Engineering Mathematics 1
Duration
- 1 Semester
Contact hours
- 60 hours
Corequisites
NilAims and objectives
This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies
After successfully completing this unit, you should be able to:
1.
1. Determine limits of functions (K2).
- Determine inverse functions and the composition of two functions (K2).
- Apply general concepts of functions and graphs to linear, quadratic, cubic and higher degree polynomials, straight lines, circles, ellipses, hyperbolae, parabolae; rational, exponential, logarithmic, trigonometric and hyperbolic functions (K2).
- Determine the partial fractions form of rational functions (K2).
- Determine first and higher order derivatives using the product, quotient and chain rules. Determine the derivatives of inverse functions and apply implicit and logarithmic differentiation. Use differentiation for detailed graph drawing (including maxima, minima and points of inflection), determining rates of change, stationary points, optimisation, simple error analysis, derivation of Taylor polynomials and series, applying L’Hopital’s rule and the Newton-Raphson method (K2,S1).
- Determine indefinite integrals of basic trigonometric, hyperbolic, rational and other functions, using substitutions and integration by parts (K2).
- Determine definite integrals exactly (and approximately, using Trapezoidal and Simpson’s rules), apply to regions under and between curves, centroids, arc length, volumes of solids of revolution (K2).
- Use vectors in two and three dimensions to determine the results of simple calculations such as dot product, projection of vectors and angles between vectors (K2).
- Determine sums and products of matrices, and determine the solution to systems of linear equations using augmented matrix form and the Gaussian algorithm (K2).
Courses with unit
Please note that unit codes have changed from 2014. Please ensure that you check the unit entry for the correct 2014 unit code.
Unit information in detail
- Teaching methods, assessment, general skills outcomes and content.
Teaching methods
Assessment
| Individual or Group task | Weighting | Assesses attainment of these ULOs |
Examination | Individual | 55% | 1-9 |
Test1 Test 2 | Individual Individual | 14% 14% | 1-4 3,5,6 |
Assignments 1-12 | Individual | 17% | 1-9 |
General skills outcomes
K2 | Maths and IT as Tools: Proficiently uses relevant mathematics and computer and information science concepts as tools. |
S1 | Engineering Methods: Applies engineering methods in practical applications. |
Content
- Matrices: determinants, inversion, Cramer's rule, rank, null space, basis, linear independence
- Applications of vectors: straight lines and planes in space, vector product
- Complex numbers: Imaginary numbers, complex numbers, complex conjugates, Argand plane in Cartesian and polar forms; de Moivre’s theorem and roots of complex numbers; complex exponential form.
- Differential equations: First order separable differential equations, first order linear differential equations, orthogonal trajectories, second order linear differential equations with constant coefficients and simple right hand sides.
- Surfaces and partial differentiation: Surfaces, partial derivatives, small increment formula, errors of measurement, chain rule, directional derivatives, stationary points.
- Curves: 2D polar coordinates, 2D parametric curves, parametric differentiation and anti-differentiation, 3D curves, velocity and acceleration, curvature in 2D, application to transition curves, curvature in 3D.
Study resources
- Reading materials, text books and recommended reading.
Reading materials
Text books
There is no textbook. However, students are expected to access the Notes for the unit:
MTH10006 Engineering Mathematics 1 Study Guide 2014 ($18 in Swinburne Bookshop).
These are also available on Blackboard.
The Texas Instruments 30XB MultiView Calculator is the only calculator permitted to be used in some of the assessments in this unit (see c) and d), above), and these assessments will be set on the assumption that students have such a calculator.
Recommended reading
Croft, A. & Davison, R. (2008). Mathematics for Engineers: A Modern Interactive Approach, 3rd Edn, Prentice Hall.
James, G. (2010). Modern Engineering Mathematics, 4th Edn, Prentice Hall.
Stroud, K.A. & Booth, D.J. (2007). Engineering Mathematics, 6th Edn, Industrial Press.
Thomas, G.B., Weir, M.D. & Hass, J. (2009). Thomas’ Calculus, 12th Edn, Addison Wesley.