TNA006 
Calculus III, 6 ECTS credits.
/Analys III/
For:
ED
ES
KTS
MT


Prel. scheduled
hours: 48
Rec. selfstudy hours: 112


Area of Education: Science
Subject area: Mathematics


Advancement level
(G1, G2, A): G1


Aim:
This course is a continuation of the first year course in single variable calculus. Consequently, the aims are similar: to give students an understanding of mathematical concepts and familiarity with mathematical methods of analysis. Here, these aims relate to the treatment of functions of several variables which arise in all branches of physics and engineering. Students will be expected to be able to do the following after completing this course:
 handle multivariable functions, e.g. to be able to determine limits,
 decide if a function is continuous, determine partial derivatives.
 solve global and local maximum and minimum problems, with and without constaints.
 quote and explain definitions of concepts like limit, contiuity, partial derivative, differentiability, gradient, tangent plane, multiple integrals.
 explain and use central theorems like the implicit function theorem, calculate double and triple integrals, derive expressions for area and volumes using multiple integrals.


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Analysis III and Linear algebra, or similar courses.
Note: Admission requirements for nonprogramme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.


Supplementary courses:
Vector analysis, Applied transform theory, Optimization, Statistics and Probability Theory.


Organisation:
The course is given in the form of lectures, tutorials, tests and a final
examination.


Course contents:
Functions of several variables. Limits and continuity. Partial derivative,
the gradient, directional derivative and differential. Tangent plane and
linearization. The chain rule. Taylor's formula. Vectorvalued functions,
the Jacobian matrix and the Jacobian. Implicit differentiation and implicit
functions. Local and global maxima and minima. Finding of maxima and minima
with and without constraints. Double and triple integrals. Iterated integrals.
Change of variables. Space curves and arc length.


Course literature:
Analys i flera variabler , Persson, BĂ¶iers, Studentlitteratur.


Examination: 

Written examination 
6 ECTS




Course language is Swedish.
Department offering the course: ITN.
Director of Studies: Clas Rydergren
Examiner: Olof Svensson
Link to the course homepage at the department

