Course syllabus adopted 2025-02-22 by Head of Programme (or corresponding).
Overview
- Swedish nameAnalys i en variabel
- CodeMVE750
- Credits7.5 Credits
- OwnerTKTKE
- Education cycleFirst-cycle
- Main field of studyMathematics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 43115
- Maximum participants235
- Open for exchange studentsNo
- Only students with the course round in the programme overview.
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0125 Examination 7.5 c Grading: TH | 7.5 c |
In programmes
Examiner
Stefan Lemurell- Associate Professor, Algebra and Geometry, Mathematical Sciences
Eligibility
General entry requirements for bachelor's level (first cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
The same as for the programme that owns the course.Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
Prerequisites equivalent to specific entry requirements.Aim
The aim of the course, together with the other mathematics courses, is to provide a general knowledge of mathematics that is as useful as possible in further studies and technical careers. The course should provide, in a logical and coherent way, the knowledge of mathematical analysis in one variable necessary for the other courses in the Engineering Chemistry and Bioengineering programs.Learning outcomes (after completion of the course the student should be able to)
- handle elementary functions.
- explain the concepts of limit, derivative and integral and their relationship
- calculate limits, derivatives and integrals
- determine extreme values
- approximate functions with polynomials and represent them as power series.
- combine knowledge of different concepts in practical problem solving
Content
- Theory of elementary functions: trigonometric functions, inverse trigonometric functions, logarithms, exponential functions serving as main examples for all constructions in calculus
- The concepts of limit and continuity, limit calculations, investigation of functions
- The concept of derivative, calculation of derivative of functions using the basic rules of calculus
- The concepts of stationary point, local and absolute maximum and minimum and their criteria and application to simple functions
- Concept of inverse function, calculation of inverse functions and their derivative
- Taylor polynomials for elementary functions; use of Taylor expansion to calculate limits
- Scalar, cross, and triple product of vectors and applications to geometric problems
- Determining geometric properties of vectors, points, lines, and planes in space using equations for these geometric objects and vice versa - writing equations for lines and planes given by geometric conditions
- Applying approximate methods with iterations such as interval bisection and Newton's method to solve non-linear equations.
- Primitive functions
- Riemann integrals and methods of integration, integration of rational functions and some other functions
- Generalised integrals
- Applications to integrals: area, volume, curve length, area and volume of rotation bodies.
Organisation
Lectures and exercise sessions.Literature
To be indicated on the course website.Examination including compulsory elements
Written examination. Optional tests during the course that can give bonus points may occur.The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.