| TATA83 |
Calculus, Several Variables , 6 ECTS credits.
/Flervariabelanalys/
For:
KeBi
TB
|
| |
Prel. scheduled
hours: 56
Rec. self-study hours: 104
|
| |
Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
|
| |
Advancement level
(G1, G2, A): G1
|
|
Aim:
The aim is that the student shall become familiar with the mathematical concepts, the reasoning, and the relations that constitute several variable calculus, and also to acquire computitional and problem solving skills, to the extent required for further studies. After completing the course, the student should be able to
- explain basic concepts and theorems for calculus in several variables.
- identify and apply relevant methods to solve problems in calculus in several variables.
|
|
Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear Algebra, Calculus, one variable
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
|
|
Organisation:
Lectures and problem classes.
|
|
Course contents:
The space R^n. Fundamental notions of topology. Functions from R^n to R^p. Function graphs, level curves and level surfaces. Limit and continuity. Partial derivatives. Differentiability. The chain rule. Gradient, normal, tangent and tangent plane. Directional derivative. Taylor's formula. Local and global extrema. Extremal problems on compact domains (parametrizing the boundary). Implicitly defined functions and implicit differentiation. Multiple integrals; iterated integration, change of variables. Area, volume, mass. Introduction to improper multiple integrals.
|
|
Course literature:
Persson, A, Böiers, L-C: Analys i flera variabler, Studentlitteratur,
Lund 1988.
Additional material published by the Department of
Mathematics.
|
|
Examination: |
|
Written examination
|
6 ECTS
|
| |
|
|
Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Joakim Arnlind
Link to the course homepage at the department
Course Syllabus in Swedish
|