Algebra and Vector Geometry

5 credits

Syllabus, Bachelor's level, 1MA008

A revised version of the syllabus is available.
Code
1MA008
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1N
Grading system
Pass with distinction, Pass with credit, Pass, Fail
Finalised by
The Faculty Board of Science and Technology, 19 March 2007
Responsible department
Department of Mathematics

Entry requirements

Mathematics D

Learning outcomes

In order to pass the course (grade 3) the student should be able to

  • give an account of important concepts and definitions in the area of the course;

  • exemplify and interpret important concepts in specific cases;

  • formulate important results and theorems covered by the course;

  • describe the main features of the proofs of important theorems;

  • express problems from relevant areas of applications in a mathematical form suitable for further analysis;

  • use the theory, methods and techniques of the course to solve mathematical problems;

  • present mathematical arguments to others.
  • Content

    Elementary functions: polynomials, power, exponential, logarithmic, and trigonometric functions. Rules for powers and logarithms, trigonometric formulas. The solving of simple algebraic equations.

    Complex numbers, real and imaginary part, polar form, geometric interpretation. Second degree equations and binomial equations with complex coefficients.

    Vectors in the plane and in the space, vector algebra, scalar product and vector product. Lines and planes. Distance computations.

    Systems of linear equation: Gaussian elimination, the coefficient matrix and the total matrix.

    Matrices: matrix algebra, the inverse. Determinants of order two and three. Eigenvalues and eigenvectors.

    Instruction

    Lectures and problem solving sessions.

    Assessment

    Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.

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