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.

Lecture A
Activity Day Time Location Weeks
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
Activity Day Time Location Weeks
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
Activity Day Time Location Weeks
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
Activity Day Time Location Weeks
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
Activity Day Time Location Weeks
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

Test A
Activity Day Time Location Weeks
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
Activity Day Time Location Weeks
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

Course Coordinator / Lecturer

Phillip Wilson

Lecturer

Michael Langton

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

Recommended Reading:
•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