Course syllabus adopted 2022-02-07 by Head of Programme (or corresponding).
Overview
- Swedish nameMatematik 1
- CodeMVE335
- Credits7.5 Credits
- OwnerTISJL
- 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 76129
- 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 |
|---|---|---|---|---|---|---|---|
| 0109 Examination 7.5 c Grading: TH | 7.5 c |
|
In programmes
Examiner
- Joakim Becker
- Senior Lecturer, Applied Mathematics and Statistics, 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
None.Aim
This course aims to provide students with the knowledge in mathematics necessary for the understanding of other subjects taken within the Marine engineering programme.Learning outcomes (after completion of the course the student should be able to)
- Apply basic knowledge about arithmetic, algebra, geometry, trigonometry and vectors in other courses in the program.- Perform basic algebraic manipulations in order to solve equations.
- Apply the concepts of congruence and similarity to solve geometrical problems.
- Account for the definitions of the basic trigonometric functions and their relations and apply in problem solving.
- Use the sine- and cosine theorems to determine sides and angels in triangles.
- Use vector algebra to solve geometrical problems in two and three dimensions.
- Use the arithmetic of the complex numbers to find all complex roots of quadratic and binomial and equations.
- Calculate the derivative of polynomials, sine and cosine functions. Account for the geometric meaning of derivatives.
Content
Arithmetic and algebra- Integers, rational and real numbers
- Powers with rational exponent
- Absolute value
- Inequalities
- Polynomials, Pascals triangle
- Rational expressions, expressions containing roots
Equations
- First and second order equations, completing the square
- Linear systems of equations
- Higher degree polynomials
- Factorization of polynomials (using for instance polynomialdivision)
Geometry and trigonometry
- Coordinate systems and analytic geometry
- Trigonometry
- Area of a triangle, laws of sine and cosine
- Trigonometric equations
Vectors
- The concept of a vector
- Addition and subtraction of vectors
- Coordinates of a vector
- Scalar product
- Vector equation of a straight line.
Complex numbers
- Complex number arithmetic
- Complex conjugate, absolute value
- Polar form
- Powers and roots
- Polynomials with complex roots
Derivatives
- Polynomials, sine and cosine functions
- Tangent line, velocity
Organisation
Lectures and exercise.Literature
Kompendium, Mathematical SciencesExamination including compulsory elements
Written examination. Voluntary quizzes may occur during 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.