# MTH1035 - Techniques for modelling (advanced) - 2017

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Unit guides

Offered

Clayton

• First semester 2017 (Day)

## Synopsis

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.

## Outcomes

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.

## Assessment

Final examination (3 hours): 65%

Assignments and tests: 30%

Participation in support classes: 5%

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