EMTH210-17S1 (C) Semester One 2017

Engineering Mathematics 2

15 points, 0.1250 EFTS
20 Feb 2017 - 25 Jun 2017

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.
  • Be cognizant of characteristic functions, 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 2017

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Tuesday 08:00 - 09:00 A1 Lecture Theatre 20 Feb - 9 Apr
1 May - 4 Jun
02 Tuesday 12:00 - 13:00 C1 Lecture Theatre 20 Feb - 9 Apr
1 May - 4 Jun
Lecture B
Activity Day Time Location Weeks
01 Wednesday 08:00 - 09:00 A1 Lecture Theatre 20 Feb - 9 Apr
1 May - 4 Jun
02 Wednesday 12:00 - 13:00 C1 Lecture Theatre 20 Feb - 9 Apr
1 May - 4 Jun
Lecture C
Activity Day Time Location Weeks
01 Thursday 08:00 - 09:00 A1 Lecture Theatre 20 Feb - 9 Apr
1 May - 4 Jun
02 Thursday 12:00 - 13:00 C1 Lecture Theatre 20 Feb - 9 Apr
1 May - 4 Jun
Lecture D
Activity Day Time Location Weeks
01 Friday 08:00 - 09:00 A1 Lecture Theatre 20 Feb - 9 Apr
1 May - 4 Jun
02 Friday 12:00 - 13:00 C1 Lecture Theatre 20 Feb - 9 Apr
1 May - 4 Jun
Tutorial A
Activity Day Time Location Weeks
01 Monday 11:00 - 12:00 Erskine 240 20 Feb - 9 Apr
1 May - 4 Jun
02 Monday 13:00 - 14:00 Erskine 240 20 Feb - 9 Apr
1 May - 4 Jun
03 Monday 13:00 - 14:00 Erskine 244 20 Feb - 9 Apr
1 May - 4 Jun
04 Monday 14:00 - 15:00 Erskine 244 20 Feb - 9 Apr
1 May - 4 Jun
05 Monday 14:00 - 15:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
06 Monday 15:00 - 16:00 Erskine 241 20 Feb - 9 Apr
1 May - 4 Jun
07 Tuesday 11:00 - 12:00 Erskine 240 20 Feb - 9 Apr
1 May - 4 Jun
08 Tuesday 11:00 - 12:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
09 Tuesday 13:00 - 14:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
10 Tuesday 13:00 - 14:00 Erskine 241 20 Feb - 9 Apr
1 May - 4 Jun
11 Tuesday 14:00 - 15:00 Erskine 446 20 Feb - 9 Apr
1 May - 4 Jun
12 Tuesday 14:00 - 15:00 Erskine 445 20 Feb - 9 Apr
1 May - 4 Jun
13 Monday 12:00 - 13:00 Erskine 111 20 Feb - 9 Apr
1 May - 4 Jun
14 Wednesday 11:00 - 12:00 Erskine 111 20 Feb - 9 Apr
1 May - 4 Jun
15 Wednesday 11:00 - 12:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
16 Wednesday 13:00 - 14:00 Erskine 240 20 Feb - 9 Apr
1 May - 4 Jun
17 Wednesday 13:00 - 14:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
18 Wednesday 14:00 - 15:00 Erskine 445 20 Feb - 9 Apr
1 May - 4 Jun
19 Monday 16:00 - 17:00 Erskine 446 20 Feb - 9 Apr
1 May - 4 Jun
20 Wednesday 15:00 - 16:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
21 Thursday 11:00 - 12:00 Erskine 241 20 Feb - 9 Apr
1 May - 4 Jun
22 Thursday 11:00 - 12:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
23 Thursday 13:00 - 14:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
24 Thursday 13:00 - 14:00 Erskine 445 20 Feb - 9 Apr
1 May - 4 Jun
25 Thursday 14:00 - 15:00 Erskine 445 20 Feb - 9 Apr
1 May - 4 Jun
26 Thursday 14:00 - 15:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
27 Friday 11:00 - 12:00 Erskine 241 20 Feb - 9 Apr
1 May - 4 Jun
28 Friday 10:00 - 11:00 Erskine 121 20 Feb - 9 Apr
1 May - 4 Jun
29 Friday 11:00 - 12:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
30 Friday 13:00 - 14:00 Erskine 441 20 Feb - 9 Apr
1 May - 4 Jun
31 Friday 14:00 - 15:00 Erskine 242 20 Feb - 9 Apr
1 May - 4 Jun
32 Monday 12:00 - 13:00 Erskine 121 20 Feb - 9 Apr
1 May - 4 Jun
33 Monday 11:00 - 12:00 Erskine 111 20 Feb - 9 Apr
1 May - 4 Jun

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
01 Tuesday 16:00 - 17:00 Erskine 035 Lab 2 20 Mar - 26 Mar
02 Tuesday 16:30 - 17:30 Erskine 035 Lab 2 20 Mar - 26 Mar
03 Tuesday 17:30 - 18:30 Erskine 035 Lab 2 20 Mar - 26 Mar
04 Tuesday 18:00 - 19:00 Erskine 035 Lab 2 20 Mar - 26 Mar
05 Tuesday 19:00 - 20:00 Erskine 035 Lab 2 20 Mar - 26 Mar
06 Wednesday 15:00 - 16:00 Erskine 035 Lab 2 20 Mar - 26 Mar
07 Wednesday 16:00 - 17:00 Erskine 035 Lab 2 20 Mar - 26 Mar
08 Wednesday 16:30 - 17:30 Erskine 035 Lab 2 20 Mar - 26 Mar
09 Wednesday 17:30 - 18:30 Erskine 035 Lab 2 20 Mar - 26 Mar
10 Wednesday 18:00 - 19:00 Erskine 035 Lab 2 20 Mar - 26 Mar
11 Wednesday 19:00 - 20:00 Erskine 035 Lab 2 20 Mar - 26 Mar
13 Thursday 15:00 - 16:00 Erskine 035 Lab 2 20 Mar - 26 Mar
14 Thursday 16:00 - 17:00 Erskine 035 Lab 2 20 Mar - 26 Mar
15 Thursday 16:30 - 17:30 Erskine 035 Lab 2 20 Mar - 26 Mar
16 Thursday 17:30 - 18:30 Erskine 035 Lab 2 20 Mar - 26 Mar
17 Thursday 18:00 - 19:00 Erskine 035 Lab 2 20 Mar - 26 Mar
18 Thursday 19:00 - 20:00 Erskine 035 Lab 2 20 Mar - 26 Mar
Test B
Activity Day Time Location Weeks
01 Tuesday 18:30 - 20:00 A2 Lecture Theatre (2/5)
C3 Lecture Theatre (2/5)
A1 Lecture Theatre (2/5)
C2 Lecture Theatre (2/5)
C1 Lecture Theatre (2/5)
1 May - 7 May

Course Coordinator / Lecturer

Chris Price (MATH)

Course Administrator

Phillipa Gourdie

Lecturers

Phillip Wilson and Blair Robertson

Assessment

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

Textbooks

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 $919.00

International fee $5,000.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

All EMTH210 Occurrences

  • EMTH210-17S1 (C) Semester One 2017