Syllabus for Several Variable Calculus
A revised version of the syllabus is available.
- 10 credits
- Course code: 1MA016
- Education cycle: First cycle
Main field(s) of study and in-depth level:
- Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Established: 2007-03-19
- Established by: The Faculty Board of Science and Technology
- Revised: 2016-03-15
- Revised by: The Faculty Board of Science and Technology
- Applies from: Autumn 2016
Single Variable Calculus together with Linear Algebra and Geometry I or Algebra and Geometry.
- Responsible department: Department of Mathematics
In order to pass the course (grade 3) the student should be able to
Polar, cylindrical and spherical coordinates. Parameterisations of curves and surfaces.
Level curves and level surfaces. Arc length. Scalar and vector valued functions of several variables. Partial derivatives, differentiability, gradient, direction derivative, differential. Derivatives of higher order. The chain rule. The Jacobian. Taylor's formula. Implicit functions. Optimisation: local and global problems, problems with equality constraints. Multiple integrals, change of variables, improper integrals, applications of multiple integrals: volume, centres of mass, etc. Line integrals and surface integrals of scalar functions and vector fields. Divergence and curl. Identities for grad, div and curl. Green's, Stokes' and Gauss's theorems. Systems of ordinary differential equations. Exact equations. Linear systems, the exponential matrix. Second order equations, variation of parameters.
Lectures, lessons and problem solving sessions.
Written examination at the end of the course, or two written tests each of five credit points. Moreover, compulsory assignments may be given during the course in accordance with instructions at the beginning of the course.
The course cannot be included in passing degree together with the course Several Variable Calculus, limited version.
- Latest syllabus (applies from Autumn 2022, version 2)
- Previous syllabus (applies from Autumn 2022, version 1)
- Previous syllabus (applies from Autumn 2020)
- Previous syllabus (applies from Spring 2019)
- Previous syllabus (applies from Autumn 2016)
- Previous syllabus (applies from Autumn 2010, version 2)
- Previous syllabus (applies from Autumn 2010, version 1)
- Previous syllabus (applies from Autumn 2007, version 2)
- Previous syllabus (applies from Autumn 2007, version 1)
Applies from: Autumn 2016
Some titles may be available electronically through the University library.
Adams, Robert A.;
Calculus : a complete course
8th ed.: Toronto: Pearson, cop. 2013