Engineering Mathematics 1
Duration
- 1 Semester
Contact hours
- 60 hours
Prerequisites
Corequisites
NilAims and objectives
After successfully completing this unit, you should be able to:
1. Determine limits of sequences (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).
Swinburne Engineering Competencies for this Unit of Study
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.
Courses with unit
Bachelor of Science (Biomedical Sciences)
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
Lectures (48 hours), Tutorials (12 hours)
Assessment
Types | Individual or Group task | Weighting | Assesses attainment of these ULOs |
Examination | Individual | 50% - 65% | 1-9 |
Test(s)/Assignments | Individual | 35% - 50% | 1-9 |
General skills outcomes
The Key Generic Skills for this unit have been incorporated into the Swinburne Engineering Competencies.
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.
Study resources
- Reading materials, text books and recommended reading.
Reading materials
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.
Text books
Recommended reading
Croft, A. & Davison, R. (2008). Mathematics for Engineers: A Modern Interactive Approach, 3^{rd} Edn, Prentice Hall.
James, G. (2010). Modern Engineering Mathematics, 4^{th} Edn, Prentice Hall.
Stroud, K.A. & Booth, D.J. (2007). Engineering Mathematics, 6^{th} Edn, Industrial Press.
Thomas, G.B., Weir, M.D. & Hass, J. (2009). Thomas’ Calculus, 12^{th} Edn, Addison Wesley.