SubjectsSubjects(version: 854)
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.
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: TAJ413 (26.06.2013)

1. Linear space, base, dimension. The space C(I). Linear mapping.

2. Linear differential equations of n-th order.

3. The system two linear and nonlinear differential equations of the first order.

4. Predator-Prey models: Lotka-Wolterra System.

5. Geometry in R^3 (R^n). Metrics in R^n.

6. Differential calculus in R^n. The functions of two and more variables.

7. Directional and partial derivatives. Tangent plane. Gradient. Newton’s method.

8. Taylor’s formula. The Hessian and extreme values. Method of least squares.

9. Implicit function theory.

10. Line integral of scalar and vector field.

11. Differential form, exact differential form, Potential vector field.

12. Line integrals independent of the path.

13. Double integrals. Fubini theorem. Substitution in double integral. Improper integrals.

14. Triple integrals. Applications. Cylindrical and spherical coordinates.

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

Mathematics I

 
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