### Mathematical Analysis 2

##### B232 - Summer 23/24
This is a grouped Moodle course. It consists of several separate courses that share learning materials, assignments, tests etc. Below you can see information about the individual courses that make up this Moodle course.

#### Mathematical Analysis 2 - B0B01MA2

##### Main course
 Credits 7 Semesters Both Completion Assessment + Examination Language of teaching Czech Extent of teaching 4P+2S
Annotation
The subject covers an introduction to the
differential and integral calculus in
several variables and basic relations between curve and surface integrals.
Other part contains function series and power series with application to Taylor and
Fourier series.
Study targets
The aim of the course is to introduce students to basics of differential and integral calculus of functions of more variables and theory of series.
Course outlines
1. Functions of more variables, limit, continuity.
2. Directional and partial derivatives - gradient.
3. Derivative of a composition of function, higher order derivatives.
4. Jacobiho matrix. Local extrema.
5. Extrema with constraints. Lagrange multipliers.
6. Double and triple integral - Fubini theorem and theorem on substitution.
7. Path integral and its applications.
8. Surface integral and its applications.
9. The Gauss, Green, and Stokes theorems.
10. Potential of vector fields.
11. Basic convergence tests for series.
12. Series of functions, the Weierstrass test. Power series.
13. Standard Taylor expansions. Fourier series.
Exercises outlines
1. Functions of more variables, limit, continuity.
2. Directional and partial derivatives - gradient.
3. Derivative of a composition of function, higher order derivatives.
4. Jacobiho matrix. Local extrema.
5. Extrema with constraints. Lagrange multipliers.
6. Double and triple integral - Fubini theorem and theorem on substitution.
7. Path integral and its applications.
8. Surface integral and its applications.
9. The Gauss, Green, and Stokes theorems.
10. Potential of vector fields.
11. Basic convergence tests for series.
12. Series of functions, the Weierstrass test. Power series.
13. Standard Taylor expansions. Fourier series.
Literature
[1] Stewart J.: Calculus, Seventh Edition, Brooks/Cole, 2012, 1194 p., ISBN 0-538-49781-5.
[2] L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973
[3] S. Lang, Calculus of several variables, Springer Verlag, 1987
Requirements
https://moodle.fel.cvut.cz/course/view.php?id=6317

#### Mathematical Analysis 2 - B0B01MA2A

 Credits 6 Semesters Summer Completion Assessment + Examination Language of teaching Czech Extent of teaching 4P+2S
Annotation
The subject covers an introduction to the differential and integral calculus in several variables and basic relations between curve and surface integrals. Other part contains function series and power series with application to Taylor and Fourier series.
Study targets
The aim of the course is to introduce students to basics of differential and integral calculus of functions of more variables and theory of series.
Course outlines
1. Functions of more variables, limit, continuity.
2. Directional and partial derivatives - gradient.
3. Derivative of a composition of function, higher order derivatives.
4. Jacobiho matrix. Local extrema.
5. Extrema with constraints. Lagrange multipliers.
6. Double and triple integral - Fubini theorem and theorem on substitution.
7. Path integral and its applications.
8. Surface integral and its applications.
9. The Gauss, Green, and Stokes theorems.
10. Potential of vector fields.
11. Basic convergence tests for series.
12. Series of functions, the Weierstrass test. Power series.
13. Standard Taylor expansions. Fourier series.
Exercises outlines
1. Functions of more variables, limit, continuity.
2. Directional and partial derivatives - gradient.
3. Derivative of a composition of function, higher order derivatives.
4. Jacobiho matrix. Local extrema.
5. Extrema with constraints. Lagrange multipliers.
6. Double and triple integral - Fubini theorem and theorem on substitution.
7. Path integral and its applications.
8. Surface integral and its applications.
9. The Gauss, Green, and Stokes theorems.
10. Potential of vector fields.
11. Basic convergence tests for series.
12. Series of functions, the Weierstrass test. Power series.
13. Standard Taylor expansions. Fourier series.
Literature
1. J. Stewart.: Calculus, Seventh Edition, Brooks/Cole, 2012, 1194 p., ISBN 0-538-49781-5.
2. L. Gillman, R. H. McDowell: Calculus, W.W.Norton & Co.,New York, 1973
3. S. Lang, Calculus of several variables, Springer Verlag, 1987

#### Mathematics-Calculus m-D - A8B01MCM

 Credits 7 Semesters Summer Completion Assessment + Examination Language of teaching Czech Extent of teaching 4P+2S
Annotation
The subject covers an introduction to the
differential and integral calculus in
several variables and basic relations between curve and surface integrals.
Other part contains function series and power series with application to Taylor and
Fourier series.
Study targets
The aim of the course is to introduce students to basics of differential and integral calculus of functions of more variables and theory of series.
Course outlines
1. Functions of more variables, limit, continuity.
2. Directional and partial derivatives - gradient.
3. Derivative of a composition of function, higher order derivatives.
4. Jacobiho matrix. Local extrema.
5. Extrema with constraints. Lagrange multipliers.
6. Double and triple integral - Fubini theorem and theorem on substitution.
7. Path integral and its applications.
8. Surface integral and its applications.
9. The Gauss, Green, and Stokes theorems.
10. Potential of vector fields.
11. Basic convergence tests for series.
12. Series of functions, the Weierstrass test. Power series.
13. Standard Taylor expansions. Fourier series.
Exercises outlines
1. Functions of more variables, limit, continuity.
2. Directional and partial derivatives - gradient.
3. Derivative of a composition of function, higher order derivatives.
4. Jacobiho matrix. Local extrema.
5. Extrema with constraints. Lagrange multipliers.
6. Double and triple integral - Fubini theorem and theorem on substitution.
7. Path integral and its applications.
8. Surface integral and its applications.
9. The Gauss, Green, and Stokes theorems.
10. Potential of vector fields.
11. Basic convergence tests for series.
12. Series of functions, the Weierstrass test. Power series.
13. Standard Taylor expansions. Fourier series.
Literature
[1] Stewart J.: Calculus, Seventh Edition, Brooks/Cole, 2012, 1194 p., ISBN 0-538-49781-5.
[2] L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973
[3] S. Lang, Calculus of several variables, Springer Verlag, 1987
Requirements
https://moodle.fel.cvut.cz/course/view.php?id=6317