Course syllabus - Mathematics for Economics and Business

Objectives

The objectives of the course are to give opportunities for students to discover practical power of mathematics in modeling economical and financial situations and to give them both technical skill and clear understanding of concepts.

Learning outcomes

At the end of the course the student is expected to be able to
- find the real and complex roots of linear, polynomial, and rational equations.
- find the real roots of exponential, logarithmic, and basic trigonometric equations.
- solve linear, polynomial, and rational inequalities.
- perform algebraic operations on functions, compose functions and find inverse functions.
- analyse graphs of linear, polynomial, rational, exponential, logarithmic, trigonometric, and piecewise defined functions.
- analyse arithmetic and geometric sequences, geometric series, understand and use mathematical induction, counting principles and the simplest probabilistic models.
- build linear, exponential, and logarithmic models of various economical, financial, business, and environmental phenomena.
- 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

Real numbers. Algebraic expressions. Exponents and radicals. Fractional expressions. Linear and quadratic equations. Equations involving radicals. Inequalities. Coordinate geometry and straight lines.
Functions and their graphs. Direct and inverse variation. Increasing and decreasing functions. Transformations of functions. Extreme values of functions. Combining functions. One-to-one functions and their inverses.
Polynomial functions and their graphs. Dividing polynomials. Real zeroes of polynomials. Complex numbers. Complex zeroes and the fundamental theorem of algebra. Rational functions, their graphs and asymptotes.
Exponential functions. Logarithmic functions and the laws of logarithms. Exponential and logarithmic equations. Modeling with exponential and logarithmic functions.
The unit circle and trigonometric functions of real numbers. Trigonometric graphs. Angle measure and trigonometry of right triangles. Trigonometric functions of angles. The laws of sines and cosines.
Sequences and summation notation. Arithmetic and geometric sequences. Applications to finance: annuities and installment buying. Mathematical induction. The binomial theorem.
Counting principles. Permutations and combinations. Probability and expected value.
Environmental aspects are studied in examples and problems.

Tuition

Lectures, problem solving classes and seminars.

Requirements

Mathematics C or Mathematics 3c.

Examination

PRO2, Project report, 3 credits, concerning learning outcomes 1-8, grades Fail (U) or Pass (G)
TEN2, Examination, 2 credits, written and/or oral examination concerning learning outcomes 1-3, 8, grades Fail (U), Pass (G) or Pass with distinction (VG).
TEN3, Examination, 2.5 credits, written and/or oral examination concerning learning outcomes 4-8, grades Fail (U), 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