Several Variable Calculus
Syllabus, Bachelor's level, 1MA016
- Code
- 1MA016
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G1F
- Grading system
- Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
- Finalised by
- The Faculty Board of Science and Technology, 11 May 2010
- Responsible department
- Department of Mathematics
Entry requirements
Linear Algebra and Geometry I, Single Variable Calculus, Series and Ordinary Differential Equations
Learning outcomes
In order to pass the course (grade 3) the student should
Content
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. Sequences of functions, function series, uniform convergence. Uniform continuity.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination at the middle and the end of the course. Moreover, compulsory assignments may be given during the course.
Reading list
- Reading list valid from Autumn 2025
- Reading list valid from Autumn 2022
- Reading list valid from Spring 2022
- Reading list valid from Autumn 2021
- Reading list valid from Autumn 2020
- Reading list valid from Autumn 2019
- Reading list valid from Spring 2019
- Reading list valid from Autumn 2016
- Reading list valid from Autumn 2010, version 3
- Reading list valid from Autumn 2010, version 2
- Reading list valid from Autumn 2010, version 1
- Reading list valid from Autumn 2009
- Reading list valid from Autumn 2007, version 2
- Reading list valid from Autumn 2007, version 1
- Reading list valid from Spring 2005