MTH1035 - Techniques for modelling (advanced) - 2018

Solution of systems of linear equations using Gaussian elimination; matrices and determinants, eigenvalues and eigenvectors; introduction to vectors; parametric curves; methods of integration - substitutions and integration by parts; solution of first-order ordinary differential equations - separable, use of integrating factor; solution of second-order linear ordinary differential equations with constant coefficients and applications; Sequences and series, Taylor series and series convergence, the remainder term.

On completion of this unit students will be able to:

1. Understand the basic concepts of linear algebra, and recognise and manipulate elements of vector spaces;
2. Formulate and solve equations involving vectors and matrices, including for three-dimensional geometry;
3. Identify and evaluate improper integrals;
4. Solve simple first and second order differential equations, and formulate them for applications to physical systems;
5. Compute Taylor series expansions, with remainder, for functions of one variable;
6. Apply Taylor series and l'Hopital's rule to compute limits;
7. Understand and compute the convergence properties of infinite series;
8. Provide written reports that contain complete mathematical arguments;
9. Understand the concept of mathematical proof and the difference between proof by construction and proof by induction;
10. Prove elementary theorems by induction and by construction.

Examination (2 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Three 1-hour lectures, one 1-hour workshop and one 2-hour support class per week.

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