Course details
Calculus 1
IMA1 Acad. year 2019/2020 Summer semester 4 credits
Limit, continuity and derivative of a function. Extrema and graph properties. Approximation and interpolation. Indefinite and definite integrals.
Guarantor
Course coordinator
Language of instruction
Completion
Time span
- 26 hrs lectures
- 26 hrs exercises
Assessment points
- 70 pts final exam
- 30 pts numeric exercises
Department
Lecturer
Instructor
Fusek Michal, Ing., Ph.D. (UMAT)
Hlavičková Irena, Mgr., Ph.D. (UMAT)
Hliněná Dana, doc. RNDr., Ph.D. (UMAT)
Vítovec Jiří, Mgr., Ph.D. (UMAT)
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
- Discrete Mathematics (IDM)
Prerequisite knowledge and skills
Secondary school mathematics.
Syllabus of lectures
- The concept of a function of a real variable. Properties of functions and basic operations with functions.
- Elementary functions of a real variable.
- Limit and continuity of a function. Limit of a sequence.
- Differential calculus of functions of one variable. Derivative at a point, derivative in an interval, a differential of a function. Numerical differentiation.
- Higher-order derivatives. Extrema of a function and inflection points.
- Graph sketching.
- Taylor theorem. Newton and Lagrange interpolation.
- Approximation. Least squares method.
- Numerical solutions of nonlinear equations.
- Integral calculus of functions of one variable. Indefinite integral, basic methods of integration.
- Definite Riemann integral and its applications. Numerical integration.
- 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