EMTH210-21S1 (C) Semester One 2021

# Engineering Mathematics 2

15 points

Details:
 Start Date: Monday, 22 February 2021 End Date: Sunday, 27 June 2021
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 7 March 2021
• Without academic penalty (including no fee refund): Friday, 14 May 2021

## 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.
• Work with 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 2021

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 08:00 - 09:00 C1 Lecture Theatre 22 Feb - 4 Apr 3 May - 6 Jun 02 Monday 13:00 - 14:00 A1 Lecture Theatre 22 Feb - 4 Apr 3 May - 6 Jun Lecture B 01 Wednesday 08:00 - 09:00 C1 Lecture Theatre 22 Feb - 4 Apr 26 Apr - 6 Jun 02 Wednesday 13:00 - 14:00 A1 Lecture Theatre 22 Feb - 4 Apr 26 Apr - 6 Jun Lecture C 01 Thursday 08:00 - 09:00 Haere-roa 118 Ngaio Marsh Theatre (25/2) A1 Lecture Theatre (4/3-1/4, 29/4-3/6) 22 Feb - 4 Apr 26 Apr - 6 Jun 02 Thursday 13:00 - 14:00 A1 Lecture Theatre 22 Feb - 4 Apr 26 Apr - 6 Jun Lecture D 01 Friday 08:00 - 09:00 C1 Lecture Theatre 22 Feb - 28 Mar 26 Apr - 6 Jun 02 Friday 13:00 - 14:00 A1 Lecture Theatre 22 Feb - 28 Mar 26 Apr - 6 Jun Tutorial A 01 Monday 09:00 - 10:00 Eng Core 129 Meeting Room 22 Feb - 4 Apr 3 May - 6 Jun 02 Monday 10:00 - 11:00 Eng Core 129 Meeting Room 22 Feb - 4 Apr 3 May - 6 Jun 03 Monday 11:00 - 12:00 Jack Erskine 242 22 Feb - 4 Apr 3 May - 6 Jun 04 Monday 13:00 - 14:00 Eng Core 128 Meeting Room 22 Feb - 4 Apr 3 May - 6 Jun 05 Monday 14:00 - 15:00 E13 22 Feb - 4 Apr 3 May - 6 Jun 06 Tuesday 09:00 - 10:00 Eng Core 129 Meeting Room 22 Feb - 4 Apr 26 Apr - 6 Jun 07 Tuesday 12:00 - 13:00 Psychology - Sociology 413 22 Feb - 4 Apr 26 Apr - 6 Jun 08 Tuesday 10:00 - 11:00 Eng Core 128 Meeting Room 22 Feb - 4 Apr 26 Apr - 6 Jun 09 Tuesday 11:00 - 12:00 E12 22 Feb - 4 Apr 26 Apr - 6 Jun 10 Tuesday 12:00 - 13:00 Eng Core 128 Meeting Room 22 Feb - 4 Apr 26 Apr - 6 Jun 11 Tuesday 15:00 - 16:00 Psychology - Sociology 413 22 Feb - 4 Apr 26 Apr - 6 Jun 12 Tuesday 14:00 - 15:00 Psychology - Sociology 413 22 Feb - 4 Apr 26 Apr - 6 Jun 13 Wednesday 09:00 - 10:00 Eng Core 128 Meeting Room 22 Feb - 4 Apr 26 Apr - 6 Jun 14 Wednesday 10:00 - 11:00 Eng Core 128 Meeting Room 22 Feb - 4 Apr 26 Apr - 6 Jun 15 Wednesday 11:00 - 12:00 Jack Erskine 241 22 Feb - 4 Apr 26 Apr - 6 Jun 16 Wednesday 12:00 - 13:00 Jack Erskine 239 22 Feb - 4 Apr 26 Apr - 6 Jun 17 Wednesday 14:00 - 15:00 Jack Erskine 239 22 Feb - 4 Apr 26 Apr - 6 Jun 18 Wednesday 15:00 - 16:00 Eng Core 128 Meeting Room 22 Feb - 4 Apr 26 Apr - 6 Jun 19 Friday 13:00 - 14:00 Eng Core 128 Meeting Room 22 Feb - 28 Mar 26 Apr - 6 Jun 20 Thursday 09:00 - 10:00 Eng Core 129 Meeting Room 22 Feb - 4 Apr 26 Apr - 6 Jun 21 Thursday 10:00 - 11:00 Eng Core 129 Meeting Room 22 Feb - 4 Apr 26 Apr - 6 Jun 22 Thursday 11:00 - 12:00 Psychology - Sociology 307 22 Feb - 4 Apr 26 Apr - 6 Jun 23 Thursday 12:00 - 13:00 James Logie 105 22 Feb - 4 Apr 26 Apr - 6 Jun 24 Thursday 14:00 - 15:00 Psychology - Sociology 307 22 Feb - 4 Apr 26 Apr - 6 Jun 25 Thursday 15:00 - 16:00 James Logie 105 22 Feb - 4 Apr 26 Apr - 6 Jun 26 Tuesday 13:00 - 14:00 Psychology - Sociology 413 22 Feb - 4 Apr 26 Apr - 6 Jun 27 Friday 09:00 - 10:00 Eng Core 129 Meeting Room 22 Feb - 28 Mar 26 Apr - 6 Jun 28 Friday 10:00 - 11:00 Eng Core 128 Meeting Room 22 Feb - 28 Mar 26 Apr - 6 Jun 29 Friday 11:00 - 12:00 Eng Core 129 Meeting Room 22 Feb - 28 Mar 26 Apr - 6 Jun 30 Friday 12:00 - 13:00 Eng Core 129 Meeting Room 22 Feb - 28 Mar 26 Apr - 6 Jun 31 Friday 14:00 - 15:00 Eng Core 128 Meeting Room 22 Feb - 28 Mar 26 Apr - 6 Jun 32 Friday 15:00 - 16:00 Eng Core 129 Meeting Room 22 Feb - 28 Mar 26 Apr - 6 Jun 33 Friday 10:00 - 11:00 Jack Erskine 240 22 Feb - 28 Mar 26 Apr - 6 Jun 34 Friday 15:00 - 16:00 Jack Erskine 443 22 Feb - 28 Mar 26 Apr - 6 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Tuesday 17:00 - 18:00 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 02 Tuesday 17:30 - 18:30 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 03 Tuesday 18:30 - 19:30 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 04 Tuesday 19:00 - 20:00 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 05 Wednesday 17:00 - 18:00 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 06 Wednesday 17:30 - 18:30 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 07 Wednesday 18:30 - 19:30 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 08 Wednesday 19:00 - 20:00 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 09 Wednesday 20:00 - 21:00 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 10 Thursday 17:00 - 18:00 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 11 Thursday 17:30 - 18:30 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 12 Thursday 18:30 - 19:30 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 13 Thursday 19:00 - 20:00 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 14 Thursday 20:00 - 21:00 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 15 Friday 16:00 - 17:00 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 16 Friday 16:30 - 17:30 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 17 Friday 17:30 - 18:30 Jack Erskine 035 Lab 2 22 Mar - 28 Mar 18 Friday 18:30 - 19:30 Jack Erskine 035 Lab 2 22 Mar - 28 Mar Test B 01 Thursday 19:00 - 20:30 C1 Lecture Theatre 26 Apr - 2 May 02 Thursday 19:00 - 20:30 C2 Lecture Theatre 26 Apr - 2 May 03 Thursday 19:00 - 20:30 C3 Lecture Theatre 26 Apr - 2 May 04 Thursday 19:00 - 20:30 E8 Lecture Theatre 26 Apr - 2 May 05 Thursday 19:00 - 20:30 E7 Lecture Theatre 26 Apr - 2 May 06 Thursday 19:00 - 20:30 Eng Core 222 & 223 Drawing Office 26 Apr - 2 May

## Assessment

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

To pass the course, there is a minimum mark required in the Final Examination of 40%, as well as achieving 50% or more in total across all the assessments.

## Textbooks / Resources

Kreyszig, Erwin. , Kreyszig, Herbert., Norminton, E. J; Advanced engineering mathematics ; 10th ed; John Wiley, 2011.

Zill, Dennis G. , Cullen, Michael R; Advanced engineering mathematics ; 3rd ed; Jones and Bartlett Publishers, 2006.

Zill, Dennis G. , Wright, Warren S., Cullen, Michael R; Advanced engineering mathematics ; 4th ed; Jones and Bartlett Publishers, 2011.

•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 \$986.00

International fee \$5,500.00

* 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

• EMTH210-21S1 (C) Semester One 2021