Engineering Mathematics 2
Duration
- 1 Semester
Contact hours
- 60 hours
On-campus unit delivery combines face-to-face and digital learning.
Prerequisites
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:
- Determine simple operations involving determinants by hand; determine the solution to simultaneous equations using Cramer’s rule and inverse matrices; determine the rank of a matrix and its nullspace, determine linear (in)dependence of vectors (K2).
- Use vectors to determine cross products, and to describe straight lines and planes in three dimensions and the relationships between them, and to determine angular velocity and torque (K2, S1).
- Determine complex solutions of equations and rewrite complex numbers in various formats; determine roots of complex numbers, describe graphically complex numbers in the Argand plane (K2).
- Determine the solution to first order separable ODEs and linear differential equations using an integrating factor. Determine the solution to second order homogeneous and non--homogeneous linear differential equations with constant coefficients (K2).
- Describe graphically the surface for a given equation and determine the gradient and second derivative at any point on the surface (K2).
- Determine small changes in a function of several variables; Determine error of measurement estimates for a function of several variables (K2, S1).
- Determine derivatives of a function of several variables using the chain rule; determine the directional derivatives atpoint on a surface; determine stationary points on a surface (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.
Courses with unit
Unit information in detail
- Teaching methods, assessment and content.
Teaching methods
Assessment
| Types | Individual or Group task | Weighting | Assesses attainment of these ULOs |
| Examination | Individual | 45-60% | 1-8 |
| Tests | Individual | 20-40% | 1-7 |
| Assignments | Individual | 10-20% | 1-8 |
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
Student Notes, published by the Mathematics Discipline, Faculty of Science Engineering and Technology, Swinburne University of Technology (these notes are available for purchase at the bookshop).
Recommended reading
Fitzgerald, G. & Peckham, I., Mathematical Methods for Engineers and Scientists, Prentice Hall, 1996 (available in the library).
Stroud, K.A., Engineering Mathematics, Macmillan, London, 6th edn., 2007 (available in the library; can be ordered from the bookshop; contains lots of solved problems).