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Multidimensional Calculus, 5 Credits

Flerdimensionell analys, 5 Högskolepoäng

Established: 2025-02-27

Established by: Department of Engineering Science

Applies from: H25

Learning outcomes

After completing of the course, the student should be able to:

• analyze functions of several variables, including limits, continuity, and differentiability.
• calculate partial derivatives, gradients, and directional derivatives, and apply the chain rule.
• evaluate double integrals in different coordinate systems.
• calculate line integrals.
• apply Green's theorem.
• handle optimization with two-variable objective functions, including constrained optimization with Lagrange multipliers.
• use multivariable calculus in two-dimensional real-world applications in physics and engineering.

Entry requirements

General entry requirements and approved result from the following course/courses: MAT101-Mathematics A and MAT220-Mathematics B or the equivalent.

The forms of assessment of student performance

Individual written exam.

Course contents

The course introduces the analysis of functions depending on multiple variables. It covers fundamental concepts such as partial derivatives and integration of functions with two variables. The course also includes line integrals and their connection to Green's theorem, as well as methods for optimizing two-variable functions, including the use of Lagrange multipliers.

Other regulations

Course grading: U/3/4/5

Course language: The teaching is conducted in English.

General rules pertaining to examination at University West are available at www.hv.se.

If the student has a decision/recommendation on special support due to disability, the examiner has the right to examine the student in a customized examination form.

Cycle

First cycle

Progressive specialization

G1F - First cycle, has less than 60 credits in first-cycle course/s as entry requirements