Courses:

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This course emphasizes the theory of the following topics that are covered in 18.03 in less detail.

• Study of ODE's, including modeling physical systems.
• Solution of first-order ODE's by analytical, graphical and numerical methods.
• Linear ODE's, especially second order with constant coefficients.
• Undetermined coefficients and variation of parameters.
• Sinusoidal and exponential signals: oscillations, damping, resonance.
• Complex numbers and exponentials.
• Fourier series, periodic solutions, Delta functions, convolution, and Laplace transform methods.
• Matrix and first order linear systems: eigenvalues and eigenvectors.
• Non-linear autonomous systems: critical point analysis and phase plane diagrams.

The pace for 18.034 is faster than in 18.03, many theorems will be proved, and some topics not covered in 18.03 will be presented.

Prerequisites

Calculus (18.02) or Calculus with Theory ( 18.014).

Text

Borrelli, R., and C. Coleman. Differential Equations: A Modeling Perspective. Wiley Text Books, 2nd ed., New York, 2003. ISBN: 0471433322.

Problem Sets

Problem sets will be due approximately every week, on Friday in lecture. Late homeworks are accepted only if there is a valid medical excuse, or in very special circumstances only with my prior consent. You are encouraged to work with other students in the class, but your final write-up should be in your own words and based on your own understanding.

In-class Exams

There will be 3 in-class exams. They are closed book, closed notes and calculators are not allowed.

Missing an exam is allowed only with a valid medical excuse or for other Institute-sanctioned reasons. For example, an away game in a team sport will typically be allowed, but you must let me know as soon as possible about the conflict. On the other hand, schedule conflict with an airline flight will typically not be allowed, oversleeping will not be allowed, etc.

Grading