Department of Applied Mathematics
Ordinary Differential Equations
Group 120501.01 - Prof. Dana-Picard
Lecture: Wyler 161 - Monday 16:15 - 18:45
Teacher: Prof. Noach Dana-Picard
Mr Y.O. Koch and Mr A. Yarden
Course coordinator: Dr V. Lender.
- 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...).
- Have a look at some vector fields and solutions of ODE .
- Introduction: pdf, pps.
- Slope fields: pps.
- Euler method: pdf.
- existence and Uniqueness: pdf.
- Linear ODEs of high order: pdf.
- Systems of differential equations of first order: pdf, pps.
- Laplace Transforms: pdf,presentation.
And here is a pdf file for the first lecture.
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...):
- Non homeogeneous linear equation with constant coefficients; method of Variation of Constants:
- Linear equation with the annihilator method:
- A non-homogeneous Cauchy-Euler equation:page 1 , page 2 .
- Linear equation with Laplace Transform:
- Targil 7 question 5b.
- Targil 7 question 5-vav
page 1 -
page 2 .
- Targil 7 question 6.
- Targil 12.
The grade will be (primarily) determined by final
exam, weekly home work assignements
and two mid-term.
- 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.