Syllabus for Linear Algebra II

Linjär algebra II

A revised version of the syllabus is available.

Syllabus

  • 5 credits
  • Course code: 1MA024
  • Education cycle: First cycle
  • Main field(s) of study and in-depth level: Mathematics G1F

    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: 2007-03-15
  • Established by: The Faculty Board of Science and Technology
  • Applies from: week 27, 2007
  • Entry requirements: Linear Algebra and Geometry I, Single Variable Calculus
  • Responsible department: Department of Mathematics

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.

    Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.

    Content

    Linear spaces: subspaces, linear span, linear dependence, basis, dimension, change of bases. Matrices: rank, column space and row space. Determinants of arbitrary order. Linear transformations: their matrix and its dependence on the bases, composition and inverse, range and nullspace, the dimension theorem. Euclidean spaces: inner product, the Cauchy-Schwarz inequality, orthogonality, ON-basis, orthogonalisation, orthogonal projection, isometry. Quadratic forms: diagonalisation, Sylvester's law of inertia. Spectral theory: eigenvalues, eigenvectors, eigenspaces, characteristic polynomial, diagonalisability, the spectral theorem, second degree surfaces. Systems of linear ordinary differential equations.

    Instruction

    Lectures and problem solving sessions.

    Assessment

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

  • Reading list

    Reading list

    Applies from: week 27, 2007

    • Anton, Howard; Rorres, Chris Elementary linear algebra : applications version

      9. ed.: Hoboken: Wiley, cop. 2005

      Find in the library