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Semester 1

Algebra and Calculus (PHYS08041)

Subject

Physics and Astronomy

College

SCE

Credits

20

Normal Year Taken

2

Delivery Session Year

2022/2023

Pre-requisites

Course Summary

This course is designed for pre-honours direct entry physics students. It covers basic and more advanced algebra, as well as basic and multivariate calculus, which are used to describe concepts in physics. The course consists of lectures to present new material, and workshops to develop understanding, familiarity and fluency.

Course Description

Basic Algebra & Calculus (20 lectures)- Basic Algebra. Manipulating expressions. Squares. Polynomials. Factorization. Quadratic and root equations (3)- Functions. Inequalities. Moduli. Exponentials and logarithms. Curve sketching. Series expansions. Harmonic potentials. (3) - Geometry and trigonometry. Trig functions. Lines and circles. Conic sections. (3)- Complex numbers. Complex algebra. Argand diagram. Euler and de-Moivre. (2)- Derivatives. Differentiation of standard functions. Composite functions. Higher derivatives. (3)- Elementary Ordinary Differential Equations. (3)- Integrals. Standard integrals. Integrating by parts. Substitution. (3)Linear Algebra & Several Variable Calculus (20 lectures)- Vectors. Basic vector algebra. (1)- Dot and cross products. Triple products. (3)- Linear independence. Expansion in a basis. Change of basis. (1)- Matrices. Matrix algebra. Orthogonal transformations. (3)- Determinant, rank and inverse. Eigenvalues and eigenvectors. Matrix diagonalisation (4)- Complex vectors. Hermitian and unitary matrices. (2)- Taylor expansions. Maxima, minima and saddle points (1)- Partial derivatives. Chain rule. Change of variables. Spherical and cylindrical polar coordinates. (3)- Multivariate integration. (2)

Assessment Information

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

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