Course details

Calculus 2

IMA2 Acad. year 2019/2020 Winter semester 4 credits

Current academic year

Course is not open in this year

Series. The Fourier transform. The limit, continuity, partial derivatives and extrema of a function of several variables. Double and triple integrals. Differential equations. Analytical and numerical solutions of the initial problem.

Guarantor

Course coordinator

Language of instruction

Czech, English

Completion

Credit+Examination (written)

Time span

  • 26 hrs lectures
  • 26 hrs exercises

Assessment points

  • 70 pts final exam
  • 30 pts mid-term test

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

The ability to understand the basic problems of higher calculus and use derivatives, integrals and differential equations for solving specific problems.

Learning objectives

The main goal of the course is to enhance the knowledge of calculus from the previous semester and explain the basic principles and methods of higher calculus. The emphasis is put on handling the practical use of these methods for solving specific problems.

Why is the course taught

The IMA2 course follows on the IMA1 course and complements the necessary knowledge of the concepts of calculus needed to understand and master advanced technical and physical subjects.

Recommended prerequisites

Prerequisite knowledge and skills

The IMA1 course.

Syllabus of lectures

  1. Number series.
  2. Power series.
  3. Fourier series.
  4. Fourier transform, discrete Fourier transform.
  5. Functions of several variables (particularly in 2 and 3 dimensions), limit and continuity.
  6. Differential calculus of functions of several variables I: partial derivatives, Hess matrix, Schwarz theorem.
  7. Differential calculus of functions of more variables II: local extrema, Sylvester criterion.
  8. Integral calculus of functions of several variables I (particularly in 2 and 3 dimensions): definitions and basic concepts.
  9. Integral calculus of functions of several variables II: multidimensional and multiple integrals, Fubini theorem.
  10. Integral calculus of functions of several variables III: evaluation and applications of double and triple integrals.
  11. Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable equations.
  12. Numerical solution of differential equations of the first order.

Syllabus of numerical exercises

Problems discussed at numerical classes are chosen so as to complement suitably the lectures.

Progress assessment

Written tests during semester (maximum 30 points).
Exam prerequisites:
At least 10 points from the tests during the semester.

Controlled instruction

Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.

Exam prerequisites

At least 10 points from the tests during the semester.

Course inclusion in study plans

  • Programme BIT, 2nd year of study, Compulsory
  • Programme IT-BC-3, field BIT, 2nd year of study, Compulsory
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