Course details
Calculus 2
IMA2 Acad. year 2019/2020 Winter semester 4 credits
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
Completion
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
- Discrete Mathematics (IDM)
- Calculus 1 (IMA1)
Prerequisite knowledge and skills
The IMA1 course.
Syllabus of lectures
- Number series.
- Power series.
- Fourier series.
- Fourier transform, discrete Fourier transform.
- Functions of several variables (particularly in 2 and 3 dimensions), limit and continuity.
- Differential calculus of functions of several variables I: partial derivatives, Hess matrix, Schwarz theorem.
- Differential calculus of functions of more variables II: local extrema, Sylvester criterion.
- Integral calculus of functions of several variables I (particularly in 2 and 3 dimensions): definitions and basic concepts.
- Integral calculus of functions of several variables II: multidimensional and multiple integrals, Fubini theorem.
- Integral calculus of functions of several variables III: evaluation and applications of double and triple integrals.
- Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable equations.
- 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