Course offering missing for current semester as well as for previous and coming semesters

## Content and learning outcomes

### Course contents

Functions of several variables: partial derivatives, the chain rule, the gradient and its properties and directional derivatives.
Total derivatives and Jacobians
Differentials and their invariance. Taylor's formula for functions of several variables
Transformation of partial derivatives by change of variables
The inverse and implicit function theorems
Local extremal points. Global extreme value problems with and without constraints.
The Lagrange multiplier method.
The method of least squares
Multipelintegral, kurvintegral och Greens formel. Tillämpningar.
Multiple integrals, contour integrals and Green's formula. Applications.

### Intended learning outcomes

Basic course in differential and integral calculus in several variables. After the course the students should know and be able to use the basic concepts in the calculus of functions of several variables: partial derivative, differentiability, differentials, gradient, directional derivative, total derivative, Jacobian, multiple integrals, contour integrals.
More specifically after finishing the course the students should be able to

• apply the chain rule and decide wether a function satisfies a certain partial differential equation
• compute tangent planes and directional derivatives using the gradient
• compute limits of certain functions of several varaibles and decide whether it is differentiable
• form differentials and Taylor expansions of functions of several varaibles
• transform partial derivatives by changing variables
• use total derivatives and Jacobians to solve problems in connections with local existence for inverse functions and implicit functions
• compute and analyze the type of stationary points
• solve optimization problems for different types of regions with or without constraints
• use the method of least squares
• compute certain multiple integrals
• use multiple integrals to compute volumes and area, and compute the length of curves using integrals
• compute contour integrals using parametrizations and Green's formula

### Course Disposition

No information inserted

## Literature and preparations

### Specific prerequisites

SF1644 Calculus in one variable and SF1645 Linear Algebra.
Compulsory for first year students, cannot be taken by other students.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

LTH/Övningar i analys i flera variabler.

## Examination and completion

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

A, B, C, D, E, FX, F

### Examination

• TEN1 - Examination, 6,0 hp, betygsskala: 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.

One written exam

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Examiner

No information inserted

### Ethical approach

• 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

### Course web

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 SF1646

SCI/Mathematics

### Main field of study

Mathematics, Technology

First cycle