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Multivariable Calculus 7,5 Credits

The course focuses on the basic theory of functions of several variables.

Course Contents

The course presents the basics of the Calculus in several variables.

The course focuses on the following topics:
- Curves and surfaces in implicit form and parameter form (in particular the quadrics)
- Basic set-theoretical concepts. Polar, cylindrical and spherical coordinates
- Functions of several variables, level curves and surfaces
- Limits and continuity, partial derivatives
- Gradient, differentiability, directional derivatives and linerization
- The chain rule, change of variables, the nabla differential operator, curl and divergence. Higher order partial derivatives, the Laplace and wave PDEs
- Second-order Taylor polynomial, classification of critical points and identification of local extremes
- Optimization on compact domains, optimization subject to constraints, Lagrange multipliers
- Double and triple integrals, Fubini evaluation, change of variables
- Basic calculus of vector-valued functions, line and surface integrals, conservative fields, potentials
- The Green's, Gauss' divergence and Stokes formulas.

Prerequisites

General entry requirements and completed course Single Variable Calculus, 6 credits and Linear Algebra, 6 credits or Basic Calculus, 6 credits and Linear Algebra and Optimization, 9 credits

Level of Education: Undergraduate G1F
Course code/Ladok code: TFVK17
The course is conducted at: School of Engineering

Previous and ongoing course occasions

Type of course
Program
Study type
Campus
Semester
Autumn 2019: Aug 19 - Oct 20
Rate of Study
100%
Language
English
Location
Jönköping
Time
Day
Examiner
Tjavdar Ivanov
Course coordinator
Tjavdar Ivanov
Tuition fees do NOT apply for EU/EEA citizens or exchange students
17498kr
Syllabus
HTML  PDF
Application code
HJ-T9312
Type of course
Single subject
Study type
Campus
Semester
Autumn 2019: Aug 19 - Oct 20
Rate of Study
50%
Language
English
Location
Jönköping
Time
Day
Number of places
30
Course coordinator
Tjavdar Ivanov
Examiner
Tjavdar Ivanov
Tuition fees do NOT apply for EU/EEA citizens or exchange students
16253kr
Syllabus
HTML  PDF
Application code
HJ-13145

Content updated 2019-10-21

Education
Content updated 2015-06-24
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