SubjectsSubjects(version: 861)
Course, academic year 2019/2020
  
Mathematics II - S413003
Title: Mathematics II
Guaranteed by: Department of Mathematics (413)
Actual: from 2011
Semester: summer
Points: summer s.:8
E-Credits: summer s.:8
Examination process: summer s.:
Hours per week, examination: summer s.:3/3 C+Ex [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Level:  
For type:  
Guarantor: Pokorný Pavel RNDr. Ph.D.
Z//Is interchangeable with: N413003A, B413002, N413003
Examination dates   Schedule   
Annotation
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)
Mathematics II develops skills obtained in Mathematics I to a level required in Master Program.
Aim of the course
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

General skills:

1. basic mathematical terms

2. knowledge and understanding of basic algorithms

3. individual problem solving

4. basic mathematical background for formulation and solving of natural and engineering problems

5. numerical algorithms (systems of differential equations).

Literature
Last update: TAJ413 (01.08.2013)

A: K. Rektorys: Survey of Applicable Mathemaics, Springer 2nd edition (March 31, 1994)

Syllabus
Last update: Borská Lucie RNDr. Ph.D. (20.02.2020)

1. Vectors and matrices, matrix algebra, scalar product. Linear independence of vectors and rank of a matrix.

2. Systems of linear algebraic equations. Determinant of a matrix, vector product.

3. Inverse matrix. Eigenvalues of matrices. Plane and space geometry.

4. Euclidean space, metric, norm, properties of subsets.

5. Functions of more real variables. Partial derivatives, partial derivatives of composite functions. Directional derivative, gradient. Total differential, tangent plane.

6. Taylor polynomial of functions of 2 variables. Newton's method for a system of 2 nonlinear equations of 2 unknowns.

7. Extremes of functions of two variables. Least squares method.

8. Implicit functions of one and more variables and their derivatives.

9. Curves given parametrically, tangent vector to a curve, smooth curve, orientation and sum of curves.

10. Vector fields in plane and space. The line integral of a vector field and its physical meaning.

11. Independence of the curve integral on the integration path. Potential vector field. Differential forms and their integration.

12. Double integral and its geometric meaning. Calculation of double integral by iterated integral - Fubini’s theorem.

13. Substitution for the double integral. Polar coordinates. Laplace integral.

14. Systems of two first-order differential equations. Solution of autonomous systems of linear differential equations with constant coefficients. "Predator-prey" model.

Registration requirements
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

Mathematics I

 
VŠCHT Praha