Engineering Mathematics 2 Product Design | Units of study... | Swinburne University of Technology

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MTH10003 12.5 Credit Points Hawthorn

Duration

1 Semester

Contact hours

60 hours

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

Prerequisites

MTH10006

Corequisites

Nil

Aims and objectives

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

Unit Learning Outcomes (ULO)

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 (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 at a point on a surface; determine stationary points on a surface (K2).
Determine the curvature and radius of curvature of a given curve, and determine conversion between polar coordinates and parametric forms (K2).
Conduct statistical studies on single variable and bivariate data (K2).

Swinburne Engineering Competencies (SECs) -

This Unit of Study will contribute to you attaining the following SECs:

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

Bachelor of Engineering (Product Design Engineering)

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	45-60%	1-9
Tests	Individual	20-40%	1-7
Assignments	Individual	10-20%	1-9
Project	Group	10-20%	8

General skills outcomes

The Key Generic Skills for this unit have been incorporated into the Swinburne Engineering Competencies.

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, curvature in 3D.
Statistics: Graphical and numerical summaries of single variable data. Bivariate data analysis, correlation and regression models. Residual analysis and transformations.

Study resources

- Text books and recommended reading.

Text books

HMS112 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).