Mathematics 3

Prerequisite:

Introduction to Algebra (X01ALG)
Mathematics 1 (X01MA1)

Lecturer:

Tutor:

Dušan Valášek

Supervisor:

Department of Mathematics

Synopsis:

Introduction to multivariable calculus. Functions of two and more variables - continuity, differentiation, gradient. Higher order derivatives and differentials, Taylor polynomial for multivariable functions, implicit functions. Maxima and minima of multivariable functions. Integration in plane and space, substitutions in integrals. Basic numerical methods for solving nonlinear eguations, interpolation polynomial, numerical differentiation and integration.

Requirements:

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

Syllabus of lectures:

1. Functions of two and more variables. Limit and continuity. Vector fields.

2. Partial derivatives, directional derivatives, gradient.

3. Differential, tangent plane to a surface.

4. Higher order derivatives.

5. Chain rule.

6. Taylor polynomial. Local extrema.

7. Absolute and constrained extrema. Implicit functions.

8. Integrals over plane and solid regions.

9. Polar, cylindrical and spherical coordinates.

10. Application of integration in geometry and physics.

11. Numerical methods for solving algebraic equations.

12. Interpolation polynomial, splines.

13. Numerical differentiation, extrapolation.

14. Numerical integration, trapezoidal and Simpson formula.

Syllabus of tutorials:

1. Functions of two and more variables. Limit and continuity. Vector fields.

2. Partial derivatives, directional derivatives, gradient.

3. Differential, tangent plane to a surface.

4. Higher order derivatives.

5. Chain rule.

6. Taylor polynomial. Local extrema.

7. Absolute and constrained extrema. Implicit functions.

8. Integrals over plane and solid regions.

9. Polar, cylindrical and spherical coordinates.

10. Application of integration in geometry and physics.

11. Numerical methods for solving algebraic equations.

12. Interpolation polynomial, splines.

13. Numerical differentiation, extrapolation.

14. Numerical integration, trapezoidal and Simpson formula.

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:

• Heavy-current Engineering- structured studies (compulsory elective course)