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.
Dr Leo Brewin (Clayton - Sem 1)
Dr John Head (Clayton - Sem 1)
Dr Leo Brewin (Clayton - Sem 2)
Associate Professor Lan Boon Leong (Malaysia Sem 1 and 2)
Vector algebra and geometry: equations of lines and planes. Linear algebra: matrix operations, up to 3x3 systems of linear equations, eigenvalues and eigenvectors. Calculus: improper integrals, integration by parts. Sequences and series: fundamentals of convergence, Taylor series, use in error analysis. Ordinary differential equations: first order, second order with constant coefficients, repeated roots, simple non-homogeneous cases. Laplace transforms: elementary functions, inversion by tables; shifting; derivatives, applications to ODEs. Multivariable calculus: partial derivatives, gradient and directional derivatives, maxima and minima.
On successful completion of this unit, students will be able to:
- Evaluate cross products of vectors, and use vectors to represent lines and planes.
- Perform matrix algebra.
- Solve up to 3x3 systems of linear equations and find eigenvalues and eigenvectors.
- Use hyperbolic functions.
- Evaluate improper integrals of elementary functions and use integration by parts.
- Appreciate convergence of numeric and power series, construct Taylor series and estimate errors in numerical approximations .
- Solve first order ordinary differential equations, including by separable variables and integrating factors.
- Solve second order linear differential equations with constant coefficients.
- Use differential equations to model simple engineering problems.
- Evaluate and invert Laplace transforms and use them to solve ordinary differential equations.
- Calculate partial derivatives, use the gradient vector to find directional derivatives, and find extreme values of two-variable functions.
- Express and explain mathematical techniques and arguments clearly in words.
Weekly assignments or quizzes: 40%
Final examination (3 hours): 60%
Students are required to achieve at least 45% in the total continuous assessment component and at least 45% in the final examination component and an overall mark of 50% to achieve a pass grade in the unit. Students failing to achieve this requirement will be given a maximum of 45% in the unit.
Three 1-hour lectures (or equivalent), one 2-hour practice class and 7 hours of private study per week
See also Unit timetable information
Dr Leo Brewin (Sem 1 and 2, Malaysia October intake 2017)
VCE Specialist Mathematics or ENG1090 (or equivalent)