|Unit level:||Level 1|
|Teaching period(s):||Semester 1|
|Offered by||School of Mathematics|
|Available as a free choice unit?:||N
The course unit aims to provide a basic course in calculus and algebra to students with A-level mathematics or equivalent in school of MACE.
Knowledge and understanding: Be familiar with functions and geometry, differentiation, integration, basic numerical methods, vectors and complex numbers, simple ordinary differential equations.
Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.
Transferable skills and personal qualities: Have a set of tools and methods that can be applied in the courses given in the host department or in subsequent years.
- Other - 20%
- Written exam - 80%
Assessment Further Information
Diagnostic Followup Coursework (week 4) Weighting within unit 10%
Coursework 2 (week 11) Weighting within unit 10%
2 hour examination (semester 1) Weighting within unit 80%
4 lectures: Intermediate Calculus.
Review of product, quotient and chain rules for differentiation. Partial differentiation in 2 variables. Review of methods of integration (by parts, substitution and partial fractions.
4 lectures: Double integrals and line integrals.
Double integrals over rectangles and disks. Line integrals and integrals with respect to arc-length. Relation through Green's theorem.
2 lectures: Basic Numerical Methods.
Trapezoidal and Simpson's rule, inc. estimation of error. Bisection and Newton-Raphson methods for solving nonlinear equations.
4 lectures: Vectors.
Review of vectors in component form; vector addition, parallelogram and triangle of vectors. Vector equation of straight line. Scalar and vector products. Triple Products. Applications including vector products and areas.
3 lectures: Complex numbers.
Definition, algebraic operations, modulus and argument. Argand
Diagram, De Moivre's theorem.
4 lectures: Ordinary Differential Equations (ODEs).
Examples of First and Second order ODEs. Role of arbitrary constants.
Solution of first-order separable, linear and exact ODEs. First order linear ODEs and integrating factors.
3 lectures: Probability.
Deterministic vs random (probabilistic) models. Random experiments and sample spaces. Definition and properties of probability; finite sample spaces. Conditional probability, independent events.
KA Stroud, Engineering Mathematics, Palgrave
Croft et al., Mathematics for Engineers, Pearson
- Lectures - 24 hours
- Tutorials - 11 hours
- Independent study hours - 65 hours