Math 207: Department of Math, University of Washington

Math 207: Introduction to Differential Equations


A differential equation is an equation that expresses a mathematical relation among the value of a function and its derivatives. Such equations arise quite naturally in almost all branches of science. Examples include growth models in the life sciences that relate the growth rate of a population to the current value of the population, and laws of motion in physics that relate the acceleration of an object in a varying force field to its location.

Math 207 studies ordinary differential equations in which there is only one independent variable (as opposed to partial differential equations with multiple variables).

The lecture material includes both the study of important models from various sciences and the mathematical methods used to find solutions. Topics covered along the way include equilibrium values and their stability, the long term behavior of certain equations of motion, and resonance phenomena in harmonic oscillation.

The prerequisite for Math 207 is a minimum grade of 2.0 in Math 125.

  • Elements of the Course:
    • Webassign. Webassign is used in all sections for the homework assignments. Consult your instructor's Canvas page to see how they are having you access Webassign. If your Webassign assignments appear on the class Canvas page, then follow the steps at this link to register and pay. Otherwise, follow the directions on your class Canvas page for logging into and paying for Webassign. For all sections, you will need to buy access (approximately $25) and have 10 days to comply. It's best to wait until you are sure which section you are in, then follow instructions at the above link to pay.
    • Textbook. The text for the class is Elementary Differential Equations by Boyce and Diprima. Since the homework is not tied to the text, you can use any edition of Elementary Differential Equations and Boundary Value Problems from Edition 6 to present. Printed versions of these editions are readily available online at a low cost.
      For your convenience there is also an etext available from the bookstore at this link which contains the part of the text used in Math 207 (chapters 1-6).
      The older printed versions may be cheaper. You don't need to buy the solutions manual. The WebAssign homework is different from the homework problems in the textbook, so the solutions manual will not be particularly useful (other than for practice).
    • 200-Level Math Lab. The department runs a lab staffed by assistants to help you with your questions in Math 207 (and a few other 200 level courses). You may also find other students there to discuss the homework with. The location and schedule can be found at this link: Math Lab Schedule
    • Math 207 Grade Policy. The department of mathematics has adopted a grade policy for this course. The median course grades for each section of Math 207 taught during the regular academic year will fall within the range of 3.0 +/- 0.2
    • Religious Accommodation Policy: Washington state law requires that UW develop a policy for accommodation of student absences or significant hardship due to reasons of faith or conscience, or for organized religious activities. The UW's policy, including more information about how to request an accommodation, is available at Religious Accommodations Policy. Accommodations must be requested within the first two weeks of the course using the Religious Accommodations Request form.

    Sample Schedule

    Week Additional Materials Topics and Textbook Sections
    1:
    • Prerequisite Skills
    • Some Basic Modelling § 1.1
    • Solutions to Differential Equations § 1.2
    • Direction Fields § 1.1
    2:
    • Separable First Order ODE's § 2.2
    • Linear First Order ODE's § 2.1
    • Modelling with First Order ODE's § 2.3
    3:
    • Population Dynamics § 2.5
    • Euler's Method § 2.7
    • Review for Midterm 1
    4: MIDTERM #1 ARCHIVE
    5:
    • Homogeneous equations with complex roots § 3.3
    • Homogeneous equations with repeated roots § 3.4
    6:
    • Method of Undetermined Coefficients § 3.5
    • Harmonic Oscillator § 3.7
    7:
    • Forced Undamped harmonic Oscillator Beats and Resonance § 3.8
    • Forced Damped Harmonic Oscillator -- Frequency Response and Phase § 3.8
    • Review for Midterm 2
    8: MIDTERM #2 ARCHIVE
    • Midterm 2
    • Laplace Transform -- definition as an integral § 6.1
    • Tables of Laplace Transforms § 6.2
    9:
    • Inverse Laplace Transform using tables § 6.2
    • Solving IVP with Laplace Transforms § 6.2
    • Step functions and time delay § 6.3 § 6.4
    10:
    • Impulse/Delta Functions §6.
    • Review for Final Exam
    11: Final Exam Archive
    • Final Exam week