EMTH210-22S1 (C) Semester One 2022

# Engineering Mathematics 2

15 points

Details:
 Start Date: Monday, 21 February 2022 End Date: Sunday, 26 June 2022
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 6 March 2022
• Without academic penalty (including no fee refund): Sunday, 15 May 2022

## 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 2022

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 11:00 - 12:00 C1 Lecture Theatre 21 Feb - 10 Apr 2 May - 5 Jun 02 Monday 13:00 - 14:00 A1 Lecture Theatre 21 Feb - 10 Apr 2 May - 5 Jun Lecture B 01 Tuesday 11:00 - 12:00 A1 Lecture Theatre 21 Feb - 10 Apr 2 May - 5 Jun 02 Tuesday 13:00 - 14:00 A1 Lecture Theatre 21 Feb - 10 Apr 2 May - 5 Jun Lecture C 01 Thursday 11:00 - 12:00 C1 Lecture Theatre 21 Feb - 10 Apr 2 May - 5 Jun 02 Thursday 13:00 - 14:00 A1 Lecture Theatre 21 Feb - 10 Apr 2 May - 5 Jun Lecture D 01 Friday 12:00 - 13:00 C1 Lecture Theatre 21 Feb - 10 Apr 2 May - 5 Jun 02 Friday 14:00 - 15:00 A1 Lecture Theatre 21 Feb - 10 Apr 2 May - 5 Jun Tutorial A 01 Monday 08:00 - 09:00 Eng Core 128 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun 02 Monday 08:00 - 09:00 Jack Erskine 240 21 Feb - 10 Apr 2 May - 5 Jun 03 Monday 12:00 - 13:00 Eng Core 128 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun 04 Monday 12:00 - 13:00 Eng Core 129 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun 05 Monday 15:00 - 16:00 Eng Core 128 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun 06 Monday 15:00 - 16:00 Eng Core 129 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun 07 Monday 16:00 - 17:00 Psychology - Sociology 213 21 Feb - 10 Apr 2 May - 5 Jun 08 Monday 16:00 - 17:00 Karl Popper 413 21 Feb - 10 Apr 2 May - 5 Jun 09 Monday 17:00 - 18:00 Psychology - Sociology 213 21 Feb - 10 Apr 2 May - 5 Jun 10 Monday 17:00 - 18:00 Psychology - Sociology 251 21 Feb - 10 Apr 2 May - 5 Jun 11 Tuesday 09:00 - 10:00 Meremere 409 21 Feb - 10 Apr 2 May - 5 Jun 12 Tuesday 09:00 - 10:00 Psychology - Sociology 213 21 Feb - 10 Apr 2 May - 5 Jun 13 Tuesday 10:00 - 11:00 E13 21 Feb - 10 Apr 2 May - 5 Jun 14 Tuesday 10:00 - 11:00 Psychology - Sociology 213 21 Feb - 10 Apr 2 May - 5 Jun 15 Tuesday 11:00 - 12:00 Meremere 409 21 Feb - 10 Apr 2 May - 5 Jun 16 Tuesday 11:00 - 12:00 Psychology - Sociology 307 21 Feb - 10 Apr 2 May - 5 Jun 17 Tuesday 12:00 - 13:00 Eng Core 128 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun 18 Tuesday 12:00 - 13:00 Psychology - Sociology 213 21 Feb - 10 Apr 2 May - 5 Jun 19 Tuesday 15:00 - 16:00 Meremere 409 21 Feb - 10 Apr 2 May - 5 Jun 20 Tuesday 16:00 - 17:00 Meremere 409 21 Feb - 10 Apr 2 May - 5 Jun 21 Tuesday 17:00 - 18:00 Psychology - Sociology 213 21 Feb - 10 Apr 2 May - 5 Jun 22 Tuesday 17:00 - 18:00 Psychology - Sociology 307 21 Feb - 10 Apr 2 May - 5 Jun 23 Wednesday 08:00 - 09:00 Psychology - Sociology 411 21 Feb - 10 Apr 2 May - 5 Jun 24 Wednesday 08:00 - 09:00 Psychology - Sociology 213 21 Feb - 10 Apr 2 May - 5 Jun 25 Wednesday 14:00 - 15:00 James Logie 104 21 Feb - 10 Apr 2 May - 5 Jun 26 Thursday 08:00 - 09:00 Jack Erskine 241 21 Feb - 10 Apr 2 May - 5 Jun 27 Thursday 08:00 - 09:00 Psychology - Sociology 413 21 Feb - 10 Apr 2 May - 5 Jun 28 Thursday 09:00 - 10:00 Psychology - Sociology 411 21 Feb - 10 Apr 2 May - 5 Jun 29 Thursday 12:00 - 13:00 E13 21 Feb - 10 Apr 2 May - 5 Jun 30 Thursday 12:00 - 13:00 Eng Core 128 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun 31 Friday 08:00 - 09:00 Jack Erskine 241 21 Feb - 10 Apr 2 May - 5 Jun 32 Friday 08:00 - 09:00 Psychology - Sociology 413 21 Feb - 10 Apr 2 May - 5 Jun 33 Friday 15:00 - 16:00 Karl Popper 508 21 Feb - 10 Apr 2 May - 5 Jun 34 Friday 15:00 - 16:00 Eng Core 129 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun 35 Friday 16:00 - 17:00 Eng Core 128 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun 36 Friday 16:00 - 17:00 Psychology - Sociology 213 21 Feb - 10 Apr 2 May - 5 Jun 37 Friday 17:00 - 18:00 Eng Core 129 Tutorial Room 21 Feb - 10 Apr 2 May - 5 Jun

## 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 (This text also covers the statistics material).

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.

## Indicative Fees

Domestic fee \$1,002.00

International fee \$5,625.00

* 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

• EMTH210-22S1 (C) Semester One 2022