BYFE1000 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 mathematical software, which will enable them to perform calculations in a work situation.

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

• determining exact values for the derivative and the anti-derivative using analytical methods
• using the definitions to determine numerical values of derivatives and of definite integrals and assess the accuracy of these values
• using the derivative and higher order derivatives to solve optimization problems, problems of related rates, and to calculate linear approximations and Taylor polynomials
• explaining how definite integrals are used to calculate area, volume and arc length
• solving separable and linear differential equations by means of anti-differentiation
• explaining how direction fields of first order differential equations can be used to visualize the solutions to equations
• finding numerical solutions of initial value problems using Euler's method
• solving equations by the halving method and Newton's method
• performing calculations using complex numbers

Skills 

The student is capable of

• using the derivative to model and analyze dynamic systems
• setting up and calculating quantities which involve integrals
• discussing the ideas underlying some analytical and numerical methods used to solve first-order differential equations
• setting up and solving differential equations for practical problems
• discussing numerical methods for solving equations
• solving equations with complex coefficients and complex solutions

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 relevant to their field of study
• using mathematics to communicate and discuss engineering problems
• evaluating results from numerical calculations and understanding basic numerical algorithms that use assignment, for-loops, if-tests, while-loops and the like, and explain key concepts such as iteration and convergence
• explain that change and change per unit of time can be measured, calculated, summed and included in equations

The teaching is organised as scheduled work sessions. During these sessions, the students practise using the subject matter that is presented. Some of the teaching will comprise problem-solving practice, using numerical software as a natural component. Exercises include discussion and cooperation, and individual practice on assignments. Between the scheduled work sessions, the students must work individually on solving problems 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 result of the exam 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 examiner. The course may be selected for grading by external examiners.