F18CE - Multivariable Calculus
Course leader(s):
Aims
The course aims to provide an introduction to the calculus for functions of several variables, which will provide sufficient expertise for use in various later courses. The students will develop their general skills in differentiation, integration and algebraic manipulation as well as seeing seom of the most elementary proofs.
Syllabus
1. LO1-LO2 (1.1 Mastering the fundamental theory and practice of integration in one or more variables)
2. LO3-LO4 (2.1 Understanding how the theory of function in several variabels differes from the one variable case)
3. LO5-LO8 (3.1 Broad variety of applications of calculus in several variables)
Learning outcomes
By the end of the course, students should be able to do the following:
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use Riemann Sums to calculate integrals and understand the fundamental theorem of calculus.
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use Iterated Integrals, or substitutions like polar coordinates to evaluate multiple
integrals, and apply this to calculate the volume of a given 3D region.
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use the definitions of continuity of multivariable functions to assess the continuity of
multivariate functions.
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use the Chain Rule to find partial derivatives for multivariate functions. Use partial derivatives to construct the equation of tangent planes.
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use the Implicit Theorem to prove the existence od a local solution function to a functional
equation.
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use Taylor Expansion to give reasonable approximations of a given multivariable function.
- use the method of Lagrange’s multiplier to solve constrained extremal problems.
- use the definitions of differentiability of multivariable functions to assess the
differentiability of multivariate functions.
Further details
Curriculum explorer: Click here
SCQF Level: 8
Credits: 15
