470-4123/02 – Elements of Higher Mathematics (EVM)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | Mgr. Bohumil Krajc, Ph.D. | Subject version guarantor | Mgr. Bohumil Krajc, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2016/2017 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
A successful student of the course will have the knowledge and skills of a typical graduate bachelor degree in Computational Mathematics .
Teaching methods
Lectures
Tutorials
Project work
Summary
Subject contains parts of higher mathematics omitted in some bachelor programs. Mastering selected parts is essential for the successful engineering degree in Computational Mathematics.
In the field of differential calculus of of functions of several variables we concetrate on the following parts: differentiating of composite functions, Taylor polynomials, implicit function theorem, constrained extremes. Students also learn the basic principles and methods of multidimensional integration. Attention to numerical methods is focused on issues of numerical differentiation and integration of functions. Some remarks are dedicated to a function approximation, search for zero points and extremal tasks.
A substantial part of the course is the interpretation of the relevant passages in the field of ordinary differential equations and their systems.
Compulsory literature:
• W. Rudin, Principles of Mathematical Analysis, McGraw-Hill Book Company, New York, 1964
• W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992
Recommended literature:
• M. Braun: Differential Equations and Their Applications. Springer, Berlin 1978.
Way of continuous check of knowledge in the course of semester
Students pass out tests and deliver projects.
E-learning
Other requirements
No additional requirements are imposed on students.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1.Diferential of a function of several variables. Gradient method.
2.Diferential of a composite function. Transformation of variables in the differential expressions.
3.Approximation of function . Taylor's theorem . Conditions for the existence of local extremes.
4.Numerical derivative. Approximate solutions of equations.
5.Theorem about implicitly defined function. Constrained extremes.
6.Construction of integral sums, numerical integration .
7.Definition of multiple integrals. Selected applications.
8.Fubini`s theorems. Substitution in multiple integrals . Geometric interpretation of Jacobian .
9.Theorems about the existence and uniqueness of solutions of initial value problems for ordinary differential equations. Euler's method.
10.Transformation of variables in differential equations .
11.Potential and its use for solving exact equations.
12.Ordinary differential equations of higher orders. Solving linear differential equations. Boundary value problems .
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks