Course syllabus - Applied mathematics for environmental engineers

Objectives

The objective of the course is to give the student the opportunity to acquire mathematical, numerical and statistical knowledge and skills that are directly applicable in environmental engineering.

Learning outcomes

Upon completion of the course, the student is expected to be able to
1. demonstrate adequate skills at managing basic mathematical concepts such as elementary functions, differentiation, integration, differential equations, graph plotting, optimization, and linear systems of equations
2. demonstrate adequate skills at using numerical methods for estimation of errors and computer assisted solution of non-linear equations
3. give an account of and apply basic concepts in probability theory, such as event, event space, probability, independent events, conditional probability, and probability laws
4. give an account of and apply basic properties of random one-dimensional variables and functions of such variables
5. give an account of and apply measures of location, dispersion and dependence for some simple distributions
6. carry out point estimation, interval estimation, hypothesis testing and linear regression
7. demonstrate familiarity with some examples of how the mathematical, numerical and statistical methods that are discussed in the course can be applied in environmental engineering or similar fields

Course content

- Elementary functions and their derivatives and integrals
- Graph plotting and interpretation of graphs of functions; change of coordinate systems
- Solution of simple optimization problems
- Examples of solution of simple differential equations, such as first-order linear differential equations and the logistic differential equation
- Basic concepts in numerical analysis, such as error, error estimation and significant digits
- Simple iterative methods for solution of non-linear equations, such as the bisection method and the secant method
- Probability theory: Basic concepts. Discrete and continuous random variables. Functions of random variables. One-dimensional distributions. Measures of location, dispersion and dependence. The uniform distribution. The binomial distribution. The normal distribution
- Statistical theory: Point estimation. Least squares and maximum likelihood methods. Interval estimation. Hypothesis testing. Linear regression
- Discussion of how mathematical tools can be applied in environmental engineering and related fields, in particular with respect to sustainable development

Specific requirements

At least 20 credits in mathematics or at least 45 credits in engineering or natural sciences including at least 7.5 credits in mathematics. In addition, English 6/English B is required.

Examination

INL1, Written assignment, 1.5 credits, concerning learning outcomes 1 and 7, grades Fail (U) or Pass (G).
INL2, Written assignment, 1.5 credits, concerning learning outcomes 2 and 7, grades Fail (U) or Pass (G).
INL3, Written assignment, 4.5 credits, concerning learning outcomes 3-7, grades Excellent (A), Very good (B), Good (C), Satisfactory (D), Sufficient (E), Insufficient, complementary work possible (Fx), Insufficient (F).

The grade on the course as a whole is given by the grade for INL3.

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

Excellent, Very good, Good, Satisfactory, Sufficient, Insufficient, complementary work possible, Insufficient

Interim Regulations and Other Regulations

This course has overlapping content with other basic courses in the areas of calculus, probability theory and numerical methods, which may affect the possibilities of fulfilling degree requirements. Contact the study advisor for more information.