 Department of Applied Mathematics
Spring 2009

## Ordinary Differential Equations Group 120501.01 - Prof. Dana-Picard

### Lecture: Wyler 161 - Monday 16:15 - 18:45

Teacher: Prof. Noach Dana-Picard

Teacher Assistents: Mr Y.O. Koch and Mr A. Yarden

Course coordinator: Dr V. Lender.

Syllabus:

• What is an ordinary differential equation? Examples from Physics, from Geometry. Slope fields.
• Equations with initial conditions.
• Solutions of an ordinary differential equation. General solution, particular solution, singular solution.
• First order equation, separable equation, exact equation, integrating factor.
• Homogeneous linear equation of first order. Non homogeneous linear equation of first order: the method of undetermined coefficients, and the method of variation of parameters. Bernoulli equations, Clairaut equations.
• Second order linear equations with constant coefficients: the homogeneous case. Reduction of order.
• Second order linear equations with constant coefficients - the non-homogeneous case: undetermined coefficients and variation of parameters.
• Cauchy-Euler equations.
• Higher order linear equations.
• The exponential of a square matrix.
• Systems of linear differential equations of first order. Matrix methods.
• Laplace transform; inverse Laplace transform. Solution of differential equations using Laplace transform.
• Solution of systems of differential equations using Laplace transform.
• Series solutions of differential equations.

### Help material, handouts and presentations:

will be available soon here (at least I hope so...).

And here is a pdf file for the first lecture.

### Homework assignement:

Registered students should download the sheets from the moodle website of the course.

### Solutions of a few exercise from past years (it seems so long ago...):

Grading: The grade will be (primarily) determined by final exam, weekly home work assignements and two mid-term.

Former Exams:

Recommended Texts:

• Nagle and Saff: Fundamentals of Differential Equations, Addison-Wesley.
• Abell and Braselton: Modern Differential Equations, Saunders College Publishing.
• Differential Equations, Schaum Series (exists in Hebrew and in English).
• G. Simmons and S. Krantz: Differential Equations: Theory, Technique, and Practice, MacGraw-Hill, 2007.

All these books are in the library. We recommend a visit to the library; there are many recent acquisitions.

In Calculus books, there is generally a chapter on Differential Equations, but this not enough for this course.