units

MTH1035

Faculty of Science

This unit entry is for students who completed this unit in 2014 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

## 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, or view unit timetables.

 Level Undergraduate Faculty Faculty of Science Organisational Unit School of Mathematical Sciences Monash Passport category Advanced Studies (Enhance Program) Offered Clayton First semester 2014 (Day) Coordinator(s) Mr Simon Teague

### 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;

1. Formulate and solve equations involving vectors and matrices, including for three-dimensional geometry;

1. Identify and evaluate improper integrals;

1. Solve simple first and second order differential equations, and formulate them for applications to physical systems;

1. Compute Taylor series expansions, with remainder, for functions of one variable;

1. Apply Taylor series and l'Hopital's rule to compute limits;

1. Understand and compute the convergence properties of infinite series;

1. Provide written reports that contain complete mathematical arguments;

1. Understand the concept of mathematical proof and the difference between proof by construction and proof by induction;

1. Prove elementary theorems by induction and by construction.

### Assessment

Continuous assessments: 40%
Final Examination: 60%