Honors differential equations

Lectures: 3 sessions / week, 1 hour / session

Recitations: 2 sessions / week, 1 hour / session

Multivariable Calculus (18.02) or other versions of Multivariable Calculus (18.02A or 18.022 or 18.023 or 18.024).

Students may take 18.02x and 18.034 during the same semester (in which case, Single Variable Calculus (18.01) or Single Variable Calculus with Theory (18.014) is a prerequisite). 18.034 develops theories of ordinary differential equations, and indeed is recommended for those who have taken 18.014.

The official title of 18.034 is (Honors) Differential Equations. A more appropriate title would be Ordinary Differential Equations with Theory. This course covers the same material as 18.03 (Differential Equations) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems. It shares in its spirit with the two semester sequence Calculus with Theory I and II (18.014 and 18.024).

Topics include: First and second-order linear equations; nth-order linear constant-coefficients equations; Green's functions, convolution, Laplace transform methods; Solutions by power series and the method of majorants; Systems of first-order equations; Existence, uniqueness and continuity; Numerical methods; Fourier series methods; Sturm-Liouville theory and bifurcation theory if time permits.

Birkhoff, Garret, and Gian-Carlo Rota. Ordinary Differential Equations. 4th ed. New York, NY: Wiley, 1989. ISBN: 9780471860037.

There will be weekly homework sets, which are given out in recitation. Assignments will be due in the following week. I encourage collaboration in this course, but students must turn in their own write-ups of all problems and list on the solution sheet the names of the students worked together. There is also an optional project.

There will be three midterm exams and a comprehensive final exam.

We will emply a series of specially written JAVA™ Applets, called "d'AIMP applets" during lectures and recitations. These are linked from the related resources section. I encourage using the d'AIMP applets or other CAD tools (computer-aided designs like Mathematica® and MATLAB®) for homework assignments or for your own benefit. However, calculators will not be allowed during exams.

The final grade will be based on a cumulative total of 100% computed as:

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