Math 20D Spring 2017

Meeting TimeMon., Wed., Fri., 3:00 PM - 3:50 PM
Location WLH 2001
Instructor Dragos Oprea
Tam Tran (Sections B01-04)
  • Office: APM 5412
  • Office Hours: Wednesday 12-2pm in APM 5412, Thursday 11am-1pm in APM B432
  • Email: tmt006 at ucsd dot edu.
Shanyang Fang (Sections B05-08)
  • Office: APM 5801
  • Office Hours: Monday 4-5 in APM 5801, Tuesday 9:50-11:50 in B432, Wednesday 4-5 in APM 5801
  • Email: sfang at ucsd dot edu.
Marc Loschen (Sections B09-10)
Announcements and Dates
  • Monday, April 3: First lecture
  • Wednesday, April 26: Midterm I
  • Friday, May 19: Midterm II
  • Friday, May 29: Memorial Day, no class
  • Thursday, June 8: Matlab Quiz in B432, at the same time as your regular discussion
  • Friday, June 9: Last Lecture
  • Wednesday, June 14: FINAL EXAM, 3:00-6:00pm in REC GYM and GALBRAITH HALL 242.
Textbook Elementary Differential Equations, tenth edition, by William E. Boyce and Richard C. DiPrima; published by John Wiley & Sons, Inc. The book is required and available at the bookstore and on reserve in the library. We will cover parts of Chapters 1, 2, 3, 5, 6 and 7 of the text.

The grade is computed as the best of the following weighed averages:

  • Homework 10%, Matlab 5%, Matlab Quiz 5%, Midterm I 20%, Midterm II 20%, Final Exam 40%.
  • Homework 15%, Matlab 5%, Matlab Quiz 5%, Midterm I 15 %, Midterm II 15%, Final Exam 45%.
Ordinary differential equations: exact, separable, and linear; constant coefficients, undetermined coefficients. Variations of parameters. Series solutions. Systems. Laplace transforms. Techniques for engineering sciences. Computing symbolic and graphical solutions using Matlab.
Prerequisites Math 20C (or Math 21C) with a grade of C- or better.
ReadingsReading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment. You are responsible for material in the assigned reading whether or not it is discussed in the lecture. It will be expected that you read the assigned material in advance of each lecture.
Calculators Calculator use will not be permitted on exams. Graphing calculators are not required for the course.
Homework Homework problems will be assigned on the course homework page. You may drop the homework in the drop box in the basement of AP&M by 5PM on Wednesday.

You may work together with your classmates on your homework and/or ask the instructors, the TA's, or tutors in the calculus lab for help on assigned homework problems. However, the work you turn in must be your own. No late homework assignments will be accepted. The two lowest homework scores will be dropped.

Please adhere to the following neatness guidelines for homework that you turn in to be graded.
  • Write your name and section clearly on the front page of your completed assignment.
  • Clearly number each solution.
  • Write clearly and legibly.
Matlab homework is due certain Fridays at 11:59PM. The homework is to be submitted online. The Matlab homework page is here. There are four Matlab Assignments and the due dates are noted on the course calendar.
There will be one Matlab Quiz on June 8, in B432, at the time of your regular discussion.
There will be two midterm exams given in class. The dates are April 26 and May 19. There will be no makeup exams. A page of notes is allowed.
The final examination will be held on Wednesday, June 14, 3-6PM in REC GYM and GALBRAITH HALL 242. There is no make up final examination. It is your responsability to ensure that you do not have a schedule conflict during the final examination; you should not enroll in this class if you cannot sit for the final examination at its scheduled time. For the final, you are allowed one page of notes, back and front.

Discussion Sections are held on Tuesdays.

Lab Sections: students don't attend regularly scheduled Lab Sections, but rather they may work on assignments on their own schedule, provided they meet the deadlines. The Lab sections are relevant during the last week when students take the MATLAB Quiz during those times.

  • Course Assistant: Tam Tran
    • Section B01, Tuesday 8-8:50AM, SOLIS 109. Lab B50, Thursday 8-8:50AM, APM B432
    • Section B02, Tuesday 9-9:50AM, SOLIS 109. Lab B51, Thursday 9-9:50AM, APM B432
    • Section B03, Tuesday 10-10:50AM, SOLIS 109. Lab B52, Thursday 10-10:50AM, APM B432
    • Section B04, Tuesday 11-11:50AM, SOLIS 109. Lab B53, Thursday 11-11:50AM, APM B432
  • Course Assistant: Shanyang Fang
    • Section B05, Tuesday 12-12:50PM, SOLIS 109. Lab B54, Thursday 12-12:50PM, APM B432
    • Section B06, Tuesday 1-1:50PM, SOLIS 109. Lab B55, Thursday 1-1:50PM, APM B432
    • Section B07, Tuesday 2-2:50PM, APM 7421. Lab B56, Thursday 2-2:50PM, APM B432
    • Section B08, Tuesday 3-3:50PM, APM 7421. Lab B57, Thursday 3-3:50PM, APM B432
  • Course Assistant: Marc Loschen
    • Section B09, Tuesday 6-6:50PM, WLH 2206. Lab B58, Thursday 6-6:50PM, APM B349
    • Section B10, Tuesday 7-7:50PM, WLH 2115. Lab B59, Thursday 7-7:50PM, APM B349

If you are having trouble with the homework or have questions about the material, the best way to get help is to attend the office hours offered by me and the teaching assistants. If you can't make the scheduled times, then email us and we'll set up an appointment.

Additional help is given by

Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university.
Lecture Summaries
  • Lecture 1: Introduction. Classification of ordinary differential equations and some examples.
  • Lecture 2: Geometric methods, direction fields, integral lines, behaviour of solutions. Solving analytically simple differential equations.
  • Lecture 3: Solving 1st order linear equations by integrating factors. How to find the integrating factor. Examples.
  • Lecture 4: More on integrating factors. Existence, uniqueness and domain of definition of solutions based on continuity of coefficients. Separable equations.
  • Lecture 5: Uniqueness, existence and domain of definition of solutions for nonlinear equations. Modeling problems: bank account, temperature models.
  • Lecture 6: More modeling: mixing problems, population growth. Autonomous equations. Critical points. Phase portrait. Stable, unstable, semistable critical points.
  • Lecture 7: Exact differential equations. Criterion for exactness. Finding the potential function. The potential function is constant along solutions.
  • Lecture 8: Second order constant coefficient differential equations and IVP. Characteristic equation. Case of real roots. General solution is found by superposition.
  • Lecture 9: Case of complex roots. Complex exponentials. Real valued solutions are found by taking real and imaginary part of the complex valued solutions. Graphs of solutions.
  • Lecture 10: Repeated roots. Finding an additional solution y=te^{at}. Midterm review.
  • Lecture 11: General theory of linear homogeneous equations. Existence and uniquness of solutions. Superposition of solutions. Wronskian as a determinant. Fundamental pairs of solutions have non-zero Wronskian. Abel's theorem.
  • Lecture 12: Inhomogeneous ODEs. Method of undetermined coefficients. Polynomial, trigonometric, exponential solutions, combinations thereof.
  • Lecture 13: Non-constant coefficient inhomogeneous linear equations. Variation of parameters.
  • Lecture 14: Systems of first order differential equations. Examples. First order linear system yield a second order differetial equation and conversely. Matrix notation.
  • Lecture 15: Matrices and vectors. Products. Determinants. Invertible matrices. Calculating inverses. Solving systems of linear equations.
  • Lecture 16: Eigenvalues. Eigenvectors. Characteristic polynomials. Using eigenvalues and eigenvectors to solve linear systems of ODEs. Superposition of solutions. Wronskian.
  • Lecture 17: Graphing solutions for real distinct eigenvalues: node sink, node source and saddles depending on the sign of the eigenvalues.
  • Lecture 18: Complex eigenvalues. Spirals, source and sink. Determining the direction of the spiral by computing the velocity vector.
  • Lecture 19: Midterm review.
  • Lecture 20: Repeated eigenvalues. Generalized eigenvectors. Finding a second solution by undertermined coefficients. Graph of solutions.
  • Lecture 21: Fundamental matrices and normalized fundamental matrices. Solving initial value problems using the normalized fundamental matrix. Matrix exponentials.
  • Lecture 22: Inhomogeneous systems. Finding solutions by variation of parameters.
  • Lecture 23: Power series solutions. Finding recursions between coefficients. Examples.
  • Lecture 24: Laplace transform. Laplace transform of the usual functions exponentials, sine, cosine, t^n. First exponential shift formula. Inverse Laplace transform. Decomposition into partial fractions.
  • Lecture 25: Laplace transforms of derivatives and second derivatives. Using Laplace transforms to solve differential equations. Examples.
  • Lecture 26: Step functions and their Laplace transforms. Discontinuous functions in terms of unit step functions. Exponential shift formulas. Applications to differential equations.
  • Lecture 27: Review for Final.