EMTH210-24S1 (C) Semester One 2024

# Engineering Mathematics 2

15 points

Details:
 Start Date: Monday, 19 February 2024 End Date: Sunday, 23 June 2024
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 3 March 2024
• Without academic penalty (including no fee refund): Sunday, 12 May 2024

## 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.

## Prerequisites

Subject to approval of the Dean of Engineering and Forestry

## Restrictions

EMTH202, EMTH204, MATH201, MATH261, MATH262, MATH264

## Timetable 2024

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 10:00 - 11:00 A1 Lecture Theatre 19 Feb - 31 Mar 22 Apr - 2 Jun 02 Monday 13:00 - 14:00 C1 Lecture Theatre 19 Feb - 31 Mar 22 Apr - 2 Jun 03 Monday 13:00 - 14:00 Online Delivery 26 Feb - 31 Mar 22 Apr - 2 Jun Lecture B 01 Tuesday 09:00 - 10:00 C1 Lecture Theatre 19 Feb - 31 Mar 22 Apr - 2 Jun 02 Tuesday 13:00 - 14:00 C1 Lecture Theatre 19 Feb - 31 Mar 22 Apr - 2 Jun 03 Tuesday 13:00 - 14:00 Online Delivery 26 Feb - 31 Mar 22 Apr - 2 Jun Lecture C 01 Thursday 09:00 - 10:00 C1 Lecture Theatre 19 Feb - 31 Mar 29 Apr - 2 Jun 02 Thursday 13:00 - 14:00 C1 Lecture Theatre 19 Feb - 31 Mar 29 Apr - 2 Jun 03 Wednesday 13:00 - 14:00 Online Delivery 26 Feb - 31 Mar 22 Apr - 2 Jun Lecture D 01 Friday 10:00 - 11:00 C1 Lecture Theatre 19 Feb - 24 Mar 22 Apr - 2 Jun 02 Friday 13:00 - 14:00 C1 Lecture Theatre 19 Feb - 24 Mar 22 Apr - 2 Jun 03 Friday 13:00 - 14:00 Online Delivery 19 Feb - 24 Mar 22 Apr - 2 Jun Drop in Class A 01 Monday 16:00 - 18:00 Jack Erskine 443 19 Feb - 31 Mar 22 Apr - 2 Jun 02 Tuesday 16:00 - 18:00 Jack Erskine 443 19 Feb - 31 Mar 22 Apr - 2 Jun 03 Wednesday 16:00 - 18:00 Jack Erskine 443 19 Feb - 31 Mar 22 Apr - 2 Jun 04 Thursday 16:00 - 18:00 Jack Erskine 443 19 Feb - 31 Mar 29 Apr - 2 Jun 05 Friday 16:00 - 18:00 Jack Erskine 443 19 Feb - 24 Mar 22 Apr - 2 Jun Tutorial A 01 Tuesday 14:00 - 15:00 Psychology - Sociology 213 19 Feb - 31 Mar 22 Apr - 2 Jun 02 Monday 12:00 - 13:00 Psychology - Sociology 213 19 Feb - 31 Mar 22 Apr - 2 Jun 03 Thursday 15:00 - 16:00 Psychology - Sociology 413 19 Feb - 31 Mar 29 Apr - 2 Jun 04 Monday 15:00 - 16:00 Psychology - Sociology 411 19 Feb - 31 Mar 22 Apr - 2 Jun 05 Tuesday 14:00 - 15:00 Psychology - Sociology 411 19 Feb - 31 Mar 22 Apr - 2 Jun 06 Wednesday 11:00 - 12:00 Psychology - Sociology 411 19 Feb - 31 Mar 22 Apr - 2 Jun 07 Wednesday 14:00 - 15:00 Psychology - Sociology 251 19 Feb - 31 Mar 22 Apr - 2 Jun 08 Wednesday 10:00 - 11:00 Psychology - Sociology 413 19 Feb - 31 Mar 22 Apr - 2 Jun 09 Thursday 12:00 - 13:00 Psychology - Sociology 413 19 Feb - 31 Mar 29 Apr - 2 Jun 10 Wednesday 15:00 - 16:00 Psychology - Sociology 251 19 Feb - 31 Mar 22 Apr - 2 Jun 11 Wednesday 15:00 - 16:00 Psychology - Sociology 413 19 Feb - 31 Mar 22 Apr - 2 Jun 12 Wednesday 12:00 - 13:00 Psychology - Sociology 251 19 Feb - 31 Mar 22 Apr - 2 Jun 13 Monday 14:00 - 15:00 Psychology - Sociology 213 19 Feb - 31 Mar 22 Apr - 2 Jun 14 Friday 14:00 - 15:00 Psychology - Sociology 251 19 Feb - 24 Mar 22 Apr - 2 Jun 15 Tuesday 12:00 - 13:00 Psychology - Sociology 413 19 Feb - 31 Mar 22 Apr - 2 Jun 16 Thursday 14:00 - 15:00 Psychology - Sociology 213 19 Feb - 31 Mar 29 Apr - 2 Jun 17 Wednesday 10:00 - 11:00 Psychology - Sociology 411 19 Feb - 31 Mar 22 Apr - 2 Jun 18 Wednesday 11:00 - 12:00 Psychology - Sociology 251 19 Feb - 31 Mar 22 Apr - 2 Jun 19 Monday 11:00 - 12:00 Psychology - Sociology 411 19 Feb - 31 Mar 22 Apr - 2 Jun 20 Tuesday 10:00 - 11:00 Psychology - Sociology 251 19 Feb - 31 Mar 22 Apr - 2 Jun 21 Wednesday 14:00 - 15:00 Psychology - Sociology 307 19 Feb - 31 Mar 22 Apr - 2 Jun 22 Monday 15:00 - 16:00 Psychology - Sociology 307 19 Feb - 31 Mar 22 Apr - 2 Jun 23 Tuesday 11:00 - 12:00 Psychology - Sociology 213 19 Feb - 31 Mar 22 Apr - 2 Jun 24 Monday 11:00 - 12:00 Psychology - Sociology 213 19 Feb - 31 Mar 22 Apr - 2 Jun 25 Friday 15:00 - 16:00 Psychology - Sociology 413 19 Feb - 24 Mar 22 Apr - 2 Jun 26 Monday 12:00 - 13:00 Psychology - Sociology 251 19 Feb - 31 Mar 22 Apr - 2 Jun 27 Thursday 11:00 - 12:00 Psychology - Sociology 413 19 Feb - 31 Mar 29 Apr - 2 Jun 28 Wednesday 13:00 - 14:00 Psychology - Sociology 251 19 Feb - 31 Mar 22 Apr - 2 Jun 29 Friday 12:00 - 13:00 Psychology - Sociology 307 19 Feb - 24 Mar 22 Apr - 2 Jun 30 Friday 15:00 - 16:00 Psychology - Sociology 213 19 Feb - 24 Mar 22 Apr - 2 Jun 31 Friday 14:00 - 15:00 Psychology - Sociology 413 19 Feb - 24 Mar 22 Apr - 2 Jun 32 Thursday 10:00 - 11:00 Psychology - Sociology 411 19 Feb - 31 Mar 29 Apr - 2 Jun 33 Friday 11:00 - 12:00 Psychology - Sociology 213 19 Feb - 24 Mar 22 Apr - 2 Jun 34 Tuesday 15:00 - 16:00 Psychology - Sociology 413 19 Feb - 31 Mar 22 Apr - 2 Jun 35 Monday 14:00 - 15:00 Psychology - Sociology 456 19 Feb - 31 Mar 22 Apr - 2 Jun 36 Tuesday 15:00 - 16:00 Psychology - Sociology 213 19 Feb - 31 Mar 22 Apr - 2 Jun 37 Thursday 11:00 - 12:00 Psychology - Sociology 213 19 Feb - 31 Mar 29 Apr - 2 Jun 38 Wednesday 09:00 - 10:00 Psychology - Sociology 307 19 Feb - 31 Mar 22 Apr - 2 Jun 39 Tuesday 10:00 - 11:00 Psychology - Sociology 413 19 Feb - 31 Mar 22 Apr - 2 Jun 40 Tuesday 12:00 - 13:00 Psychology - Sociology 213 19 Feb - 31 Mar 22 Apr - 2 Jun 41 Wednesday 12:00 - 13:00 Psychology - Sociology 213 19 Feb - 31 Mar 22 Apr - 2 Jun 42 Wednesday 13:00 - 14:00 Psychology - Sociology 213 19 Feb - 31 Mar 22 Apr - 2 Jun 43 Thursday 14:00 - 15:00 Psychology - Sociology 307 19 Feb - 31 Mar 29 Apr - 2 Jun 44 Wednesday 09:00 - 10:00 Psychology - Sociology 251 19 Feb - 31 Mar 22 Apr - 2 Jun

## Examinations, Quizzes and Formal Tests

Activity Day Time Location Weeks Test A 01 Friday 19:00 - 20:30 C1 Lecture Theatre 22 Apr - 28 Apr 02 Friday 19:00 - 20:30 C2 Lecture Theatre 22 Apr - 28 Apr 03 Friday 19:00 - 20:30 C3 Lecture Theatre 22 Apr - 28 Apr 04 Friday 19:00 - 20:30 A1 Lecture Theatre 22 Apr - 28 Apr 05 Friday 19:00 - 20:30 A2 Lecture Theatre 22 Apr - 28 Apr 06 Friday 19:00 - 20:30 Meremere 108 Lecture Theatre 22 Apr - 28 Apr Test B 01 Thursday 19:00 - 20:30 A1 Lecture Theatre 20 May - 26 May

## Assessment

Assessment Due Date Percentage
Tutorials 10%
Quizzes 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 \$1,059.00

International fee \$6,000.00

* 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

• EMTH210-24S1 (C) Semester One 2024