DAFE1000 Mathematics 1000 Course description

Through the work in this course, the students will gain insight into areas of mathematics that are important to the modelling of technical and natural science systems and processes. The topics covered are included in engineering programmes the world over. The topics are necessary in order to enable engineers to communicate professionally in an efficient and precise manner and to participate in professional discussions. Students will practise using, and to some extent also develop, mathematical software in the work on the course, which will enable to perform calculations in a work situation. Such implementations are exclusively motivated by numerical problems solving and understanding mathematical concepts.

No requirements over and above the admission requirements.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence.

Skills

The student is capable of

• using the derivative to model and analyse dynamical systems.
• explain how the integral may be used in order to calculate quantities such as areas, volumes and work.
• discussing numerical methods for solving equations.
• discussing methods for solving systems of linear equations by means of matrix calculations.
• accounting for the number of solutions a system of linear equations has.
• solving equations which involve complex numbers.
• discussing the ideas behind some analytical and numerical methods which are used for solving first order differential equations.
• explaining key concepts such as iteration and convergence in relation to numerical methods.

Knowledge

This requires that the student is capable of

• determining exact values for the derivative and the antiderivative using analytical methods.
• using the definitions as a point of departure for computing approximate numerical values of the derivative and the definite integral and assessing the accuracy of these values.
• using the derivative to solve optimization problems.
• calculating sums and products of matrices, inverting matrices and determining determinants.
• performing calculations with complex numbers.
• solving equations by implementing numerical methods such as the bi-section method and Newton method.
• using Taylor-polynomials for approximating functions and determining the error for certain numerical methods.
• solving separable and linear differential equations using anti-differentiation.
• finding numerical solutions to initial value problems using the Euler method
• implementing basic numerical algorithms by means of assignment, for and while loops, if tests and similar.

General competence:

The student is capable of

• transferring a practical problem into a mathematical formulation, so that it can be solved, either analytically or numerically.
• writing precise explanations and motivations for using procedures, and demonstrating the correct use of mathematical notation.
• using mathematical methods and tools in numerical problems solving.
• using mathematics in communicating engineering issues.
• assessing the results of mathematical calculations.

The teaching is organised as scheduled work sessions. During the work sessions, the students shall practise the subject matter that is presented. Some of the teaching will comprise problem-solving practice, where implementing numerical algorithms is a natural component. The content of the practice includes discussions and cooperation, and individual practice on assignments. Between the scheduled work sessions, the students must work individually on calculating exercises and studying the syllabus.

The following coursework is compulsory and must be approved before the student can sit the exam:

• at least 3 individual written assignments in which the use of software in an integral part.

Individual written exam, 3 hours.

The exam result can be appealed.

All written an printed aids are allowed.Handheld calculator that cannot be used for wireless communication or to perform symbolic calculations. Random checks may be carried out.

Grade scale A-F.

One internal examiner. External examiners are used regularly.