contents

1. Ordinary differential equations (ODEs)
Introduction. Meaning and interpretation of a solution.
First order ODEs: separate variables and linear.
ODEs of order n: second order linear and constant coefficients.
Brief reference to systems of ODEs.

2. Laplace transform
Definition and convergence region.
Signs: unit step (Heaviside step function); rectangular pulse; Unit impulse (Dirac delta
function).
Properties and calculation of the Laplace transform.
Inverse transform.
Application of Laplace transform in solving ODEs.

3. Functions of several variables
Definition and forms of representation. Contours.
Continuity and differentiability: partial derivatives, differential and geometrical
interpretation.
Composition of functions and the calculation of the derivative.
Applications (gradient).

4. Double integral
Concept and properties.
Calculation and applications.