470-8746/02 – Differential and Integral Calculus of Functions of Real and Complex Variables (DIP)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | prof. RNDr. Jiří Bouchala, Ph.D. | Subject version guarantor | prof. RNDr. Jiří Bouchala, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2016/2017 | Year of cancellation | 2020/2021 |
| Intended for the faculties | USP | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
Upon the successful completion of the course, students will be able to actively use new terms in the field of differential
and integral calculus.
Teaching methods
Lectures
Tutorials
Summary
The aim of the course Differential and Integral Calculus of Functions of Real and Complex Variables is to introduce students to differential and integral calculus of real and complex functions including functional series. Simultaneously, they should acquire a certain computational skill and ability to apply the taught theory on practical problems.
Compulsory literature:
1. James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics, Addison-Wesley
Publishing Company, 1994.
Recommended literature:
Way of continuous check of knowledge in the course of semester
During the semester we will write two tests.
E-learning
Other requirements
There are no additional requirements on a student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures + exercises:
Multi-variable Differential and Integral Calculus of Real Functions.
1.Sequence Convergence. Limits, Functions, and Continuity.
2.Total Differential, Partial Derivatives, Directional Derivative, Gradient.
3.Higher Order Differentials, Taylors Polynomial, Taylor’s Theorem.
4.Implicit Function Theorem.
5.Local, Global, and Constrained Extrema, Lagrange multipliers.
6.Double and Triple Integral. Fubini’s Theorem for Double and Triple Integral.
7.Substitution Theorem. Application of Multiple Integrals.
Functions of a Complex Variable.
8.Complex Numbers, Extended Gaussian Images.
9.Complex Functions of a Real and Complex variable.
10.Limits, Continuity, and Complex Functions Derivatives. Conformal Mapping.
11.Complex Function Integration, Cauchy Theorem.
12.Power and Taylor Series. Laurent Series. Rezidue Theorem.
13.Scalar Multiplication, Norm, Orthogonal Systems.
14.Fourier Series.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.