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MATH285

MATH285 (Intro Differential Equations) is a 3-credit hour course that is required for ECE majors as a part of the Foundational Mathematics and Science requirement. It is also required for many other engineering majors. It is offered in the fall, spring, and summer semesters.

Content Covered

  • First order ODEs
  • Second-order ODE's
  • Damped/Undamped/Forced/Unforced Harmonic Oscillators
  • Higher order ODEs
  • Boundary Value Problems
  • Fourier Series / Periodically Forced Oscillators
  • Heat Equation
  • Wave Equation
  • Laplace's Equation
  • Sturm-Liouville Theory and Eigenfunction Series

MATH285 is a foundational course in many concepts crucial for any ECE major. Its impact is most directly seen in ECE210 and courses that depend on ECE210.

Prerequisites

The official prerequisite for MATH285 is MATH241, which provides a background in multivariable calculus. Since MATH285 goes into partial differential equations and 2-D heat equations towards the end, this knowledge is very helpful.

When to Take It

ECE majors typically take MATH285 in their freshman year spring semester or during their sophomore year, depending on how much math credit they come in with. MATH285 is a vital pre/corequisite for ECE210, so taking this course as soon as possible is highly recommended, especially for EE majors.

Course Structure

This class meets three times a week for a 50-minute Lecture-Discussion. There are weekly homeworks on PrairieLearn, with an additional written homework nearly every week. There are three 50-minute Midterm Exams and a Final.

Instructors

This course is often taught by Professors Bronski and Manfroi.

Course Tips

This course is definitely one of the easier math classes in the ECE curriculum. The theory gets a little bit abstract towards the end, but the concepts remain fairly easy to apply if the student spends enough time practicing problems. Take care to review concepts and techniques from MATH231, as many problems require a proficient understanding of integration and differentiation techniques that the student may have forgotten after MATH241. That being said, also be sure to review partial derivatives and 3-dimensional coordinates from MATH241.

Life After

In terms of ECE courses, ECE210 extensively uses concepts from this class: first and second-order linear ODEs, harmonic oscillators, Fourier series, and periodic forcing. Other classes that depend on ECE210 such as ECE310, ECE329, and ECE350, also frequently refer to differential equations in topics such as electromagnetic waves and discrete-time Fourier transforms.

Infamous Topics

  • Fourier Series: The integration when calculating the coefficients can be quite tough, so make sure to really brush up on integration techniques from MATH231. Understanding this is absolutely crucial for success in ECE210.

Resources

  • https://www.youtube.com/blacktshirtmathprofessor