EMFE1000 Mathematics 1000 Course description

The course will give the students insight into areas of mathematics that are important when modelling technical and natural science systems and processes. The subjects covered are included in engineering programmes the world over. The subjects are necessary in order to enable engineers to communicate professionally in an efficient and precise manner and to participate in professional discussions. Through the coursework, the students will gain practice in the use of mathematical software, which will enable them to carry out calculations in work situations.

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:

Knowledge

The student is capable of

• explaining the derivative as instantaneous change
• using the definition of the derivative as a point of departure and explaining how to compute an approximate numerical value of the derivative
• calculating exact values of derivatives using analytical methods, and comparing the answers to numerical values
• using the derivative to solve optimisation problems  
• explaining indefinite integrals as antiderivatives
• using numerical and analytical methods to calculate definite integrals
• explaining how the definite integral can be used to calculate parameters such as areas, volumes, area moments, charges and other variables  
• explaining analytical and numerical methods of solving first-order differential equations, for example separation of variables, direction fields and the Euler method
• calculating with complex figures
• solving second-order homogeneous and inhomogeneous differential equations with constant coefficients, both with real and complex solutions of the characteristic equation
• using the intrinsic value method to solve systems of linear first-order differential equations  
• calculating with vectors, matrices and determinants
• transforming augmented matrices for equation systems to reduced row echelon form
• explaining conditions that must be present for it to be possible to find the inverse of a matrix
• explaining the number of solutions in a linear equation system
• describing linear transformations using matrices
• using computer tools to solve problems in linear algebra
• solving equations using, for example, the bi-section method, the secant method and Newton method

Skills

The student is capable of

• using the derivative to model and analyse dynamic systems
• discussing how the idea behind the definition of the definite integral can be used to set up integrals for calculating sizes
• discussing the ideas behind some analytical and numerical methods used to solve differential equations and setting up and solving differential equations that address practical problems in his/her own field
• discussing methods of solving linear equation systems using matrix calculations and numerical methods of solving equations, and setting up and solving equations that adress practical problems in his/her own field

General competance

The student is capable of

• assessing the results of mathematical calculations
• implementing basic numerical algorithms in the course by means of assignment, for loops, if tests, while loops etc. and explaining key concepts such as iteration and convergence
• writing precise explanations and reasons for using procedures, and demonstrating the correct use of mathematical notations
• assessing his/her own academic work and that of other students, and formulating written and oral assessments of these works in an academically correct and precise manner
• translating a practical problem from his/her own field into mathematical form, so that it can be solved analytically or numerically
• using mathematical methods and tools relevant to his/her field
• using mathematics to communicate about engineering issues
• explaining how changes and changes per time unit can be measured, calculated, summed up and incorporated into equations

The teaching is organised as scheduled work sessions. During the work sessions, the students practise using the material with which they are presented. Exercises include group discussions, individual practice in solving assignments, formulating and solving problems and assessing one's own and other's answers.

The students shall learn how to assess their own and other's academic work and to formulate assessments of them in such a way that the assessment can serve as advice on further studies. These practical exercises will take place in the scheduled part of the work sessions. Students will therefore carry out weekly assessments of exercises set for the week. Information about how the weekly assessment will take place will be given in the lectures.

The students are required to complete exercises between work sessions. The proposed exercises will be directly linked to the course goals. Self-assessment of answers will give students insight into whether they have achieved the goals.

There are no mandatory coursework requirements in this course.

Individual written exam, 3 hours

The result of the exam can be appealed.

All printed and written aids. Calculator. MATLAB if feasible.

A grade scale with grades from A to E for pass (with A being the highest grade and E being the lowest pass grade) and F for fail is used for the final assessment.

One internal examiner. External examiners are used regularly.

The course is equivalent (overlap of 10 credits) to: TRFE1000, BYFE1000, ELFE1000, DAFE1000, KJFE1000, MAFE1000, MEK1000, FO010A and FO010D.

Under the rule that students may register for an exam three times, attempts in equivalent courses also count.