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.

Lecture A
Activity Day Time Location Weeks
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
Activity Day Time Location Weeks
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
Activity Day Time Location Weeks
01 Thursday 09:00 - 10:00 C1 Lecture Theatre
19 Feb - 31 Mar
22 Apr - 2 Jun
02 Thursday 13:00 - 14:00 C1 Lecture Theatre
19 Feb - 31 Mar
22 Apr - 2 Jun
03 Wednesday 13:00 - 14:00 Online Delivery
26 Feb - 31 Mar
22 Apr - 2 Jun
Lecture D
Activity Day Time Location Weeks
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 - 31 Mar
22 Apr - 2 Jun
Drop in Class A
Activity Day Time Location Weeks
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
22 Apr - 2 Jun
05 Friday 16:00 - 18:00 Jack Erskine 443
19 Feb - 24 Mar
22 Apr - 2 Jun
Tutorial A
Activity Day Time Location Weeks
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
22 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
22 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
22 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
22 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
22 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
22 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
22 Apr - 2 Jun
44 Wednesday 09:00 - 10:00 Psychology - Sociology 251
19 Feb - 31 Mar
22 Apr - 2 Jun

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
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 K1 Lecture Theatre
22 Apr - 28 Apr

Course Coordinator

Michael Langton

Lecturer

Chris Stevens

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

Recommended Reading

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