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Multivariable Calculus, 4 ECTS credits.
/Flervariabelanalys/
For:
D
IT
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Prel. scheduled
hours: 46
Rec. self-study hours: 61
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G1
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Aim:
The student should acquire the proficiency in multivariable calculus
required for subsequent studies. After completing the course the student should be able to:
- define and explain the central concepts of the course e.g., basic topological notions, function, limit, continuity, functional determinant, volume, area, mass, potential and the different kinds of derivatives and integrals that are used in the course.
- quote, explain, use and in occurring cases prove the central theorems of the course e.g., the theorem of global extrema, differentiability implies existence of partial derivatives, the chain rule, variable substitution in multiple integrals and the connection between gradients and directional derivatives.
- verify that results and partial results are correct or reasonable.
- calculate limits for functions of several variables
- solve partial differential equations by using the chain rule.
- calculate directional derivatives and equations for tangents, normals and tangent planes as well as explain and use the geometric interpretations of these objects and use them to solve problems.
- calculate multiple integrals by means of iterated integration and variable substitutions (e.g., polar, spherical and linear substitutions).
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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.
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Organisation:
Lectures and lessons.
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Course contents:
The space R^n. Fundamental notions from topology. Functions from R^n to R^p. Function graphs, level surfaces and level curves. Definitions of limit and continuity. Partial derivatives. Differentiability and differential. The chain rule. Gradient, normal, tangent and tangent plane. Directional derivative. Multiple integrals. Iterated integration. Variable substitution. Area, volume and mass.
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Course literature:
Persson, A, Böiers, L-C: Analys i flera variabler, Studentlitteratur,
Lund 1988.
Additional material published by the Department of
Mathematics.
Alternative course literature: Neymark, M: Matematisk analys, flera variabler, Liber.
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Examination: |
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Written examination
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4 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Fredrik Andersson
Link to the course homepage at the department
Course Syllabus in Swedish
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