EMTH210-15S1 (C) Semester One 2015

# Engineering Mathematics 2

15 points

Details:
 Start Date: Monday, 23 February 2015 End Date: Sunday, 28 June 2015
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 6 March 2015
• Without academic penalty (including no fee refund): Friday, 22 May 2015

## Description

This course covers material in multivariable integral and differential calculus, linear algebra and statistics which is applicable to the engineering professions.

Mathematics underpins almost every aspect of modern engineering. This is reflected by the fact that all first professional year students must take EMTH210. With the centrality of this course to your professional development in mind, considerable effort has gone into selecting mathematical and statistical topics which will provide the groundwork for you to appropriately mathematise your engineering work. Throughout the course, your lecturers will also endeavour to relate the rigour of the mathematics to the practicality of the situations in which it will be applied, as we concentrate on your ability to apply the techniques to realistic situations.

The following topics will be covered, subject to the time available:
• Partial differentiation, chain rule, gradient, directional derivatives, tangent planes, Jacobian, differentials, line integrals, divergence and curl, extreme values and Lagrange multipliers.
• Second order linear differential equations and their applications.
• Fourier series.
• Double and triple integrals: elements of area, change of order of integration, polar coordinates, volume elements, cylindrical and spherical coordinates.
• Eigenvalues and eigenvectors and their applications.
• Laplace transforms.
• Statistics: approximating expectations, characteristic functions, random vectors (joint distributions, marginal distributions, expectations, independence, covariance), linking data to probability models (sample mean and variance, order statistics and the empirical distribution function, convergence of random variables, law of large numbers and point estimation, the central limit theorem, error bounds and confidence intervals, sample size calculations, likelihood).

## Learning Outcomes

• Upon successful completion of the course, students will:

• have a good basic understanding of the above concepts and techniques
• be able to apply the above to engineering applications
• understand the limits of applicability of the above
• be aware of their own limits of understanding of the course topics
• have been introduced to some of the historical developments of the topics, as well as the historical linkages between mathematics and engineering, although this historical aspect is not directly examinable

## Prerequisites

Subject to approval of the Dean of Engineering and Forestry

## Restrictions

EMTH202, EMTH204, MATH201, MATH261, MATH262, MATH264

## Course Coordinator

For further information see Mathematics and Statistics Head of Department

## Assessment

Assessment Due Date Percentage
Tutorial Assessment 10%
Mid-course Test 30%
Final Examination 60%

## Textbooks / Resources

•“Advanced Engineering Mathematics” by Erwin Kreyszig. (This text also covers the statistics material.)
•“Advanced Engineering Mathematics” by Zill and Wright.
•“Advanced Engineering Mathematics” by Zill and Cullen.

## Indicative Fees

Domestic fee \$874.00

International fee \$4,725.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

## All EMTH210 Occurrences

• EMTH210-15S1 (C) Semester One 2015