EMTH210-19S1 (C) Semester One 2019

# Engineering Mathematics 2

15 points

Details:
 Start Date: Monday, 18 February 2019 End Date: Sunday, 23 June 2019
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 1 March 2019
• Without academic penalty (including no fee refund): Friday, 10 May 2019

## 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

• A student achieving total mastery of this course will be able to:
• Show proficiency in multivariable calculus, including partial differentiation, implicit partial differentiation, the multidimensional chain rule, gradient, directional derivative, tangent planes, Jacobians, differentials, line integrals (exact and inexact), divergence, curl, and Lagrange multipliers.
• Solve homogeneous constant coefficient ODEs and also inhomogeneous constant coefficient ODEs using undetermined coefficients.   This includes ODEs of order other than two.
• Solve elementary second order boundary value problems, and appreciate some applications of BVPs in engineering.
• Calculate real Fourier series of arbitrary period, and employ them to solve ODEs with periodic driving functions.  The student will also be knowledgeable of concepts such as harmonics and Gibbs phenomenon in Fourier series analysis.
• Integrate in multiple dimensions using Cartesian, polar and spherical polar coordinate systems.
• Calculate the eigenpairs of matrices.
• Familiar with orthogonal decomposition, and use it to find the principal axes of an ellipse.
• Proficient in the solution of systems of first and second order ODEs via eigenvalues and eigenvectors, and familiar with the implications defective matrices in such situations.
• Apply Laplace transforms to differential and some integral equations, including those with piecewise functions via the Heaviside step function.
• Approximate expectations.
• Be cognizant of characteristic functions, random vectors, joint and marginal distributions, independence and covariance.
• Link data to probability models, sample mean, variance, order statistics, and the empirical distribution function.
• Be familiar with convergence of random variables, the law of large numbers, point estimation, the central limit theorem, likelihood, error bounds, and confidence intervals.
• Do sample size calculations.

## Pre-requisites

Subject to approval of the Dean of Engineering and Forestry

## Restrictions

EMTH202, EMTH204, MATH201, MATH261, MATH262, MATH264

## Timetable 2019

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 08:00 - 09:00 K1 Lecture Theatre 18 Feb - 7 Apr 29 Apr - 2 Jun 02 Monday 12:00 - 13:00 A1 Lecture Theatre 18 Feb - 7 Apr 29 Apr - 2 Jun Lecture B 01 Tuesday 08:00 - 09:00 K1 Lecture Theatre 18 Feb - 7 Apr 29 Apr - 2 Jun 02 Tuesday 12:00 - 13:00 A1 Lecture Theatre 18 Feb - 7 Apr 29 Apr - 2 Jun Lecture C 01 Wednesday 08:00 - 09:00 K1 Lecture Theatre 18 Feb - 7 Apr 29 Apr - 2 Jun 02 Wednesday 12:00 - 13:00 K1 Lecture Theatre 18 Feb - 7 Apr 29 Apr - 2 Jun Lecture D 01 Thursday 08:00 - 09:00 K1 Lecture Theatre 18 Feb - 7 Apr 29 Apr - 2 Jun 02 Thursday 12:00 - 13:00 A1 Lecture Theatre 18 Feb - 7 Apr 29 Apr - 2 Jun Tutorial A 01 Wednesday 10:00 - 11:00 Jack Erskine 235 18 Feb - 7 Apr 29 Apr - 2 Jun 02 Monday 16:00 - 17:00 Jack Erskine 242 18 Feb - 7 Apr 29 Apr - 2 Jun 03 Friday 13:00 - 14:00 Jack Erskine 121 18 Feb - 7 Apr 29 Apr - 2 Jun 04 Thursday 13:00 - 14:00 Jack Erskine 235 18 Feb - 7 Apr 29 Apr - 2 Jun 05 Thursday 14:00 - 15:00 Jack Erskine 121 18 Feb - 7 Apr 29 Apr - 2 Jun 06 Tuesday 13:00 - 14:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 07 Monday 15:00 - 16:00 Jack Erskine 315 18 Feb - 7 Apr 29 Apr - 2 Jun 08 Friday 11:00 - 12:00 Jack Erskine 242 18 Feb - 7 Apr 29 Apr - 2 Jun 09 Monday 15:00 - 16:00 Jack Erskine 101 18 Feb - 7 Apr 29 Apr - 2 Jun 10 Wednesday 16:00 - 17:00 West 213A 18 Feb - 7 Apr 29 Apr - 2 Jun 11 Wednesday 13:00 - 14:00 Jack Erskine 235 18 Feb - 7 Apr 29 Apr - 2 Jun 12 Tuesday 14:00 - 15:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 13 Tuesday 11:00 - 12:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 14 Tuesday 15:00 - 16:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 15 Friday 13:00 - 14:00 West 213A 18 Feb - 7 Apr 29 Apr - 2 Jun 16 Wednesday 16:00 - 17:00 Jack Erskine 445 18 Feb - 7 Apr 29 Apr - 2 Jun 17 Tuesday 13:00 - 14:00 Jack Erskine 121 18 Feb - 7 Apr 29 Apr - 2 Jun 18 Tuesday 16:00 - 17:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 19 Tuesday 11:00 - 12:00 Jack Erskine 239 18 Feb - 7 Apr 29 Apr - 2 Jun 20 Wednesday 11:00 - 12:00 Jack Erskine 239 18 Feb - 7 Apr 29 Apr - 2 Jun 21 Friday 11:00 - 12:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 22 Thursday 15:00 - 16:00 Jack Erskine 241 18 Feb - 7 Apr 29 Apr - 2 Jun 23 Tuesday 16:00 - 17:00 Jack Erskine 121 18 Feb - 7 Apr 29 Apr - 2 Jun 24 Friday 14:00 - 15:00 Jack Erskine 241 18 Feb - 7 Apr 29 Apr - 2 Jun 25 Friday 14:00 - 15:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 26 Wednesday 11:00 - 12:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 27 Wednesday 15:00 - 16:00 Jack Erskine 244 18 Feb - 7 Apr 29 Apr - 2 Jun 28 Wednesday 13:00 - 14:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 29 Thursday 13:00 - 14:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 30 Wednesday 14:00 - 15:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 31 Thursday 11:00 - 12:00 West 213A 18 Feb - 7 Apr 29 Apr - 2 Jun 32 Thursday 10:00 - 11:00 Jack Erskine 240 18 Feb - 7 Apr 29 Apr - 2 Jun 33 Wednesday 15:00 - 16:00 Jack Erskine 241 18 Feb - 7 Apr 29 Apr - 2 Jun 34 Thursday 11:00 - 12:00 Ernest Rutherford 225 18 Feb - 7 Apr 29 Apr - 2 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test B 01 Tuesday 18:30 - 20:00 C1 Lecture Theatre 1 Apr - 7 Apr 02 Tuesday 18:30 - 20:00 C2 Lecture Theatre 1 Apr - 7 Apr 03 Tuesday 18:30 - 20:00 C3 Lecture Theatre 1 Apr - 7 Apr 04 Tuesday 18:30 - 20:00 A1 Lecture Theatre 1 Apr - 7 Apr 05 Tuesday 18:30 - 20:00 A2 Lecture Theatre 1 Apr - 7 Apr

## Course Coordinator

For further information see Mathematics and Statistics Head of Department

## Assessment

Assessment Due Date Percentage  Description
Tutorial Assessment 10%
MapleTA Test 19 Mar 2019 10% Due 19-22 March
Mid-course Test 02 Apr 2019 35%
Final Examination 45%

To pass the course, there is a minimum mark required in the written Mid-Course Test and the Final Examination of 30% in each, as well as achieving 50% or more in total across all the assessments.

## 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 \$956.00

International fee \$5,250.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

## All EMTH210 Occurrences

• EMTH210-19S1 (C) Semester One 2019