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SF1609 Mathematics II 9.0 credits

Matematik II

Basic course in differential calculus of several variables and introductory linear algebra.

  • Educational level

    First cycle

  • Academic level (A-D)

    A

  • Subject area

    Mathematics
    Techonology

  • Grade scale

    A, B, C, D, E, FX, F

At present this course is not scheduled to be offered.

Learning outcomes

After finished course a student should be able to

  • recognize and use the basic concepts of linear algebra: vectors and their operations, straight lines and planes, linear dependence and independence, base vectors, linear transformations, matrices and determinants, eigenvalues and eigenvectors, quadratic forms.
  • recognize and use the basic concepts of differential multivariable calculus: partial derivative, differentiability, differential, gradient, directional derivative, functional matrix and functional determinant.
  • understand and explain the interaction between linear algebra and differential calculus, e.g. in connection with linearization of functions or analysis of the stationary points of multivariable functions.
  • More precisely, after finished course the student should be able to:
  • solve geometric problems involving points, lines and planes by means of dot and cross product.
  • apply chain rules on partial derivations and decide whether a function satisfies a certain partial differential equation.

Course main content

Systems of linear equations and matrices; determinants, Cramerís rule, geometric interpretation of determinants. Vectors and geometry in two and three dimensions, dot product, cross product. Matrices as linear transformations from Rn to Rm. The least-squares method. Quadratic forms and diagonalization. Functions of several variables; partial derivatives, gradient, chain rule. Differentials. Curves and their parametrization in R2 and R3. Extreme value problems, the method of Lagrangeís multipliers. Implicit functions. Taylor approximation.

Eligibility

Mathematics I (SF1608) or equivalent.

Literature

Andersson Lennart m.fl./Linjär algebra med geometri.

Persson&Böiers/Analys i flera variabler.

LTH/Övningar i analys i flera variabler.

Examination

  • TEN1 - Examination, 9.0 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

One written exam (TEN1; 9 hp).

Offered by

SCI/Mathematics

Examiner

Version

Course plan valid from: Autumn 08.
Examination information valid from: Autumn 07.