Syllabus for Geometry and Analysis III

Geometri och analys III

A revised version of the syllabus is available.

Syllabus

  • 5 credits
  • Course code: 1MA212
  • 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: 2012-03-08
  • Established by: The Faculty Board of Science and Technology
  • Applies from: week 30, 2012
  • Entry requirements: Geometry and calculus II
  • Responsible department: Department of Mathematics

Learning outcomes

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

  • account for basic concepts and theorems within the vector calculus;
  • demonstrate basic calculational ability concerning the concepts in the previous point such as to be able to calculate line and surface integrals and manipulate formulae involving the nabla operator;
  • account for basic concepts in the theory of infinite series;
  • demonstrate basic calculational ability concerning the concepts in the previous point such as to be able to use convergence criteria and handle power series.

Content

Vector fields. Cartesian and curvilinear coordinates. The nabla operator. Divergence and rotation. Line integrals. Conservative fields. Divergence free and rotation free fields. Scalar and vector potentials. Surface integrals. Green's, Gauss' and Stokes' theorems. The Laplace operator. The equations of Laplace and Poisson. Physical interpretations. Complex number sequences and series. Convergence. Comparison criteria. The integral criterion. The quotient criterion. Absolute and conditional convergence. Power series and their properties. Applications.

Instruction

Lessons in large and small groups.

Assessment

Written examination at the end of the course possibly combined with continuous examination according to instructions delivered at the beginning of the course.

Other directives

The course may not be included in the same higher education qualification as Calculus of several variables.

Syllabus Revisions

Reading list

Reading list

Applies from: week 30, 2012

Some titles may be available electronically through the University library.

  • Adams, Robert A.; Essex, Christopher. Calculus : a complete course

    7th ed.: Toronto: Pearson Addison Wesley, c2009

    Find in the library

    Mandatory