2667 105961 `MATH650` Advanced Mathematics

Students completing this course will have knowledge of a range of techniques and concepts in advanced mathematics. Students will have formalised the notion of rigor and proof thus providing an insight into the elegance of mathematics processes and structure, and will have a skill level by which they will be able to 'teach' themselves the mathematics encountered in higher studies of science and engineering. Completion of the course also facilitates an easy mathematical transition into 2 nd or 3 rd year degree study.

399 `CH3823` Diploma in Engineering (Mechanical) L6 410 `CH3806` Bachelor of Engineering Technology (Electrotechnology) L7 296 `CH3964` Diploma in Science (L6) 295 `CH3963` Diploma in Science (L5) 396 `CH3802` Diploma in Engineering (Civil) L6 20.0 6 Engineering 200.0 Perform partial differentiation Sketch level surfaces Apply chain rule to surfaces and paths Find directional derivatives Apply the grad operator to problems Find saddle points Understand the vector space Rn and know vector identities Distinguish scalar and vector fields Find and apply div, grad and curl Understand any apply Stoke's theorem and Green's Theorem in the plane Recognise and use special (named) functions Solve ordinary differential equations of first and second order Apply laws of proof and understand mathematical symbolism in its correct contexts Find multiple integrals and change the order of integration Evaluate multiple integrals in polar coordinates Apply multiple integrals to centroids and moments Use cylindrical and spherical coordinate systems Understand tensor notation as applied to div, grad and curl Prove vector identities in tensor form Apply tensors to stress/strain and Maxwell's Equations Use tests for diffentiability in complex functions Perform complex integration Investigate the Fourier Transform Understand the language of linear algebra Perform orthogonal transformations Describe the Sturm-Liouville Problem Solve problems numerically Perform numerical integration and differentiation Use Exploratory Data Analyses to test data Use normal and t-tests to solve problems Find confidence intervals and apply hypothesis tests Apply PERT to project management Apply Quality assurance techniques to engineering and scientific processes Solve systems of differential equations and express as an uncoupled form Solve simple partial differential equations