XX10052/118: Mathematics & Computing 2
(8W 1.1) and Thursday (8W 1.1)
in weeks 29-33.
Lecturer: Simon Shaw; s.c.shaw at maths.bath.ac.uk
Requisites: Before taking this unit you must take ME10196
Aims & Learning Objectives:
To extend the students previous knowledge of mathematics and provide the basic core of mathematical tools required throughout the engineering course. To introduce the student to statistical techniques used for data analysis. To give the student a sound basic knowledge of computer programming in C++ upon which they can subsequently build. After taking this unit the student should be able to: Employ elementary numerical methods for the solution of algebraic equations and integration. Set up and solve differential equations of typical engineering problems by analytical and numerical methods . Apply rules of partial differentiation to small increment and change of variable problems for functions of several variables. Solve simultaneous linear equations. Find eigenvalues and eigenvectors of matrices. Interpret experimental data, carry out elementary statistical analysis and calculate best least-squares fit to data. Write well structured simple programs in C++.
First and second order differential equations with step and sinusoidal input, including simultaneous differential equations. Linear algebra; vectors, matrices and determinants, Gaussian elimination, eigenvalues and eigenvectors. Newton-Raphson method, numerical integration, elementary nonlinear equations. Statistical analysis: normal distribution, probability, linear interpolation, curve fitting using least squares. C++: main variable types, input, output. Procedures, control stuctures.
The course is divided into six components: ordinary differential equations, linear equations, eigenvalues and eigenvectors, introduction to numerical methods, curve fitting, and statistics. The first two are covered by Glen Mullineux, the next two by Patrick Keough, and the last two by me. This webpage contains the information pertaining to the last two. The general XX10052/118 page is here
Lecture 1 (28 Apr 04): Introduction to probability,
probability axioms, calculating probabilities.
Lecture 2 (29 Apr 04): Consequences of the probability axioms, conditional probability, theorem of total probability, Bayes’ theorem.
Lecture 3 (5 May 04): Worked example using theorem of total probability and Bayes’ theorem, independent events, random quantities, probability distributions.
Lecture 4 (6 May 04): Binomial distribution, Poisson distribution, Poisson approximation to the Binomial, expectation.
Lecture 5 (12 May 04): Variance, standard deviation, continuous random quantities.
Lecture 6 (13 May 04): Standard normal distribution, normal distribution.
Lecture 7 (19 May 04): Introduction to linear regression, least squares regression line.
Lecture 8 (20 May04): Statistical properties of the estimated slope and intercept, confidence intervals.
Lecture notes: pdf or postscript (up to, and including, Lecture 8)
Homework - Question Sheet One: pdf or postscript
Solution Sheet One: pdf or postscript
Question Sheet Two: pdf or postscript
Solution Sheet Two: pdf or postscript