Algebra and Calculus (PHYS08041)
Physics and Astronomy
Normal Year Taken
Delivery Session Year
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.
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)
Written Exam 80%, Coursework 20%, Practical Exam 0%
All course information obtained from this visiting student course finder should be regarded as provisional. We cannot guarantee that places will be available for any particular course. For more information, please see the visiting student disclaimer: