Engineering Mathematics 1
Unit code: HMS111
| Credit points | 12.5 Credit Points |
| Duration | 1 Semester |
| Contact hours | 60 hours |
| Campus | Hawthorn, Sarawak |
| Prerequisites | VCE Mathematical Methods or equivalent |
| Corequisites | Nil |
Related course(s)
A unit of study in the;
Bachelor of Engineering (Robotics and Mechatronics)/ Bachelor of Science (Computer Science and Software Engineering)
Bachelor of Science (Biomedical Sciences) ( S061)
Bachelor of Science (Biomedical Sciences) ( S061)
And an elective unit of study in the
Aims 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. Use vectors in two and three dimensions to determine the results of simple calculations, such as dot and cross products, to describe straight lines and planes in three dimensions and the relationships between them, and to determine angular velocity and torque. (K2, S1)
2. Determine real solutions of inequalities, quadratic and cubic equations. (K2)
3. Use algebra to transpose and evaluate formulae. (K2)
4. Determine inverse functions and the composition of two functions. (K2)
5. 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)
6. Determine the partial fractions form of rational functions. (K2)
7. Determine first and higher order derivatives using standard results, the product, quotient, function of a function and inverse function rules, implicit and logarithmic differentiation and (for simple functions) first principles. (K2)
8. 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)
9. Determine indefinite integrals of functions involving basic, trigonometric, hyperbolic, rational and other functions using standard results, substitutions, and integration by parts. (K2)
10. Determine definite integrals exactly (and approximately, using Trapezoidal and Simpson’s rules), apply to areas under and between curves, centroids, arc length, volumes of solids of revolution. (K2)
This Unit of Study will contribute to you attaining the following Swinburne Engineering Competencies:
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.
Assessment
| Types | Individual or Group Assessment | Weighting |
| Examination | Individual | 50% - 65% |
| Test(s)/Assignments | Individual | 35% - 50% |
Content
- Sequences and limits: Definition of a sequence, convergence of a sequence.
- Functions and Graphs: Review of functions and graphs, including polynomials, rational and trigonometric functions, domain, limits, asymptotes, partial fractions, inverse trigonometric functions, hyperbolic and inverse hyperbolic functions.
- Differentiation of functions of a single variable: Definition and interpretation, standard derivatives, rules, implicit and logarithmic differentiation, optimisation, detailed graphing including points of inflection, rates, approximations, error analysis, Taylor polynomials, indeterminate forms, Newton-Raphson method.
- Integration of functions of a single variable: Anti-differentiation, substitution, parts, general techniques, use of integration tables, numerical integration, application to areas, centroids, volumes, arc lengths.
- Introduction to vectors: Basic operations in 2D, introduction to 3D space, basic vectors in 3D, scalar product, projections.
- Introduction to matrices: definition and application to solving systems of linear algebraic equations by Gaussian elimination.
Reading materials
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.
