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.

No requirements over and above the admission requirements.

After completing this course, the student has the following learning outcomes, defined as knowledge, skills and general competence:

Knowledge

The student can:

• explain what a thermodynamic system is and can determine whether a system is isolated, closed or open.
• explain what is meant by work, heat and internal energy in thermodynamics.
• explain the content of the 1st and 2nd Law of Thermodynamics.
• explain the difference between reversible and irreversible processes.
• explain what entropy is a measure of.
• utilize the properties of state functions (eg enthalpy, entropy and inner energy) in calculations.
• explain what is meant by a thermal power machine in thermodynamics and know the examples of heat engine from daily life.
• explain the behavior of heat pumps down to component level.
• explain the term humidity, including specific and absolute humidity.
• reproduce and explain the contents of the phase diagram.
• explain how the Mollier diagram is used.
• describe phase transitions.

Skills

The student is capable of:

• calculate the energy transferred between the system and the environment in reversible and irreversible processes, e.g. in terms of work and heat.
• use equation of state in calculations
• calculate entropy differences for reversible and irreversible processes, e.g. in a heat pump.
• calculate the efficiency of heat engines, power factor for cooling machines and COP for heat pumps.
• calculate relative and absolute humidity.
• determine the dew point when calculating and using the Mollier chart.​​

General competence

The student is capable of:

• identify issues where thermodynamics can be used. evaluate the quality of their own and others' work within thermodynamics.
• communicating in an academically correct and precise manner

Lectures and exercises. During the lectures, the subject matter is presented, and the students will participate in problem solving, discussions and collaboration.

The content of the exercises includes practice in problem solving, individually or in collaboration with others. The subject teacher is present and provides help and guidance.

There are no coursework requirements in this course.

Individual written exam, 3 hours.

The exam result can be appealed.

A resit or rescheduled exam may take the form of an oral exam. If oral exams are used for resit and rescheduled exams, the result cannot be appealed.

All printed and written aids, as well as a calculator. MATLAB if possible technically