Math 53: Winter 2014

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Course Description

This is a first course in Ordinary Differential Equations. The material includes separation of variables; integrating factors and exact differential equations; systems of linear differential equations; eigenvalues and eigenvectors; the method of variation of parameters; the Laplace transform; systems of nonlinear differential equations, and conservation laws.

This course will focus on teaching "cookbook-style" methods for solving of concrete problems. Students interested in a proof-oriented course should look into Math 53H.

For a more detailed syllabus see the schedule of topics.

Prerequisites: Single Variable Calculus (Math 19-20-21, or 41-42, or equivalent); Linear Algebra and Multivariable Calculus (Mathematics 51 or equivalent)

Enrollment in lectures and sections

Math 53 students attend lectures on MWF and discussion sections on TTh. After you have enrolled in a MWF lecture on Axess, you need to use CourseWork to enroll in a TTh section as explained here.


The text for the course is Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications - Second Edition, by Brannan and Boyce. If you have problems finding the textbook at the campus bookstore, please contact your instructor.

Grading and Exams: Policies and Dates

Your final grade is calculated by averaging your homework, midterm, and final examination scores as follows:

Homework: 15%
This is a non-trivial portion of your grade, so be sure to spend time completing your homework assignments. (Your lowest homework score will be dropped before this average is computed; this policy is to accomodate exceptional circumstances such as a serious illness.)

Two Midterm Exams: 25% each
The first midterm is on January 28 from 7-9 PM in the Cubberley Auditorium. See the Exams page for details.
The second midterm is on February 25 from 7-9 PM in the Cubberley Auditorium.

Final Exam: 35%
The final exam will be held on (has to be confirmed) Monday, March 17, from 7-10pm the rooms will be anounced. According to Math Department policy, you must take the exam at this time.

See the Exams page for details.

A note regarding exams: All exams for Math 53 are closed-book, closed-notes, with no calculators or other electronic aids permitted. If you have a course-related or competition-related schedule conflict with a midterm exam, you must contact your instructor at least a week in advance of the exam to make arrangements for an alternate (early) sitting. No other schedule conflicts are accommodated. For more information on exams, including previous exams, see the Exams Page.


Completing homework assignments is an integral part of this course. Problems are designed to reinforce concepts covered in lecture as well as to encourage students to explore implications of the results discussed in class. Very few students will be able to go through the entire course without struggling on many problems, so do not be discouraged if you do not immediately know how to solve a problem. In confronting difficult questions you should consider how the problem at hand connects to topics, definitions and/or theorems discussed in class.

When you have worked on a problem for a while and remain stuck, you are encouraged to ask for hints from your instructor or TA. Students may also discuss problems with one another, but must write solutions on their own. In particular if you have taken notes while discussing homework problems with friends or instructors, you must put these notes away when writing your solution. The Honor Code applies to this and all other written aspects of the course. Be warned: watching someone else solve a problem will not make homework a good preparation for tests. Don't get caught in the trap of relying on others to get through homework assignments.

Students are expected to take care in writing their assignments. For instance,
  • assignments should be written neatly;
  • assignments should contain clear, complete solutions;
  • solutions sets which contain multiple pages should be stapled; and
  • never forget to put your name, your section number and your TA's name on the top of your work.
  • Partial progress toward solutions on problems will be awarded partial credit, but simply writing answers down without justification will receive zero credit. Your solutions should be readable and complete: this means that the grader should see a sufficient explanation and details to give you full credit, even if the question only asks for a numerical answer.

    If necessary, please write out your complete solutions neatly on a new sheet of paper after doing your scratch calculations; this is a courtesy to the grader and will also improve your grade, since graders cannot give credit for work they cannot follow.

    Logistics: Assignments are due Thursdays and must be turned in to your TA at the beginning of your discussion session -- you will not receive credit for work turned into another section leader. (If you're unable to turn in your homework in section contact your TA how to hand in your HW. Homework handed in after 5 PM will not be accepted and graded. To accommodate exceptional situations such as a serious illness, your lowest homework score will be dropped at the end of the quarter. Solutions will be posted on this page by the following morning, and homework will be returned in Thursday sections.

    All problems not designated otherwise are taken from the indicated section of the textbook.

    Getting Help, Links, and Other Resources

  • You are encouraged to attend the office hours provided by the instructors and teaching assistants. You may attend the office hours of any instructor or teaching assistant.

  • The Stanford University Mathematics Organization (SUMO) offers free drop-in tutoring for students in the 50's sequence. Tutoring is available on Mondays and Wednesdays from 6:00-10:00 p.m. in room 380-381U.

  • Free Tutoring at the Center for Teaching & Learning (Runs only through the last day of classes, June 6)

  • The math department offers a "Homework Night" where students in any math course can get together to work on assignments. It takes place Tuesdays from 6-10 PM in room 380-381U.

  • Math Department Web Page

  • Tips for Success in Undergraduate Math Courses by Jessica Purcell
    Some very good advice for college calculus students. Read this carefully and do as it suggests.
    Note: Pay particular attention to #3 under "Weekly" and #6 and #7 under "Before the exam". Students who think they're following these tips often overlook those parts, and they're the most important ones!

  • Common Errors in Undergraduate Mathematics by Eric Schechter
    Although this document is a bit on the long side, you should read at least some of it carefully -- you'll do better in your math classes because of it. We encourage you to pay particular attention to the sections: bad handwriting, all of the algebra errors, stream-of-consciousness notations, and going over your work.

  • Statement from the Registrar concerning students with documented disabilities:
    "Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Student Disability Resource Center (SDRC) located within the Office of Accessible Education (OAE). SDRC staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the SDRC as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."

  • Honor Code and Fundamental Standard

  • Winter 2014 -- Department of Mathematics, Stanford University