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MAU11E01 Engineering mathematics I

Module Code MAU11E01
Module Title Engineering mathematics I
Semester taught Semester 1
ECTS Credits 5
Module Lecturer Prof. Patrick Fritzsch
Module Prerequisites N/A

Assessment Details

  • This module is examined in a 2-hour examination at the end of Semester 1.
  • Continuous assessment contributes 20% towards the overall mark.
  • Re-assessment, if needed, consists of 100% exam.

Contact Hours

11 weeks of teaching with 3 lectures and 1 tutorial per week.

Learning Outcomes

On successful completion of this module, students will be able to

  • Recognise mathematical structures in practical problems, translate these problems into mathematical language, and then analyse them using methods from single-variable calculus.
  • Use derivatives to find the minimum and maximum values of a function of one real variable.
  • Compute definite integrals using a variety of methods of integration.
  • Use integrals to compute various physical quantities such as volume, area and length.

Module Content

  • Functions: domain and range, operations with functions, inverse function, algebraic function, rational and trigonometric functions.
  • Limits and continuity: limits and one-sided limits, limits at infinity, asymptotes, continuity, intermediate value property.
  • Differentiation: definition of derivative, rules of differentiation, implicit differentiation, linear approximation.
  • Applications of derivatives: graphs of functions, optimisation problems, related rates, Newton-Raphson method.
  • Integration: definite integral, Riemann sums, antiderivatives, integration by substitution, fundamental theorem of calculus.
  • Applications of integrals: area between two curves, volumes and areas of solids of revoution, length of a plane curve.

Recommended Reading

  • Calculus: Late transcendentals by Anton, Bivens and Davis.