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. Chaolun Wu
Module Prerequisites	N/A

11 weeks of teaching with 6 lectures and 2 tutorials per week.

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.

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.