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XX10052/118: Mathematics & Computing 2 |
Timetable: Wednesday
Lecturer: Simon Shaw;
s.c.shaw at maths.bath.ac.uk
Credits: 6
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Level: Certificate |
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Semester: 2 |
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Assessment: EX75CW25 |
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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++.
Content:
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
Question Sheet Three: pdf or postscript
Solution Sheet Three: pdf or postscript
Question Sheet Four: pdf or postscript
Solution Sheet Four: pdf or postscript