TNA004 
Calculus II, 6 ECTS credits.
/Analys II/
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:
To give basic proficiency in mathematical concepts, reasoning and relations contained in singlevariable 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
 explain Taylors formula and the concepts series, power series and convergence of series.
 use expressions for, and calculate, geometrical quantities such as plane areas, arc length, surface area, volumes of solids of revolution and areas of surfaces of revolution
 utilize ordinary differential equations (linear of first order: linear and separable and linear equations of higher order with constant coefficients) and integral equations
 use Taylors Theorem in approximating functions with polynomial, calculating limits and estimation errors and estimate local properties of functions.
 carry out convergence tests for improper integrals, series and power series and find derivatives and antiderivatives for power series
 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)
Analysis I
Note: Admission requirements for nonprogramme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.


Organisation:
Lectures and problem classes or classes alone. The IT programme has a different organization, due to the study programme syllabus.


Course contents:
Functions of a real variable. Limits and continuity. Derivatives. Rules of differentiation. Properties of differentiable functions. Derivative and monotonicity. Graph sketching, tangents and normals, asymptotes. Local and global extrema. Derivatives of higher order. Convex and concave functions. How to find primitive functions. The Riemann integral. Definition and properties. Connection between the definite integral and primitive function. Methods of integration. Applications of integrals: area, length of curves, volume of solids of revolution, area of surfaces of revolution. Generalised integrals. Estimation of sums. The formulas of Taylor and Maclaurin. The Maclaurin expansion of elementary functions. Applications, e.g. estimation of errors and finding limits. Ordinary differential equations. Equations of the first order: linear and separable equations. Integral equations. Linear equations of higher order with constant coefficients. Applications will be given of mathematical models from various fields. Series.


Course literature:
Forsling, G. and Neymark, N.: Matematisk analys, en variabel. Liber.


Examination: 

Written examination 
6 ECTS




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

