# Syllabus for Several Variable Calculus, Limited Version

Flervariabelanalys, allmän kurs

A revised version of the syllabus is available.

## Syllabus

• 5 credits
• Course code: 1MA017
• Education cycle: First cycle
• Main field(s) of study and in-depth level: Mathematics G1F
• Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
• Established: 2007-03-19
• Established by: The Faculty Board of Science and Technology
• Revised: 2016-03-15
• Revised by: The Faculty Board of Science and Technology
• Applies from: Autumn 2016
• Entry requirements:

Single Variable Calculus together with Linear Algebra and Geometry I or Algebra and Geometry.

• Responsible department: Department of Mathematics

## Learning outcomes

In order to pass the course (grade 3) the student should be able to

• give an account of the concepts of limit, continuity, partial derivative, gradient and differentiability for functions of severable variables;
• parametrise curves and surfaces;
• compute partial derivatives of elementary functions;
• use partial derivatives to compute local and global extreme values - with and without constrains;
• outline the definition of the multiple integral, compute multiple integrals and use multiple integrals to compute volumes, centres of gravity, etc.;
• compute line integrals of vector fields in the plane;
• exemplify and interpret important concepts in specific cases;
• formulate important results and theorems covered by the course;
• express problems from relevant areas of applications in a mathematical form suitable for further analysis;
• use the theory, methods and techniques of the course to solve mathematical problems;
• present mathematical arguments to others.

## Content

Polar, cylindrical and spherical coordinates. Parameterisations of curves and surfaces.

Level curves and level surfaces. Arc length. Scalar and vector valued functions of several variables. Partial derivatives, differentiability, gradient, direction derivative, differential. Derivatives of higher order. The chain rule. Taylor’s formula. Optimisation: local and global problems, problems with equality constraints. Multiple integrals, change of variables especially polar coordinates, improper integrals, applications of multiple integrals: volume, centres of mass, etc. Line integrals of vector fields. Green's theorem in the plane.

## Instruction

Lectures and problem solving sessions. Team-working may occur.

## Assessment

Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.

## Syllabus Revisions

Applies from: Autumn 2016

Some titles may be available electronically through the University library.

• Adams, Robert A.; Essex, Christopher Calculus : a complete course

8th ed.: Toronto: Pearson, cop. 2013

Find in the library

Mandatory