Calculus in Several Variables, 6 credits (TAIU08)
Flervariabelanalys, 6 hp
Main field of study
Mathematics Applied MathematicsLevel
First cycleCourse type
Programme courseExaminer
Vitalij TjatyrkoDirector of studies or equivalent
Jesper ThorénCourse offered for | Semester | Period | Timetable module | Language | Campus | VOF | |
---|---|---|---|---|---|---|---|
6IDAT | Computer Engineering, B Sc in Engineering (Embedded Systems) | 5 (Autumn 2017) | 1 | 3 | Swedish | Linköping | v |
6IDAT | Computer Engineering, B Sc in Engineering (Software Engineering) | 5 (Autumn 2017) | 1 | 3 | Swedish | Linköping | v |
6IELK | Engineering Electronics | 5 (Autumn 2017) | 1 | 3 | Swedish | Linköping | v |
6IKEA | Chemical Analysis Engineering, B Sc in Engineering | 5 (Autumn 2017) | 1 | 3 | Swedish | Linköping | v |
6IMAS | Mechanical Engineering, B Sc in Engineering | 5 (Autumn 2017) | 1 | 3 | Swedish | Linköping | v |
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G1XCourse offered for
- Computer Engineering, B Sc in Engineering
- Engineering Electronics
- Chemical Analysis Engineering, B Sc in Engineering
- Mechanical Engineering, B Sc in Engineering
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Linear algebra and CalculusIntended learning outcomes
The course will give basic proficiency in several-variable calculus required for subsequent studies. After completing this course, students should be able to
- define and explain basic notions from topology and concepts as function, limit, continuity, partial derivative, extremal point, and multiple integral
- cite, explain and use central theorems such as differentiability implies existence of partial derivatives, the chain rule, Taylor's formula, the characterization of stationary points, the theorem on local maxima and minima, the implicit function theorem, and the theorem on change of variables in multiple integrals
- investigate limits, continuity, differentiability, and use the chain rule for transforming and solving partial differential equations
- explain the geometric significance of directional derivatives and gradients, and determine equations for tangent lines and tangent planes
- investigate local maxima and minima
- explain the behavior of an implicitly given function, for example by Taylor expansion and implicit differentiation
- calculate multiple integrals by means of iterated integration and using various changes of variables, notably linear, plane polar and spherical
- investigate convergence of improper multiple integrals and calculate their values
- verify that results and partial results are correct or reasonable
Course content
The space R^n. Fundamental notions from topology. Functions from R^n to R^p. Function graphs, level curves and level surfaces. Limit and continuity. Partial derivatives. Differentiability and differential. The chain rule. Gradient, normal, tangent and tangent plane. Directional derivative. Taylor's formula. Local extrema. Implicitly defined functions and implicit differentiation. Multiple integrals. Iterated integration. Change of variables. Area, volume, mass and center of mass. Improper multiple integrals.
Teaching and working methods
Lectures and lessons
Examination
TEN1 | Written examination | U, 3, 4, 5 | 6 credits |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Vector analysis
Department
Matematiska institutionenDirector of Studies or equivalent
Jesper ThorénExaminer
Vitalij TjatyrkoCourse website and other links
http://www.mai.liu.se/kurser/index-amne-tm.htmlEducation components
Preliminary scheduled hours: 64 hRecommended self-study hours: 96 h
Course literature
Persson, A, Böiers, L-C: Analys i flera variabler, Studentlitteratur, Lund 2005. Problemsamling utgiven av matematiska institutionen.TEN1 | Written examination | U, 3, 4, 5 | 6 credits |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
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