SF1686 Calculus in Several Variable 7.5 credits

Euclidian n-space. Functions of several variables and vector-valued functions, including the following concepts: Graph, level curve, level surface. Limits and continuity, differentiability, partial derivatives, the chain rule, differentials. Tangent planes and linear approximation. Taylor’s Formula. Gradient and directional derivative. Jacobian matrix and Jacobian determinant. Invertibility and implicitly defined functions. Coordinate changes.

Extreme-value problems. Multiple integrals. Line integrals and Green’s theorem. Flux integrals and the divergence theorem. Stokes’ theorem. Applications.

After finishing the course the student is expected to

• Be able to use terminology, results and methods to solve, and present solutions of, problems in calculus in several variables described within the course contents.
• Read and understand mathematical text.

Completed course SF1625 Calculus in One Variable or SF1685 Calculus in One Variable.

Basic knowledge of calculus in one variable and linear algebra as presented in SF1624 Algebra and Geometry and SF1625 Calculus in One Variable.

Announced no later than 4 weeks before the start of the course on the course web page.

If the course is discontinued, students may request to be examined during the following two academic years.

• TEN1 - Examination, 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. 

Written exam, possibly with the possibility of continuous examination.

Roy Skjelnes

• 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.

Language: English

Mandatory for first year, can not be read by other students