Course syllabus for Mathematics 2

The course syllabus contains changes
See changes

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameMatematik 2
  • CodeMVE340
  • 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 76141
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0109 Examination 7.5 c
Grading: TH		0 c0 c0 c7.5 c0 c0 c
  • 31 Maj 2024 am L
  • 06 Okt 2023 am L
  • 19 Aug 2024 pm L

In programmes

Examiner

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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

Knowledge and skills corresponding to the learning outcomes of the following courses:

MVE335 Mathematics 1

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)

To pass the course, you should be able to:

- Sketch the graph of a function from a table of values.
- Determine the domain and the range of a given function .
- Determine the composition of two functions.
- Using linear interpolation to calculate the approximate value of the function .
- Sketch the graph of polynomials of degree one and two, power functions, exponential and logarithmic functions , and trigonometric functions .
- Calculate the limit of a function from the limit rules and standard limits .
- Calculate the limit of the rational function as $ x goes to infty $.
- Calculate the zero of the function (root to the equation) using bisection method.
- Differentiate simple functions using derivation rules .
- Determine the equation of the tangent and normal at a point on a function graph .
- Determine if a function is increasing / decreasing with the help of the derivative.
- Determine largest / smallest value of a function on a closed interval by using the derivative zeros when the derivative and its zeros are simple to calculate.
- Sketch the graph of a function using the derivative as the derivative and its zeros are simple to calculate.
- Using Newton's method for the equation f(x) = 0 when the derivative is easy to calculate.
- Setting up an integral for calculating the area .
- Setting up an integral for calculating the average value of a function on an interval.
- Calculate the integral when the primitive function is easy to determine .
- Calculate the integral using the proposed partial integration .
- Calculate the integral using the proposed substitution.
- Determine whether a given function is the solution to a given differential equation.
- Solve a homogeneous , linear first order differential equation with constant coefficients ay'(t) + by(t) = 0 - Solving homogeneous linear second-order differential equation with constant coefficients ay¿(t) + by¿(t)+cy(t) = 0.
- Calculate the vector product of two vectors in space.
- Determine a vector perpendicular to two given vectors in space.
- Determine the equation of a line through the given point and given direction vector.
- Determine the equation of a line through two given points. - Determine the equation of a plane through the given point and a given normal vector .
- Determine the equation of the plane through three given points.
- Determine the intersection between a line and a plane.
- Determine the intersection points between two or more planes.
- Solve linear least squares problems.
- Solve systems of linear equations and linear least squares problems using Matlab.

In order to obtain higher grades must also be able to :

- Determine if a function is injective , and if so, determine the inverse of the function .
- Calculate limits with the help of the squeeze theorem and when it is necessary to rewrite the expression.
- Determine asymptotes to the curve y = f(x) , where f is a rational function .
- Determine whether a given function is continuous.
- Differentiate more complicated function using derivation rules .
- Finding maxima and minima of a function in more complex cases .
- Solve more complex problems using derivatives .
- Determine by yourself which integration method that is appropriate.
- Set up a differential equation based on a physical / technical situation .
- Solving a linear second-order differential equation with constant coefficients my¿(t) + cy¿(t) + ky(t) = p cos(rt) + q sin(rt).
- Solve a separable differential equation f(y(t))y'(t) = g(t). - Using vectors in problem solving.
- Calculate the area and volume using vectors.
- Determine the distance between point and line .
- Determine the intersection of two or more lines in space.
- Determine the distance between points and planes.

Content

- The concept of function and the elementary functions.
- Limits and continuity.
- Derivative with applications to construction of curves and max / min problems.
- Numerical solution of equations and Newton's method.
- Integrals, integration by parts, substitution of variables.
- Numerical integration.
- Ordinary differential equations: first and second order.
- System of Equations.
- Determinants and the vector product.
- Lines and planes in space.
- Least squares method.
- Matlab.

Organisation

Lectures and exercises.

Literature

Compendium, Dept. of Mathematical Sciences, 2013.
See also course home-page.

Examination including compulsory elements

Written exam.

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.

The course syllabus contains changes

  • Changes to course:
    • 2024-01-30: Litterature Litterature changed by Examinator
      Modern differential- och integralkalkyl not available