Till KTH:s startsida Till KTH:s startsida

Flervariabelanalys

Logga in till din kurswebb

Du är inte inloggad på KTH så innehållet är inte anpassat efter dina val.

Kurswebben har varit stängt för redigering sedan första juni 2025 och kommer stängas ned helt första oktober 2026. Utifrån hur kurswebben har använts finns det några olika alternativ för ersättare:

  • Sidan "Inför kursval" i Om kursen
  • Kurs-PM (i Om kursen)
  • Publikt utrymme i Canvas

Är du intresserad av mer information om detta, kontakta e-learning@kth.se.

Overview

Literature: Calculus: A Complete Course, Adams R. A. and Essex C., 9th ed, Pearson, 2018.

Module 1. 3-dimensional geometry and functions of several variables

Lecture 1 

  • 10.1 Analytic geometry in three dimensions

Exercises: 11, 25, 27, 29, 31, 33, 35, 37, 39

  • 10.6 Cylindrical and spherical coordinates

Exercises: 3, 5, 9, 13 

Lecture 2

  • 11.1 Vector values functions in on variable

Exercises: 17, 21, 33

  • 11.2 Applications of vector differentiation

Exercises: 3

  • 11.3 Curves and parametrizations

Exercises: 5, 7, 11, 13, 15

Lecture 3

  • 12.1 Functions in several variables

Exercises: 5, 9, 13,15, 17, 23, 27, 33

  • 12.2 Limits and continuity

Exercises: 5, 7, 9, 11, 15

Module 2. Partial derivatives and linear approximation

Lecture 4

  • 12.3 Partial derivatives

Exercises: 5, 7, 13, 23

  • 12.4 Higher order derivatives

Exercises: 5, 7, 11, 15, 17

  • 12.5 The chain rule

Exercises: 7, 11, 17, 21

Lecture 5

  • 12.6 Linear approximation, differentiability and differentials

Exercises: 3, 5, 17, 19

  • 12.7 Gradient and directional derivatives

Exercises: 3, 5, 13, 17, 25

Module 3. Applications of derivatives

Lecture 6

  • 12.8 Implicit functions

Exercises: 13, 17

  • 12.9 Taylor's formula, Taylor series and approximation

Exercises: 1, 3, 5, 7, 11

Lecture 7

  • 13.1 Extreme values

Exercises: 5, 7, 9, 19, 23, 25

  • 13.2 Extreme values of functions with constraints

Exercises: 3, 5, 9, 15

�Lecture 8

  • 13.3 Lagrange multipliers

Exercises: 3, 9, 11, 15

  • 13.4 Lagrange multipliers in higher-dimensional spaces

Exercises: 1, 3

Module 4. Multiple integrals

Lecture 9

  • 14.1 Double integrals

Exercises: 15, 19, 21

  • 14.2 Iterated integration in cartesian coordinates

Exercises: 3, 5, 15, 23

Lecture 10

  • 14.3 Generalized integrals and the mean value theorem

Exercises: 1, 3, 13, 27

  • 14.4 Double integrals in polar coordinates

Exercises: 5, 9, 15, 19, 21

Lecture 11

  • 14.5 Tripple integrals

Exercises: 5, 7, 9

  • 14.6 Change of variables in triple integrals

Exercises: 3, 7, 11

  • 14.7 Applications of multiple integrals

Exercises: 5, 9, 13, 21,27

Module 5. Line and surface integrals

Lecture 12

  • 15.1 Vector fields and scalar fields

Exercises: 3, 5, 17

  • 15.2 Conservative fields

Exercises: 3, 5, 7, 21

Lecture 13

  • 15.3 Line integrals

Exercises: 7, 11

  • 15.4 Line integrals of vector fields

Exercises: 1, 5, 7, 15

Lecture 14

  • 15.5 Surfaces and surface integrals

Exercises: 1, 7, 13

  • 15.6 Oriented integrals and flux integrals

Exercises: 5, 9, 13, 15

Module 6. Vector Calculus

Lecture 15

  • 16.1 Gradient, divergence and curl

Exercises: 3, 7, 11

  • 16.2 Some identities involving grad, div and curl

Exercises: 9, 15, 17

Lecture 16

  • 16.3 Green's Theorem in the plane

Exercises: 3, 5, 9

Lecture 17

  • 16.4 The Divergence Theorem in three-dimensional space

Exercises: 5, 11, 15

  • 16.5 Stoke's Theorem in three-dimensional space

Exercises: 1, 3, 5

Lecture 18

  • Recap for examination
Anmäl missbruk