Course Convenor:Dr A Mazumdar
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CMod descriptionback to top
This module covers basic algebra and functions,
leading to the practice and application of differentiation. Topics covered
include equations and inequalities, dependent and independent variables; graphs
and curve sketching; polynomial functions, inverse functions, and functions of
functions; trigonometric and exponential functions. Derivatives of functions,
methods of differentiation, products and chain rule.
Curriculum Design: Outline Syllabusback to top
Symbolic manipulation. Distinction between arithmetic of numbers and algebra of symbols.
Symbols representing real numbers, their powers and inequalities.
Cartesian coordinates, real valued functions and their graphs in 2D and 3D
Angular measures (radians and degrees) and 2D and 3D polar coordinates.
Periodic functions. Trigonometric functions.
Graphical location of real roots of quadratic and cubic equations
Graphs of a xn for constant a > 0.
Exponential function and notion of limits. Natural logarithm. Hyperbolic functions.
Slope of a graph. The derivative of a real valued function of one variable.
Rates of change and derivative of xn.
Derivatives of sums and multiplication by constants
Derivatives of exponentials, logs and trig functions
Higher order derivatives
Product and chain rule
Logarithmic, parametric and implicit differentiation
Determination of extrema of graphs and curve sketching. Extraction of small changes.
Based on FLAP modules
Curriculum Design: Pre-requisites/Co-requisites/Exclusionsback to top
Part I Entry Requirements
A level Maths
Educational Aims: Subject Specific: Knowledge, Understanding and Skillsback to top
This module aims to
- to provide a sound basis knowledge of algebra and vectors. To give a sound understanding of differentiation and to apply these to modelling physical systems.
Learning Outcomes: Subject Specific: Knowledge, Understanding and Skillsback to top
On completion of the module, students should be able to:
- recognise basic mathematical functions used in the description of physical phenomena, and their graphical representation
- solve elementary equations involved in mathematical modelling
- understand the fundamental principle of differentiation, and its relation to the slope of a graph
- differentiate basic functions directly, and to use systematic techniques for combinations of functions
- apply their knowledge to modelling real phenomena and situations.
Curriculum Design: Select Bibliographyback to top
(E) FLAP mathematics package.
(E) D W Jordan & P Smith Mathematical Techniques, OUP