- UCAS course code
- UCAS institution code
Year of entry: 2021
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Course unit details:
|Unit level||Level 1|
|Teaching period(s)||Semester 1|
|Offered by||Department of Physics & Astronomy|
|Available as a free choice unit?||No|
To allow students to develop their mathematical competence with functions, calculus, complex numbers, power series, linear algebra and differential equations to a level where they can cope with the demands of the first year of the physics course and beyond.
This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact. Please see Blackboard / course unit related emails for any further updates.
On completion successful students will be able to:
- describe the properties of different types of functions and be able to sketch them in both 2D cartesian and polar cordinates
- integrate and differentiate functions of one variable using a range of techniques and be able to apply integration and differentiation to a range of physical problems.
- show how smooth functions can be expressed in terms of power series.
- explain the properities of complex numbers and construct some basic complex functions.
- employ matrix notation, carry out matrix algebra and use matrices to solve systems of linear equations.
- compute the properities of determinants, be able to evaluate them, and use them to test for unique solutions of linear equations.
- solve first and second order ordinary differential equations using a range of techniques.
1. Functions and 2D coordinates
Properties of functions. 2D and 3D coordinate systems. Index notation, Sketching functions, logarithmic functions.
2. Complex numbers
Definition, modulus and argument; addition, multiplication, division; roots of quadratic equations; complex numbers in polar form; De Moivre's theorem; Hyperbolic functions.
3. Differential Calculus
Review of differentiation, the differential; differentiation of products, functions of functions; maxima, minima and inflexions; partial differentiation; examples and applications from physics.
4. Power Series
Series, limits of series; binomial expansion; Taylor's and Maclaurin's series expansions.
5. Integral Calculus
Review of integration; integration by parts, substitution, standard integrals, partial fractions and completing the square; simple line integrals; physical applications.
6. Linear Algebra
Matrix algebra, inverse matrix. Definition and properties of determinants, scalar triple product, test of unique solution to linear equations. Eigenvalues and eigenvectors, eigenanalysis.
7. Ordinary Differential Equations
Physical motivation. 1st order separable. 1st order homogeneous. 1st order linear: integrating factors. 2nd order with constant coefficients. Physical applications.
Feedback will be offered by tutors on students’ written solutions to weekly examples sheets, and model answers will be issued.
Jordan, D. & Smith, P. Mathematical Techniques (OUP)
Tinker, M. & Lambourne, R. Further Mathematics for the Physical Sciences (Wiley)
Lambourne, R. & Tinker, M. Basic Mathematics for the Physics Sciences (Wiley)
|Scheduled activity hours|
|Assessment written exam||1.5|
|Practical classes & workshops||11|
|Independent study hours|
|Roger Jones||Unit coordinator|
|Justin Evans||Unit coordinator|