Course objectives:
|
The course focuses on the following areas:
Vector-valued and complex functions of one real variable. Elementary curves. Sequences and series of functions, Fourier series. Boundary value problems for ordinary differential equations of the second order. Local solvabnility of functional equations (implicit function theorem). Integrals depending on parameters, integral transforms.
|
Requirements on student
|
It is necessary to obtain at least 50% points from the assignments given lecturer.
|
Content
|
1. Vector functions one real variable; curves in Rn.
2. Complex functions one real variable.
3. Sequences and series of functions.
4. Trigonometric Fourier series.
5. General Fourier series.
6. Differential mappings, vector field.
7. Two dimensional manifold in Rn. Differential characteristics of vector fields.
8. Integral calculus of functions of several variables.
9. Integral with parameter.
10. Methods of calsulus of triple integrals.
|
Activities
|
|
Fields of study
|
|
Guarantors and lecturers
|
|
Literature
|
|
Time requirements
|
All forms of study
|
Activities
|
Time requirements for activity [h]
|
Preparation for comprehensive test (10-40)
|
26
|
Contact hours
|
26
|
Total
|
52
|
|
Prerequisites
|
Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
There is no prerequisite for this course. Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/MA1. |
|
Learning outcomes
|
Knowledge - knowledge resulting from the course: |
By the end of the course, a successful student should be able to:
1. Deal with function sequences and function series;
2. Expend a function into a power of Fourier series;
3. Describe curves in Rn and work with them;
4. Determine properties of functions of more variables;
5. Compute directional and partial derivatives of functions of more variables;
6. Formulate basic min/max problems and solve them using differential calculus;
7. Evaluate double and triple integrals;
8. Deal with integrals depending on parameters;
9. Use developed theory in solving problems on physical systems. |
|
Assessment methods
|
Knowledge - knowledge achieved by taking this course are verified by the following means: |
Test |
|
Teaching methods
|
Knowledge - the following training methods are used to achieve the required knowledge: |
Seminar |
|