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Unit information: Numerical Analysis 23 in 2018/19

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Unit name Numerical Analysis 23
Unit code MATH30010
Credit points 20
Level of study H/6
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Dr. Sieber
Open unit status Not open
Pre-requisites

First year core units (MATH11006 Analysis 1 (or MATH10003 Analysis 1A and MATH10006 Analysis 1B), MATH11007 Calculus 1, MATH11005 Linear Algebra and Geometry)

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

Description

This unit is intended to serve as a first course in numerical analysis. As such the fundamental areas of root finding, numerical differentiation, numerical integration and solving ordinary differential equations will be covered. The emphasis will be to explore numerical techniques for solving these problems theoretically. Computer programming is not required for this unit.

Unit aims

To introduce students to the basics of numerical analysis; this is broadly the study of numerical methods for solving mathematical problems.

Syllabus

  • Root finding. Linear systems: Gaussian elimination and LU decomposition. Nonlinear equations: bisection, fixed point iteration, Newton-Raphson, accelerating convergence. Systems of nonlinear equations, Newton's method, steepest descent.
  • Numerical differentiation and integration. Interpolation polynomial, trapezoidal rule, Simpson's rule, Richardson's extrapolation, Romberg integration, Gaussian quadrature.
  • Ordinary differential equations. Initial value problems: Euler's methods, Runge-Kutta methods, multistep methods, stability, time stability, stiffness. Boundary value problems: Shooting, finite difference methods, spectral methods.

Relation to other units

This unit is a more advanced version of the Level I/5 unit, Numerical Analysis 2. The lectures for Numerical Analysis 2 and Numerical Analysis 23 are the same, but the problem sheets and examination questions for Numerical Analysis 23 are more challenging. Students may NOT take both Numerical Analysis 2 and Numerical Analysis 23.

Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html

Intended learning outcomes

At the end of this unit, students should be able to

  • solve nonlinear equations
  • numerically differentiate
  • evaluate complicated integrals and
  • estimate the solutions to ordinary differential equations to any required accuracy.

Transferable Skills: Computational techniques; interpretation of computational results; relation of numerical results to mathematical theory.

Teaching details

Lectures; weekly problem classes; theoretical and computational exercises to be done by students.

Assessment Details

The final assessment mark will be entirely based upon a 2 ½-hour examination

Reading and References

Reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html

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