Monash University Handbook

Solution of systems of linear equations using Gaussian elimination; matrices, determinants, eigenvalues and eigenvectors; introduction to vectors; 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; Taylor series and series convergence; the remainder term.

Outcomes

On completion of this unit students will be able to:

Understand the basic concepts of linear algebra, recognise and manipulate elements of vector spaces;
Formulate and solve equations involving vectors and matrices, including for three-dimensional geometry;
Identify and evaluate improper integrals;
Solve simple first and second order differential equations, and formulate them for applications to physical systems;
Compute Taylor series expansions, with remainder, for functions of one variable;
Apply Taylor series and l'Hopital's rule to compute limits;
Understand and compute the convergence properties of infinite series;
Provide written reports that contain complete mathematical arguments.

Assessment

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 2 hours and 10 minutes.

End of semester examination (2 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

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