Course Convenor:Dr MH Denton
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CMod descriptionback to top
Several important topics are considered in this module,
including series and their summation, the binomial theories, infinite series,
Taylor expansion. The use of matrices to describe physical phenomena and solve
mathematical problems is described. Basic ideas in probability are introduced,
permutations and combinations, distributions expectation and variance, and the
relevance to data analysis.
Curriculum Design: Outline Syllabusback to top
Series and their formal representation, summation sign. Convergence of infinite sums. Geometric series and summation of infinite geometric series. Binomial expansion and binomial coefficients Taylor expansion and Taylor polynomials. Series representations of trigonometric and exponential functions.
Differential equations and their role in physics. Separable first order differential equations. Second order differential equations for conservative systems and the method of integrating multiplier. Example of a harmonic oscillator problem.
Linear ordinary differential equations. General and particular solutions of ODE. Properties of the function exp(Dx). The method of auxiliary equation for solving homogeneous ODE's. ODE's describing driven systems, harmonic force and the phenomenon of resonance.
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
To develop a knowledge of series and functions
To introduce ordinary differential equations (first and second order) and train in methods of their solution.
Learning Outcomes: Subject Specific: Knowledge, Understanding and Skillsback to top
On completion of the module, students should be able to :
- appreciate the representation of functions by series and approximations, in particular binomial and Taylor expansions
- display a familiarity with differential equations and their use in physics
- to solve separable 1st order differential equations and linear 2nd order differential equations
Curriculum Design: Select Bibliographyback to top
(E) FLAP mathematics package.
(E) D W Jordan & P Smith Mathematical Techniques, OUP