Department of Physics, Unit Catalogue 2008/09 |
PH20020 Mathematics for scientists 4 |
| Credits: 6 |
| Level: Intermediate |
| Semester: 2 |
| Assessment: EX 100% |
| Requisites: |
| Before taking this unit you must take PH20019 |
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Aims: The aim of this unit is to introduce mathematical concepts and techniques required by science students, and to show how these may be used for different applications. It also aims to continue the development of students' problem-solving skills and their understanding of mathematical results.
Learning Outcomes: After taking this unit the student should be able to: * evaluate Fourier series and Fourier and Laplace transforms, and use their properties to solve problems; * use transform methods to solve differential equations; * apply transform methods in optics. Skills: Numeracy T/F A, Problem Solving T/F A. Content: Fourier series (5 hours): Periodic functions. Harmonic synthesis. Representation as a Fourier series, Fourier components. Expansion of finite range functions. Applications of Fourier series. Complex form of Fourier series and coefficients. Discrete amplitude spectra. Transition to aperiodic functions (7 hours): The Fourier transform. Integral definition and properties of the Fourier transform. Use of tables in evaluating transforms. Solution of differential equations. Dirac delta function. Convolution. Sampling theorem and applications to signal processing (2 hours). Transform methods in optics (5 hours): Review of wave theory of light. Fraunhofer diffraction. Introduction to Fourier optics. The Laplace transform (3 hours): Integral definition and properties. Use of tables in evaluating transforms. Solution of differential equations. |