Mathematical Studies
MA212: Calculus II (5 ECTS)
An introduction to the calculus of functions of two variables, and vector valued functions. The topics include: Vectors; Multivariate Calculus; Optimization of elementary multivariate functions; Integration of elementary multivariate functions over polygons.
Taught in Semester(s) 2. Examined in Semester(s) 2.
Workload: 116 hours (24 Lecture hours, 12 Tutorial hours, 80 Self study hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Apply vectors to describe lines and planes in 3-d;
- Solve 3-d geometric problems using vectors;
- Compute partial derivatives of chains of elementary multivariate functions;
- Interpret gradient and tangent planes graphically;
- Classify extreme values of elementary multivariate functions;
- Solve a range of optimization problems modelled by multivariate functions;
- Compute iterated integrals of multivariate functions over polygons;
- Solve problems related to computing volumes in 3-d.
Indicative Content
This course introduces the calculus of functions of two variables, and vector valued functions. The topics include:
- Vectors, scalar product, cross product in $\mathbb{R}^3$, equations of lines and planes in parametric form;
- Functions of several variables, vector-valued functions (in $\mathbb{R}^2$ and $\mathbb{R}^3$), partial derivatives, gradients, tangent planes, the chain rule;
- Maxima and minima of functions of 2 variables, Lagrange multipliers;
- Integration of functions of 2 variables and the computation of volumes.
Module Resources
- James Stewart. "Calculus" (Thomson Brooks/Cole)
- G.B. Thomas & R.I. Finney, "Calculus and Analytic Geometry" (Addison Wesley)
- S.L. Salas, E. Hille & J.T. Anderson, "Calculus, One and Several Variables" (Wiley)
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