SF1674 Multivariable Calculus 7.5 credits
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Content and learning outcomes
Functions of several variables. Fundamental topological concepts in Rⁿ. Differentiability and linear approximation of mappings.
Partial derivatives, differentials, gradient.
The chain rule in general form. The implicit function theorem.
Extreme value problems with and without constraints. Multiple integrals, coordinate changes, geometric applications. Elementary Vector Analysis: Line integrals and surface integrals, Gauss, Green’s and Stokes’ formulas.
Intended learning outcomes
After the course the student should be able to
- use concepts. theorems and methods to solve and present solutions to problems within the parts of multivariable calculus described by the course content,
- read and comprehend mathematical text.
Literature and preparations
Active participation in SF1673 Analysis in one variable.
SF1672 Linear Algebra or similar.
The literature is published on the course webpage no later than four weeks before the course starts.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- TEN1 - Final Exam, 7.5 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.Course web SF1674