Course syllabus - Mathematics for Economics, Business and Environmental Engineering

Objectives

The objectives of the course are to give opportunities for students to discover the practical power of mathematics in modeling problems and situations in economics, finance and environmental engineering, and to give them both technical skills and clear understanding of concepts.

Learning outcomes

Upon completion of the course, students are expected to be able to

1. find the real and complex roots of linear, polynomial, rational, exponential, and logarithmic equations
2. solve linear, polynomial, and rational inequalities
3. perform algebraic operations on functions, compose functions and find inverse functions
4. analyse graphs of linear, polynomial, rational, exponential, logarithmic, and piecewise defined functions
5. find real roots of basic trigonometric equations and analyze graphs of trigonometric functions
6. analyse arithmetic and geometric sequences, geometric series, and use and explain mathematical induction, counting principles and the simplest probabilistic models
7. build linear, exponential, and logarithmic models of various economic, financial, business, and environmental phenomena
8. explain, in both oral and written form, mathematical arguments and solutions to problems that are related to the 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. Trigonometric equations
• Sequences and summation notation. Arithmetic and geometric sequences. Mathematical induction. The binomial theorem
• Counting principles. Permutations and combinations. Probability and expected value
• Applications to finance: annuities and installment buying. Environmental aspects are studied in examples and problems

Examination

MUN1, Oral examination, 3 credits, oral examination concerning learning outcomes 1-8, grades Fail (U) or Pass (G).
TEN1, Written examination, 2 credits, written examination concerning learning outcomes 1-3 and 8, grades Fail (U), Pass (G) or Pass with distinction (VG).
TEN2, Written examination, 2.5 credits, written examination concerning learning outcomes 4-8, grades Fail (U), Pass (G) or Pass with distinction (VG).

For Pass with distinction (VG) on the course as a whole, the student must have earned that grade for TEN1 and TEN2.

A student who has a certificate from MDU regarding disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.

Grade

Three-grade scale