EMTH210-23S1 (C) Semester One 2023

# Engineering Mathematics 2

15 points

Details:
 Start Date: Monday, 20 February 2023 End Date: Sunday, 25 June 2023
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 5 March 2023
• Without academic penalty (including no fee refund): Sunday, 14 May 2023

## 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 2023

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 10:00 - 11:00 A1 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun 02 Monday 13:00 - 14:00 A1 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun Lecture B 01 Tuesday 11:00 - 12:00 A1 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun 02 Tuesday 13:00 - 14:00 A1 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun Lecture C 01 Wednesday 10:00 - 11:00 K1 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun 02 Wednesday 13:00 - 14:00 K1 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun Lecture D 01 Thursday 10:00 - 11:00 A1 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun 02 Thursday 13:00 - 14:00 A1 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun Drop in Class A 01 Monday 15:00 - 18:00 Jack Erskine 340 24 Apr - 30 Apr 02 Thursday 15:00 - 18:00 Jack Erskine 446 24 Apr - 30 Apr 03 Friday 15:00 - 18:00 Jack Erskine 446 24 Apr - 30 Apr 04 Wednesday 15:00 - 18:00 Jack Erskine 340 24 Apr - 30 Apr Tutorial A 01 Tuesday 12:00 - 13:00 Jack Erskine 241 20 Feb - 2 Apr 24 Apr - 4 Jun 02 Monday 14:00 - 15:00 Jack Erskine 241 20 Feb - 2 Apr 24 Apr - 4 Jun 03 Monday 15:00 - 16:00 Jack Erskine 242 20 Feb - 2 Apr 24 Apr - 4 Jun 04 Monday 14:00 - 15:00 Jack Erskine 240 20 Feb - 2 Apr 24 Apr - 4 Jun 05 Monday 16:00 - 17:00 Jack Erskine 242 20 Feb - 2 Apr 24 Apr - 4 Jun 06 Monday 16:00 - 17:00 Jack Erskine 241 20 Feb - 2 Apr 24 Apr - 4 Jun 07 Tuesday 15:00 - 16:00 Jack Erskine 242 20 Feb - 2 Apr 24 Apr - 4 Jun 08 Tuesday 15:00 - 16:00 Jack Erskine 240 20 Feb - 2 Apr 24 Apr - 4 Jun 09 Tuesday 16:00 - 17:00 Jack Erskine 241 20 Feb - 2 Apr 24 Apr - 4 Jun 10 Tuesday 16:00 - 17:00 Jack Erskine 240 20 Feb - 2 Apr 24 Apr - 4 Jun 11 Friday 15:00 - 16:00 Rata 128 Tutorial Room 20 Feb - 2 Apr 24 Apr - 4 Jun 12 Tuesday 14:00 - 15:00 Jack Erskine 235 20 Feb - 2 Apr 24 Apr - 4 Jun 13 Wednesday 15:00 - 16:00 Jack Erskine 242 20 Feb - 2 Apr 24 Apr - 4 Jun 14 Wednesday 15:00 - 16:00 Jack Erskine 241 20 Feb - 2 Apr 24 Apr - 4 Jun 15 Wednesday 16:00 - 17:00 Jack Erskine 240 20 Feb - 2 Apr 24 Apr - 4 Jun 16 Wednesday 16:00 - 17:00 Jack Erskine 242 20 Feb - 2 Apr 24 Apr - 4 Jun 17 Thursday 12:00 - 13:00 - 20 Feb - 2 Apr 24 Apr - 4 Jun 18 Thursday 13:00 - 14:00 - 20 Feb - 2 Apr 24 Apr - 4 Jun 19 Thursday 15:00 - 16:00 Jack Erskine 242 20 Feb - 2 Apr 24 Apr - 4 Jun 20 Thursday 15:00 - 16:00 Jack Erskine 239 20 Feb - 2 Apr 24 Apr - 4 Jun 21 Thursday 16:00 - 17:00 Jack Erskine 241 20 Feb - 2 Apr 24 Apr - 4 Jun 22 Thursday 16:00 - 17:00 Jack Erskine 240 20 Feb - 2 Apr 24 Apr - 4 Jun 24 Thursday 14:00 - 15:00 Jack Erskine 242 20 Feb - 2 Apr 24 Apr - 4 Jun 25 Monday 15:00 - 16:00 Jack Erskine 235 20 Feb - 2 Apr 24 Apr - 4 Jun 26 Friday 09:00 - 10:00 Rata 128 Tutorial Room 20 Feb - 2 Apr 24 Apr - 4 Jun 27 Friday 09:00 - 10:00 Meremere 409 20 Feb - 2 Apr 24 Apr - 4 Jun 28 Friday 10:00 - 11:00 Rata 128 Tutorial Room 20 Feb - 2 Apr 24 Apr - 4 Jun 29 Friday 10:00 - 11:00 Meremere 409 20 Feb - 2 Apr 24 Apr - 4 Jun 30 Friday 11:00 - 12:00 Rata 128 Tutorial Room 20 Feb - 2 Apr 24 Apr - 4 Jun 31 Friday 11:00 - 12:00 Meremere 409 20 Feb - 2 Apr 24 Apr - 4 Jun 32 Friday 12:00 - 13:00 Rata 128 Tutorial Room 20 Feb - 2 Apr 24 Apr - 4 Jun 33 Friday 12:00 - 13:00 Meremere 409 20 Feb - 2 Apr 24 Apr - 4 Jun 34 Tuesday 13:00 - 14:00 Jack Erskine 235 20 Feb - 2 Apr 24 Apr - 4 Jun 35 Friday 14:00 - 15:00 Psychology - Sociology 307 20 Feb - 2 Apr 24 Apr - 4 Jun 36 Friday 13:00 - 14:00 Meremere 409 20 Feb - 2 Apr 24 Apr - 4 Jun 37 Friday 13:00 - 14:00 Rata 129 Tutorial Room 20 Feb - 2 Apr 24 Apr - 4 Jun 38 Friday 14:00 - 15:00 Rata 128 Tutorial Room 20 Feb - 2 Apr 24 Apr - 4 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Friday 18:30 - 20:00 C1 Lecture Theatre 24 Apr - 30 Apr 02 Friday 18:30 - 20:00 C2 Lecture Theatre 24 Apr - 30 Apr 03 Friday 18:30 - 20:00 C3 Lecture Theatre 24 Apr - 30 Apr 04 Friday 18:30 - 20:00 A1 Lecture Theatre 24 Apr - 30 Apr 05 Friday 18:30 - 20:00 A4 Lecture Theatre 24 Apr - 30 Apr 06 Monday 16:00 - 18:00 Jack Erskine 235 8 May - 14 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 \$1,030.00

International fee \$5,750.00

* 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

• EMTH210-23S1 (C) Semester One 2023