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Description
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 firstorder 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.

Nonlinear 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 writeup should be in your own words and based on your own understanding.
Inclass Exams
There will be 3 inclass 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 Institutesanctioned 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
10 Problem Sets 
500 (50 points each) 
3 Inclass Exams (50 minutes each) 
300 (100 points each) 
Final Exam (3 hour) 
200 
Total 
1000 
