MTH1035 - Techniques for modelling (advanced)

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

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



Organisational Unit

School of Mathematical Sciences


Dr Andy Hammerlindl

Unit guides



  • First semester 2017 (Day)


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.


Final examination (3 hours): 65%

Assignments and tests: 30%

Participation in support classes: 5%

Workload requirements

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

See also Unit timetable information

Chief examiner(s)

This unit applies to the following area(s) of study


VCE Specialist Mathematics with an ATAR/ENTER score of 95 or above; a VCE study score of 35 or above in Specialist Mathematics; a High Distinction in MTH1020; or by approval of the Head of School of Mathematical Sciences. In order to enrol in this unit students will need to apply via the Science Student Services office.


ENG1005, ENG1091, MTH1030