16
    • 2.3 (Conrad): 18, 21, 25, 26
    • 2.4 (Conrad): 2, 22
  • HW5: Due 4pm Fri October 29: [Solutions are here]
    • 2.5 (Conrad): 5, 6, 7, 8, 10, 20, 29
    • 3.1 (Conrad): 5, 7, 8
    • 3.2 (Conrad): 6, 10, 14
  • HW6: Due 4pm Fri November 5: [Solutions are here]
    • 3.4 (Conrad): 8, 15, 16
    • 3.5 (Conrad): 1, 5
    • 4.1 (Conrad): 2, 4, 14, 15
    • 4.2 (Conrad): 3, 4, 8, 15, 16
  • HW7: Due 4pm Fri November 12: [Solutions are here]
    • 4.3 (Conrad): 1, 3, 5, [Optional: 7, 9]
    • 4.4 (Conrad): 4, 8a, 8b, 10a, 11, [Optional: 6, 7, 10c]
    • 2.2 (Conrad): 1, 2, 15, 16, 22, 23

    ----- MIDTERM 2 (HW 4-7): Friday November 19 (Sample Midterm 2 and Score Histogram) -----
    ----- Solutions to the actual Midterm 2 are here -----

  • HW8: Due 4pm Mon November 22: [Solutions are here]
    • 5.1 (Conrad): 1, 2, 7
    • 5.2 (Conrad): 1, 10, 14
    • 5.3 (Conrad): 3, 5, 13, 17
    • 5.5 (Conrad): 3, 4, 11, 15, 21
  • HW9: Due 4pm Mon November 29: [Solutions are here]
    • 5.8 (Conrad): 1, 7, 17
    • 6.1 (Conrad): 1, 5, [Optional: 10]
  • HW10: Due 4pm Fri December 3: [Solutions are here]
    • 6.3 (Conrad): 1, 13, 31, 41, 44, [Optional: 30]
    • 6.4 (Conrad): 1, 3, 9, 11, 19, [Optional: 33]
    • 7.1 (Conrad): 3, 11, 16, [Optional: 19]
    • 7.2 (Conrad): 3, 15, 25, 31, [Optional: 4]

    ----- FINAL (HW 8-10 and Cummulative): Thu December 9 (Some Sample Final Problems and Solutions. -----