EMTH210-17S1 (C) Semester One 2017

# Engineering Mathematics 2

 15 points, 0.1250 EFTS20 Feb 2017 - 25 Jun 2017

## 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 2017

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Tuesday 08:00 - 09:00 A1 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun 02 Tuesday 12:00 - 13:00 C1 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Lecture B 01 Wednesday 08:00 - 09:00 A1 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun 02 Wednesday 12:00 - 13:00 C1 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Lecture C 01 Thursday 08:00 - 09:00 A1 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun 02 Thursday 12:00 - 13:00 C1 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Lecture D 01 Friday 08:00 - 09:00 A1 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun 02 Friday 12:00 - 13:00 C1 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Tutorial A 01 Monday 11:00 - 12:00 Erskine 240 20 Feb - 9 Apr 1 May - 4 Jun 02 Monday 13:00 - 14:00 Erskine 240 20 Feb - 9 Apr 1 May - 4 Jun 03 Monday 13:00 - 14:00 Erskine 244 20 Feb - 9 Apr 1 May - 4 Jun 04 Monday 14:00 - 15:00 Erskine 244 20 Feb - 9 Apr 1 May - 4 Jun 05 Monday 14:00 - 15:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 06 Monday 15:00 - 16:00 Erskine 241 20 Feb - 9 Apr 1 May - 4 Jun 07 Tuesday 11:00 - 12:00 Erskine 240 20 Feb - 9 Apr 1 May - 4 Jun 08 Tuesday 11:00 - 12:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 09 Tuesday 13:00 - 14:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 10 Tuesday 13:00 - 14:00 Erskine 241 20 Feb - 9 Apr 1 May - 4 Jun 11 Tuesday 14:00 - 15:00 Erskine 446 20 Feb - 9 Apr 1 May - 4 Jun 12 Tuesday 14:00 - 15:00 Erskine 445 20 Feb - 9 Apr 1 May - 4 Jun 13 Monday 12:00 - 13:00 Erskine 111 20 Feb - 9 Apr 1 May - 4 Jun 14 Wednesday 11:00 - 12:00 Erskine 111 20 Feb - 9 Apr 1 May - 4 Jun 15 Wednesday 11:00 - 12:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 16 Wednesday 13:00 - 14:00 Erskine 240 20 Feb - 9 Apr 1 May - 4 Jun 17 Wednesday 13:00 - 14:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 18 Wednesday 14:00 - 15:00 Erskine 445 20 Feb - 9 Apr 1 May - 4 Jun 19 Monday 16:00 - 17:00 Erskine 446 20 Feb - 9 Apr 1 May - 4 Jun 20 Wednesday 15:00 - 16:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 21 Thursday 11:00 - 12:00 Erskine 241 20 Feb - 9 Apr 1 May - 4 Jun 22 Thursday 11:00 - 12:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 23 Thursday 13:00 - 14:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 24 Thursday 13:00 - 14:00 Erskine 445 20 Feb - 9 Apr 1 May - 4 Jun 25 Thursday 14:00 - 15:00 Erskine 445 20 Feb - 9 Apr 1 May - 4 Jun 26 Thursday 14:00 - 15:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 27 Friday 11:00 - 12:00 Erskine 241 20 Feb - 9 Apr 1 May - 4 Jun 28 Friday 10:00 - 11:00 Erskine 121 20 Feb - 9 Apr 1 May - 4 Jun 29 Friday 11:00 - 12:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 30 Friday 13:00 - 14:00 Erskine 441 20 Feb - 9 Apr 1 May - 4 Jun 31 Friday 14:00 - 15:00 Erskine 242 20 Feb - 9 Apr 1 May - 4 Jun 32 Monday 12:00 - 13:00 Erskine 121 20 Feb - 9 Apr 1 May - 4 Jun 33 Monday 11:00 - 12:00 Erskine 111 20 Feb - 9 Apr 1 May - 4 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Tuesday 16:00 - 17:00 Erskine 035 Lab 2 20 Mar - 26 Mar 02 Tuesday 16:30 - 17:30 Erskine 035 Lab 2 20 Mar - 26 Mar 03 Tuesday 17:30 - 18:30 Erskine 035 Lab 2 20 Mar - 26 Mar 04 Tuesday 18:00 - 19:00 Erskine 035 Lab 2 20 Mar - 26 Mar 05 Tuesday 19:00 - 20:00 Erskine 035 Lab 2 20 Mar - 26 Mar 06 Wednesday 15:00 - 16:00 Erskine 035 Lab 2 20 Mar - 26 Mar 07 Wednesday 16:00 - 17:00 Erskine 035 Lab 2 20 Mar - 26 Mar 08 Wednesday 16:30 - 17:30 Erskine 035 Lab 2 20 Mar - 26 Mar 09 Wednesday 17:30 - 18:30 Erskine 035 Lab 2 20 Mar - 26 Mar 10 Wednesday 18:00 - 19:00 Erskine 035 Lab 2 20 Mar - 26 Mar 11 Wednesday 19:00 - 20:00 Erskine 035 Lab 2 20 Mar - 26 Mar 13 Thursday 15:00 - 16:00 Erskine 035 Lab 2 20 Mar - 26 Mar 14 Thursday 16:00 - 17:00 Erskine 035 Lab 2 20 Mar - 26 Mar 15 Thursday 16:30 - 17:30 Erskine 035 Lab 2 20 Mar - 26 Mar 16 Thursday 17:30 - 18:30 Erskine 035 Lab 2 20 Mar - 26 Mar 17 Thursday 18:00 - 19:00 Erskine 035 Lab 2 20 Mar - 26 Mar 18 Thursday 19:00 - 20:00 Erskine 035 Lab 2 20 Mar - 26 Mar Test B 01 Tuesday 18:30 - 20:00 A2 Lecture Theatre (2/5)C3 Lecture Theatre (2/5)A1 Lecture Theatre (2/5)C2 Lecture Theatre (2/5)C1 Lecture Theatre (2/5) 1 May - 7 May

## Assessment

Assessment Due Date Percentage
Tutorial Assessment 10%
MapleTA Test 10%
Mid-course Test 35%
Final Examination 45%

## Textbooks

•“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 \$919.00

International fee \$5,000.00

* 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

• EMTH210-17S1 (C) Semester One 2017