Module Descriptors

Mathematics

MA286: Analysis I (5 ECTS)

Introduction to functions of several variables and vector valued functions. Topics include partial derivatives, local extrema, curvature, parametric curves, double integrals, Green's Theorem .

Taught in Semester(s) 1. Examined in Semester(s) 1.

Workload: 108 hours (24 Lecture hours, 12 Tutorial hours, 72 Self study hours).

Module Learning Outcomes. On successful completion of this module the learner should be able to:

  1. Sketch or describe graphs of 2-variable functions;
  2. Determine equations of tangent planes;
  3. Find parametrisations of common curves;
  4. Compute arc length and curvature of a curve;
  5. Optimise certain functions; apply method of Lagrange multipliers;
  6. Compute line integrals and double integrals over specified domains;
  7. Know and be able to apply Green's Theorem.

Indicative Content

This course introduces functions of several variables, parametric curves and vector valued functions. The material covered includes:

  1. Functions of several variables: partial derivatives, gradient, level curves, tangent planes, local extrema, Hessian matrix, double integrals.
  2. Parametric curves: parametrisation of line segments and ellipses, derivatives, curvature, normal vector, oculating plane.
  3. Vector valued functions: examples of vector fields, Green's Theorem.

Module Resources

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