Course details

Calculus 1

IMA1 Acad. year 2019/2020 Summer semester 4 credits

Current academic year

Limit, continuity and derivative of a function. Extrema and graph properties. Approximation and interpolation. Indefinite and definite integrals.

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 numeric exercises

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

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

Learning objectives

The main goal of the course is to explain the basic principles and methods of calculus. The emphasis is put on handling the practical use of these methods for solving specific tasks.

Why is the course taught

Fundamentals of calculus are a necessary part of a study at a technical university because virtually all technical and physical subjects employ the concepts of a derivative and integral.

Recommended prerequisites

Prerequisite knowledge and skills

Secondary school mathematics.

Syllabus of lectures

  1. The concept of a function of a real variable. Properties of functions and basic operations with functions.
  2. Elementary functions of a real variable.
  3. Limit and continuity of a function. Limit of a sequence.
  4. Differential calculus of functions of one variable. Derivative at a point, derivative in an interval, a differential of a function. Numerical differentiation.
  5. Higher-order derivatives. Extrema of a function and inflection points.
  6. Graph sketching.
  7. Taylor theorem. Newton and Lagrange interpolation.
  8. Approximation. Least squares method.
  9. Numerical solutions of nonlinear equations.
  10. Integral calculus of functions of one variable. Indefinite integral, basic methods of integration.
  11. Definite Riemann integral and its applications. Numerical integration.
  12. Improper integral.

Syllabus of numerical exercises

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

Progress assessment

Written tests during the semester (maximum 30 points).

Exam prerequisites:
The condition for receiving the credit is active work during the semestr and obtaining 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

The condition for receiving the credit is active work during the semestr and obtaining at least 10 points from the tests during the semester.

Course inclusion in study plans

  • Programme BIT, 1st year of study, Compulsory
  • Programme IT-BC-3, field BIT, 1st year of study, Compulsory
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