Course details
Calculus 2
IMA2 Acad. year 2020/2021 Winter semester 4 credits
Series. 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
- 90 pts final exam (written part)
- 10 pts numeric exercises
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.
- Differential calculus of functions of several variables I: limit, continuity, partial derivatives, Schwarz theorem.
- Differential calculus of functions of several variables II: differential, tangent plane, Taylor polynomial.
- Differential calculus of functions of more variables III: local extrema, Hess matrix, Sylvester criterion,.
- Integral calculus of functions of several variables I: double integral, normal domain in plane, Fubini's theorem, change of variables.
- Integral calculus of functions of several variables II: triple integral, normal domain in space, Fubini's theorem.
- Integral calculus of functions of several variables III: change of variables in triple integral.
- Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable equation. Linear equation
- 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
Home assignments during the semester.
Exam prerequisites:
The condition for receiving the credit is obtaining at least a given minimum of points from the activities during the semester.
Controlled instruction
Classes are not compulsory.
Exam prerequisites
The condition for receiving the credit is obtaining at least a given minimum of points from the activities during the semester.
Course inclusion in study plans