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Semester 1

Mathematics for Physics 1 (PHYS08035)

Subject

Physics and Astronomy

College

SCE

Credits

20

Normal Year Taken

1

Delivery Session Year

2022/2023

Pre-requisites

Course Summary

This course is designed for pre-honours physics students, primarily to develop their mathematical and problem solving skills in the context of basic algebra and calculus. A key element in understanding physics is the ability to apply elementary mathematics effectively in physical applications. For this, knowledge of mathematics is not enough, one also needs a deep understanding of the underlying concepts and practice in applying them to solve problems. The course is centred on problem solving workshops, and supported by lectures.

Course Description

The course content is divided into six sections, each with a dedicated workbook of worked examples and exercises:1. Solving equations and simplifying the answer: Linear and quadratic equations; arithmetic with complex numbers; expansion and factorisation; combining and decomposing fractions.2. Functions: Definition of a function and inverse; even-odd symmetries; trigonometric functions, their inverses and reciprocals; exponential and logarithm; modulus and argument of complex numbers; Euler's formula; hyperbolic functions; trigonometric and hyperbolic identities; roots of a polynomial in the complex plane; singularities.3. Lines and regions in the plane: equation of a straight line; conic sections; graphical representation of modulus function and polynomials; graphical representation of products and ratios of functions; algebraic and graphical representation of scaling and translation operations; relationship between regions and inequalities.4. Differentiation. First-principles definition of a derivative and application to elementary functions; higher derivatives; product rule; chain rule; differentiating an inverse; tangent and normal to a curve; stationary points; preview of differential equations and partial derivatives.5. Power series expansions. Power series as an approximation to a complicated function; Maclaurin and Taylor series expansion of elementary functions; ratio test for convergence; sums, products and ratios of power series; L'Hopital's rule for evaluating limits.6. Integration. Definite and indefinite integrals. Improper integrals. Infinite range of integration. Integration by substitution and by parts. Common substitutions and other integration strategies.Key concepts will be outlined in lectures. Students can get assistance in working through the workbooks at workshops, and a second set of workshops will be devoted to learning how to solve longer and more complex problems in groups.

Assessment Information

Written Exam 80%, Coursework 20%, Practical Exam 0%

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