Syllabus for Geometry and Analysis III
Geometri och analys III
A revised version of the syllabus is available.
- 5 credits
- Course code: 1MA212
- Education cycle: First cycle
Main field(s) of study and in-depth level:
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:
- 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
- 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
- Revised: 2013-04-29
- Revised by: The Faculty Board of Science and Technology
- Applies from: Autumn 2013
Geometry and Calculus II.
- Responsible department: Department of Mathematics
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.
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.
Lessons in large and small groups.
Written examination at the end of the course.
The course may not be included in the same higher education qualification as Calculus of several variables.
- Latest syllabus (applies from Autumn 2022)
- Previous syllabus (applies from Autumn 2019)
- Previous syllabus (applies from Autumn 2013)
- Previous syllabus (applies from Autumn 2012)
Applies from: Autumn 2013
Some titles may be available electronically through the University library.
Adams, Robert A.;
Calculus : a complete course
8th ed.: Toronto: Pearson, cop. 2013