TATA42 Calculus in one variable, 2 2007

Study Guide@lith

Valid for year : 2007

TATA42	Calculus in one variable, 2, 6 ECTS credits. /Envariabelanalys 2/ For: BKM D Fys I Ii IT KeBi M Mat TB Y Yi
	Prel. scheduled hours: 68 Rec. self-study hours: 92
	Area of Education: Science Subject area: Mathematics
	Advancement level (G1, G2, A): G1
	Aim: To give basic proficiency in mathematical concepts, reasoning and relations contained in single-variable calculus. To provide the skills in calculus and problem solving required for subsequent studies. After a completed course, the student should be able to read and interpret mathematical text quote and explain Taylor's formula and the concepts involved in numerical series, power series, and convergence of series derive expressions for, and compute, geometrical quantities such as plane area, arc length, and volume and surface area of solids of revolution solve ordinary differential equations (first order linear and separable equations, and higher order linear equations with constant coefficients) and integral equations use Taylor expansions to approximate functions by polynomials, compute limits and rational approximations, and to investigate local properties of functions carry out investigations of convergence of improper integrals, numerical series, and power series, and also compute derivatives and integrals of power series perform routine calculations with confidence carry out inspections of results and partial results, in order to verify that these are correct or reasonable.
	Prerequisites: (valid for students admitted to programmes within which the course is offered) Calculus in one variable 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.
	Supplementary courses: Calculus in several variables, Vector analysis, Complex analysis, and Fourier analysisLectures and problem classes. The IT programme has a different organisation, due to the study programme syllabus.
	Organisation: Lectures and problem classes. The IT programme has a different organisation, due to the study programme syllabus.
	Course contents: Applications of integrals: plane area, arc length, volume and surface area of solids of revolution, mass, and centre of mass. Taylor's and Maclaurin's formulae: Maclaurin expansions of the elementary functions, the Lagrange and Ordo forms of the remainder term, applications, e.g. error estimates for approximations and computations of limits. Ordinary differential equations: first order linear and separable equations, integral equations, higher order linear equations with constant coefficients. Improper integrals: investigation of convergence, absolute convergence. Numerical series: investigation of convergence, absolute convergence, Leibniz criterion. Power series: radius of convergence, solution of differential equations, Maclaurin series.
	Course literature: Forsling, G. and Neymark, N.: Matematisk analys, en variabel. Liber. Complementary material and a collection of problems edited by the Department of Mathematics.
	Examination:
	Written examination	4 p	/	6 ECTS


Course language is . Department offering the course: MAI. Director of Studies: Göran Forsling Examiner: Mats Aigner, Bengt Josefson, Thomas Karlsson och Mikael Langer Course Syllabus in Swedish

Linköping Institute of Technology
Contact: TFK , val@tfk.liu.se Last updated: 09/11/2013