Mathematics 2

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Introduction to solving differential equations and systems of thereof. First order linear differential equations, equations with constant coeficient of second and higher orders. Elimination method for systems of first order linear differential equations with constant coefficients. Laplace transform with applications to solving differential equations. Sequences and series, series of functions. Powe and Taylor series, Fourier series.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Syllabus of lectures:

1. Ordinary differential equations.

2. Linear differential equations of the first order.

3. Higher order linear differential equations with constant coefficients.

4. Differential equations with non-zero right-hand side.

5. Systems of linear differential equations with constant coefficients.

6. Laplace transform.

7. Inverse Laplace transform.

8. Solving differential equations using Laplace transform.

9. Complex sequences, series.

10. Convergence of real and complex series.

11. Pover series.

12. Taylor series.

13. Fourier series.

14. Back-up class.

Syllabus of tutorials:

1. Ordinary differential equations.

2. Linear differential equations of the first order.

3. Higher order linear differential equations with constant coefficients.

4. Differential equations with non-zero right-hand side.

5. Systems of linear differential equations with constant coefficients.

6. Laplace transform.

7. Inverse Laplace transform.

8. Solving differential equations using Laplace transform.

9. Sequences of complex numbers, real and complex series.

10. Convergence of real and complex series.

11. Power series.

12. Taylor series.

13. Fourier series.

14. Back-up class.

Study Objective:

Study materials:

1. P. Pták: Calculus II. ČVUT Praha, 1997.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Common plan- structured studies (compulsory course)
• Computer Technology- structured studies (compulsory course)
• Electronics and Communication Technology - structured studies (compulsory course)
• Cybernetics and Measurements- structured studies (compulsory course)
• Heavy-current Engineering- structured studies (compulsory course)