Syllabus for Algebra and Vector Geometry

Algebra och vektorgeometri

Syllabus

  • 5 credits
  • Course code: 1MA008
  • Education cycle: First cycle
  • Main field(s) of study and in-depth level: Mathematics G1N

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle

    • G1N: has only upper-secondary level entry requirements
    • G1F: has less than 60 credits in first-cycle course/s as entry requirements
    • G1E: contains specially designed degree project for Higher Education Diploma
    • G2F: has at least 60 credits in first-cycle course/s as entry requirements
    • G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    • GXX: in-depth level of the course cannot be classified

    Second cycle

    • A1N: has only first-cycle course/s as entry requirements
    • A1F: has second-cycle course/s as entry requirements
    • A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    • A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    • AXX: in-depth level of the course cannot be classified

  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2007-03-19
  • Established by:
  • Revised: 2021-03-04
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: Autumn 2022
  • Entry requirements: General entry requirements and Physics 2, Chemistry 1, Mathematics 3c/Mathematics D
  • Responsible department: Department of Mathematics

Learning outcomes

On completion of the course, the student should be able to:

  • solve simple algebraic equations and use power and logarithm laws;
  • count with complex numbers;
  • define and count with the elementary functions;
  • use vectors and vector calculations;
  • solve systems of linear equations and count with matrices.

Content

Elementary functions: polynomials, rational functions, 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 (4 credits) and assignments during the course (1 credit).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Reading list

Reading list

Applies from: Autumn 2022

Some titles may be available electronically through the University library.

For course instances given in Uppsala in Swedish

  • Rodhe, Staffan; Sollervall, Håkan Matematik för ingenjörer

    6. uppl.: Lund: Studentlitteratur, 2010

    Find in the library

    Mandatory

For course instances given in Visby in English

  • Croft, Tony Engineering mathematics : a foundation for electronic, electrical, communications and systems engineers

    Fifth edition.: Harlow, England: Pearson, 2017

    Find in the library

    Mandatory