Course syllabus - Calculus II 7.5 credits

Kalkyl II

Course code: MAA305
Valid from: Autumn semester13
Level of education: First cycle
Subject: Mathematics
Main Field(s) of Study: Mathematics/Applied Mathematics,
In-Depth Level: G1F (First cycle, has less than 60 credits in first-cycle course/s as entry requirements),
School: UKK
Ratification date: 2013-02-01


The objective of the course is to give the students clear understanding of concepts of calculus of many variables and technical skill in solving both theoretical exercises and applied economical and financial problems.

Learning outcomes

At the end of the course the student is expected to be able to
- use derivatives, antiderivatives, and integrals of vector-valued functions to calculate velocity, curvature, tangent and normal components of acceleration of the moving body in two and three dimensions.
- calculate limits of functions of several variables and finds sets of continuity.
- use partial and directional derivatives to find tangent planes, extrema of functions of several variables, and to solve ordinary and constrained optimization problems in economics and finance.
- calculate double and triple integrals by Fubini theorem and by the change of variables in different coordinate systems.
- use double and triple integrals for calculating areas and volumes.
- build mathematical models of various economical, financial, business, and environmental phenomena, and use techniques of calculus of several variables for solving applied problems.
- explain, in both oral and written form, mathematical arguments and solutions to problems that are solved in the process of achieving knowledge and abilities specified above

Course content

The calculus of vector-valued functions. Motion in space. Curvature, velocity and acceleration. Parametric surfaces. Limits and continuity of functions of several variables. Partial derivatives. Tangent planes and linear approximations. The chain rule. The gradient and directional derivatives. Extrema of functions of several variables. Constrained optimization and Lagrange multipliers. Applied optimization problems in economics and finance.
Double and triple integrals. Direct calculation of multiple integrals by Fubini theorem. Change of variables in multiple integrals. Applications to areas and volumes.
Environmental aspects are studied in examples and problems.

Teaching methods

Lectures, problem solving classes and seminars.

Specific entry requirements

Algebra 7,5 hp and Calculus I 7,5 credits or equivalent and a TOEFL test result, minimum score 173 (CBT), 500 (PBT) or 61 (iBT) or an IELTS test result with an overall band score of minimum 5,0 and no band score below 4,5. The English test is COMPULSORY for all applicants except citizens of Australia, Canada, Ireland, New Zealand, United Kingdom and USA.


Project (PRO1), 3 credits, marks Pass (G)
Examination (TEN1), 4.5 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDH regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2016/0601). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Rules and regulations for examinations


Three-grade scale

Enviromental aspects

The environmental aspects of the course have been considered in the learning objectives.

Course literature is preliminary until 3 weeks before the course starts. Literature may be valid over several terms.

Valid from: Autumn semester13

Decision date: 2013-07-18

Last update: 2013-07-18


Stewart, James;

Calculus : early transcendentals

ISBN: 0-538-49887-0 (hbk) LIBRIS-ID: 12448003

XXVIII, 1170, 146 p.