Engineering Mathematics 1 | Units of study... | Swinburne University of Technology

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MTH10006 12.5 Credit Points Hawthorn, Sarawak

Duration

One Semester

Contact hours

60 hours

On-campus unit delivery combines face-to-face and digital learning.

Prerequisites

Anti-Requisite:

Successfully completed a unit that is very similar in content or the content overlaps with another unit.

MTH10012 Calculus and Applications

MTH10013 Linear Algebra and Applications

Aims and objectives

From 2017 MTH10006 will be replaced by MTH10012 - Calculus and Applications

This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies

Unit Learning Outcomes (ULO)

After successfully completing this unit, you should be able to:

1. Determine limits of functions (K2).
2. Determine inverse functions and the composition of two functions (K2).
3. 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).
4. Determine the partial fractions form of rational functions (K2).
5. 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).
6. Determine indefinite integrals of basic trigonometric, hyperbolic, rational and other functions, using substitutions and integration by parts (K2).
7. 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).
8. 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).
9. Determine sums and products of matrices, and determine the solution to systems of linear equations using augmented matrix form and the Gaussian algorithm (K2).

Unit information in detail

- Teaching methods, assessment, general skills outcomes and content.

Teaching methods

Lectures (48 hours), Tutorials (12 hours)

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

Stroud, K.A. (2007). Engineering Mathematics, 6th edn, Industrial Press.

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.