Syllabus for Several Variable Calculus, Limited Version
Flervariabelanalys, allmän kurs
A revised version of the syllabus is available.
- 5 credits
- Course code: 1MA017
- 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
- Applies from: Autumn 2007
Linear Algebra and Geometry I, single Variable Calculus, Series and Ordinary Differential Equations
- Responsible department: Department of Mathematics
In order to pass the course (grade 3) the student should be able to
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.
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. Taylor's formula. Optimisation: local and global problems, problems with equality constraints. Multiple integrals, change of variables especially polar coordinates, improper integrals, applications of multiple integrals: volume, centres of mass, etc.
Lectures and problem solving sessions.
Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.
- Latest syllabus (applies from Autumn 2022, version 2)
- Previous syllabus (applies from Autumn 2022, version 1)
- Previous syllabus (applies from Spring 2019)
- Previous syllabus (applies from Autumn 2016)
- Previous syllabus (applies from Autumn 2012)
- Previous syllabus (applies from Spring 2008)
- Previous syllabus (applies from Autumn 2007, version 2)
- Previous syllabus (applies from Autumn 2007, version 1)
Applies from: Autumn 2007
Some titles may be available electronically through the University library.
Adams, Robert A.
Calculus : a complete course. p Student solutions manual
6. ed.: Toronto, Ont.: Addison-Wesley, cop. 2006