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Graduate courses

Departments' graduate courses for PhD-students.

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Course syllabus for

Academic year
MVE013 - Introductory course in mathematics
Inledande matematik
 
Course syllabus adopted 2021-02-05 by Head of Programme (or corresponding)
Owner: TKIEK
6,0 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Main field of study: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish
Application code: 51127
Open for exchange students: No

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0121 Examination 6,0 c Grading: TH   6,0 c   24 Oct 2022 am J,  05 Jan 2023 pm J,  17 Aug 2023 am J

In programs

TKIEK INDUSTRIAL ENGINEERING AND MANAGEMENT, Year 1 (compulsory)

Examiner:

Jan-Alve Svensson

  Go to Course Homepage


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.

Aim

The purpose of the course is to strengthen, deepen and develop the knowledge in secondary school mathematics and to thereby give a solid ground for further studies in mathematics.

Learning outcomes (after completion of the course the student should be able to)

After completed course the students shall

- know the elementary functions, what computational rules applies to them, how they relate, how their graphs can be constructed and be able to use this in solving problems of a fairly complex nature and basic modelling

- understand, be able to define, determine and use various basic properties of real valued functions of one real variable, such as domain/range, increasing/decreasing, even/odd, asymptotes and invertibility.

-  understand and be able to define various types of limits of real valued functions of one real variable, know the basic theorems that applies to them and with judgement be able to use these when solving problems.

- understand and be able to define the concept of a continuous real valued function of one real variable, know the basic theorems that applies to them and use these when solving problems. 

- understand and be able to define the concepts of differentiable real valued function of one real variable and the derivative of such a function, know and be able to prove basic theorems that applies to them and with judgement use these when solving problems.

- be able to solve systems of linear equations with several rows and variables using row operations to echelon form and be able to determine the number of solutions to such systems.

- understand and be able to use the complex numbers and the complex exponential function when solving problems.

- be able to use basic concept with respect to linear analytical geometry in three dimensions to determine equations for planes and lines, the distance between such object and area of parallelograms and volume of prallelepipeds.


Content

Elementary functions and their properties.
- Basic theory of functions.
- Limits, continuity and derivative of real valued functions of one real variable and how these concepts relate.
- Linearization of a function and tangent line and normal to a plane curve.
- Construction of graphs.
- Modelling and optimization of basic nature.
- Handling undetermined expressions in limits.
- Complex numbers and the complex exponential function.
- Systems of linear equations and row operations.
- Linear analytic geometry in three dimensions.

Organisation

Instruction is given in lectures and smaller classes. More detailed information will be given on the course web page before start of the course.

Literature

Literature will be announced on the course web page before start of the course.

Examination including compulsory elements

More detailed information about the examination will be given on the course web page before start of the course.
Examples of assessments are:
- selected exercises are to be presented to the teacher orally or in writing during the course,
- optional assessments during the course that can result in bonus points,
- project work, individually or in group,
- written exam at the end of the course.



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 on educational support due to disability.


Page manager Published: Thu 04 Feb 2021.