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MAU11S01 Mathematics for scientists I

Module Code MAU11S01
Module Title Mathematics for scientists I
Semester taught Semester 1
ECTS Credits 10
Module Lecturers
 
Prof. Kyle Parfrey
Prof. Kirk Soodhalter
Module Prerequisites N/A

Assessment Details

  • This module is examined in a 3-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 6 lectures and 2 tutorials per week.

Learning Outcomes

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

  • Explain basic ideas relating to functions of a single variable and their graphs such as limits, continuity, invertibility and differentiability.
  • State basic properties and compute limits, derivatives and integrals for a wide range of functions including rational and transcendental functions.
  • Use derivatives to find the minimum and maximum values of a function of one real variable.
  • Use various techniques of integration to compute definite and indefinite integrals.
  • Apply techniques from calculus to a variety of applied problems.
  • Manipulate vectors to perform alegebraic operations such as dot products and orthogonal projections, and apply vector concepts to manipulate lines and planes in Rn.
  • Use Gaussian elimination techniques to solve systems of linear equations, find inverses of matrices, and solve problems that can be reduced to systems of linear equations.
  • Manipulate matrices algebraically and use concepts related to matrices such as invertibility, symmetry, triangularity, nilpotence.
  • Manipulate numbers in different number systems.
  • Use computer algebra and spreadsheets for elementary applications.

Module Content

  • Calculus part: functions, limits and continuity, derivatives, graphs of functions, optimisation problems, integration, exponential functions, logarithmic functions, inverse trigonometric functions.
  • Discrete part: vectors, dot product, system of linear equations, Gauss-Jordan elimination, inverse matrix, diagonal and triangular matrices, symmetric matrices, number systems, spreadsheets.

Recommended Reading

  • Calculus: Late transcendentals by Anton, Bivens and Davis.
  • Elementary linear algebra by Anton and Rorres.