Course syllabus - Calculus I

Objectives

The objective of the course is to give the students clear understanding of concepts of one variable calculus and technical skills 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:

- calculate limits of functions and find intervals of continuity
- differentiate elementary functions
- find antiderivatives and calculate definite integrals by substitution and by parts
- use trigonometric techniques of integration and integrate rational functions using partial fractions
- solve simple first-order differential equations and systems of differential equations
- test infinite series for convergence and absolute convergence, represent functions as power and Taylor series
- build mathematical models of various economical, financial, business, and environmental phenomena, and use techniques of one variable calculus 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

Limits; definition.and calculation. Continuity
The derivative; definition, the power, product, quotient, and chain rules, implicit differentiation. The Mean Value Theorem
Applications of differentiation; tangent lines, velocity, linear approximation, extrema, concavity, curve sketching, optimization, related rates and rates of change in economics and finance
Antiderivatives. Area and the definite integral. The Fundamental Theorem of Calculus. Integration by substitution and by parts. Trigonometric techniques of integration. Integration of rational functions using partial fractions. Improper integrals
Applications of the definite integral. Arc length, areas, volumes, consumers and producers surplus, probability
Modeling with differential equations. Separable equations and systems. Applications to growth and decay problems and compound interest.
Sequences of real numbers. Infinite series. The integral, comparison, and ratio tests. Alternating series and absolute convergence. Power and Taylor series
Environmental aspects are studied in examples and problems

Tuition

Lectures, folder sessions and seminars.

Requirements

Mathematics D or Mathematics 3c.

Examination

Project (PRO1), 2.5 credits, marks Pass (G)
Seminar (SEM1), 2 credits, marks Pass (G)
Written examination (TEN1), 3 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDU 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 (2020/1655). 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.

Grade

Pass with distinction, Pass, Fail