TAIU01 Calculus, several variables 2014

Study Guide@lith

Valid for year : 2014

TAIU01	Calculus, several variables, 4 ECTS credits. /Flervariabelanalys/ For: DI EL KA
	Prel. scheduled hours: 44 Rec. self-study hours: 63
	Area of Education: Science Main field of studies: Mathematics, Applied Mathematics
	Advancement level (G1, G2, A): G1
	Aim: To give the basic knowledge about concepts and methods in analysis of several variables which is used in technical courses. To pass this course students will need to be able to formulate and understand definitions of the following concepts: topological types of sets, a function of several variables, a limit, continuity, partial derivatives, extreme points and values, multiple integrals. formulate, explain and apply the following theorems: the max-min theorem for continuous functions on compact sets, the chain rule, the Taylor formula, the classifying of critical points via quadratic forms, the theorem about local extreme points under one or two conditions, the change of variables in multiple integrals. do calculations with limits, continuity and differentiability, apply the chain rule to solve partial differential equations. understand the geometric meaning of gradient find equations of the tangent plan carry out investigations of local and global max and min. compute multiple integrals by iteration. compute multiple integrals with the help of change of variables (in particular, the polar and spherical coordinates).
	Prerequisites: (valid for students admitted to programmes within which the course is offered) Analysis of one variable and linear algebra Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
	Organisation: Teaching is done through lectures and problem classes.
	Course contents: Functions of several variables, limits, continuity. Partial derivatives, differentiability, chain rule, gradient. Taylor formula, local extreme points and values, quadratic forms. Max and min values, optimization on compact and non-compact sets. Optimization under conditions, Multiple integrals. Change of variables in multiple integrals.
	Course literature: Persson & Böiers: Analys i flera variabler. Studentlitteratur, Lund 1988, 2005. Forsling: Exempelsamling i flerdimensionell analys för ingenjörslinjerna, utgiven av institutionen.
	Examination:
	Written examination	4 ECTS


Course language is Swedish. Department offering the course: MAI. Director of Studies: Göran Forsling Examiner: Vitalij Tjatyrko Link to the course homepage at the department Course Syllabus in Swedish

Linköping Institute of Technology
Contact: TFK , val@tfk.liu.se Last updated: 06/19/2013