EMTH119-18S2 (C) Semester Two 2018

# Engineering Mathematics 1B

 15 points, 0.1250 EFTS16 Jul 2018 - 18 Nov 2018

## Description

A continuation of EMTH118. Topics covered include methods and Engineering applications of calculus, differential equations, and linear algebra, along with an introduction to probability. This course is a prerequisite for many courses in engineering mathematics and other subjects at 200 level.

EMTH119 consolidates concepts from EMTH118 and introduces more advanced ideas in calculus and linear algebra. It includes applications of this mathematics to applied and engineering problems.
It also incorporates some study of probability. It is a prerequisite for many courses in engineering mathematics and other subjects at the  200-level.

Topics:
First-order ordinary differential equations with applications. Review of complex numbers. Second-order ordinary differential equations with applications.
Introduction to convergence of sequences and series. Applications of differentiation to approximation. Approximation by Taylor polynomials. Landau’s notation and order of magnitude.
Determinants, eigenvalues and eigenvectors.
Probability. Sets and probability. Discrete random variables. Continuous random variables. Expectation, mean, and variance.
Techniques and applications of integration. Integration of rational functions. Arc length. Improper integrals.
Multivariate differentiation and classification of critical points.

## Learning Outcomes

Students who have succeeded in this course will be able to

• use calculus, algebra or probability to
- evaluate integrals arising in mathematics and engineering
- solve first and second order differential equations
- find Taylor approximations to functions
- calculate mean and variance of random variables and solve probability problems arising in engineering applications
- calculate determinants, eigenvalues and eigenvectors
- investigate the geometry of multivariable functions and classify critical points
• demonstrate understanding of the mathematical topics in the course by
- giving definitions of fundamental concepts
- competent manipulation of functions, matrices, random variables and complex numbers
- choosing effective solution techniques for given problems
- verifying correctness of mathematical calculations
• describe and interpret the meaning of mathematical solutions to engineering problems (particularly differential equations and random variables)
• synthesise material from different sections of course (for example, using integration techniques and limit evaluation to solve differential equation or probability problems)

This course will provide students with an opportunity to develop the Graduate Attributes specified below:

 Critically competent in a core academic discipline of their award Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

## Restrictions

MATH103, MATH109, MATH199

## Timetable 2018

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 08:00 - 09:00 A1 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct 02 Monday 12:00 - 13:00 A1 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct Lecture B 01 Tuesday 08:00 - 09:00 A1 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct 02 Tuesday 12:00 - 13:00 A1 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct Lecture C 01 Wednesday 08:00 - 09:00 A1 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct 02 Wednesday 12:00 - 13:00 A1 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct Lecture D 01 Thursday 08:00 - 09:00 A1 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct 02 Thursday 12:00 - 13:00 A1 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct Tutorial A 01 Monday 09:00 - 10:00 Jack Erskine 241 23 Jul - 26 Aug 10 Sep - 21 Oct 02 Monday 09:00 - 10:00 Ernest Rutherford 260 23 Jul - 26 Aug 10 Sep - 21 Oct 03 Monday 10:00 - 11:00 Ernest Rutherford 260 23 Jul - 26 Aug 10 Sep - 21 Oct 04 Monday 10:00 - 11:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 05 Monday 11:00 - 12:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 06 Monday 15:00 - 16:00 Putaiao Koiora 275 23 Jul - 26 Aug 10 Sep - 21 Oct 07 Monday 16:00 - 17:00 Putaiao Koiora 275 23 Jul - 26 Aug 10 Sep - 21 Oct 08 Monday 16:00 - 17:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 09 Wednesday 14:00 - 15:00 Jack Erskine 443 23 Jul - 26 Aug 10 Sep - 21 Oct 10 Tuesday 09:00 - 10:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 11 Tuesday 09:00 - 10:00 Jack Erskine 242 23 Jul - 26 Aug 10 Sep - 21 Oct 12 Tuesday 10:00 - 11:00 Jack Erskine 445 23 Jul - 26 Aug 10 Sep - 21 Oct 13 Tuesday 11:00 - 12:00 Ernest Rutherford 260 23 Jul - 26 Aug 10 Sep - 21 Oct 14 Tuesday 13:00 - 14:00 Ernest Rutherford 260 23 Jul - 26 Aug 10 Sep - 21 Oct 15 Tuesday 14:00 - 15:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 16 Tuesday 16:00 - 17:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 17 Wednesday 09:00 - 10:00 Jack Erskine 241 23 Jul - 26 Aug 10 Sep - 21 Oct 18 Wednesday 11:00 - 12:00 Jack Erskine 445 23 Jul - 26 Aug 10 Sep - 21 Oct 19 Wednesday 12:00 - 13:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 20 Wednesday 13:00 - 14:00 Jack Erskine 241 23 Jul - 26 Aug 10 Sep - 21 Oct 21 Wednesday 14:00 - 15:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 22 Wednesday 16:00 - 17:00 Jack Erskine 242 23 Jul - 26 Aug 10 Sep - 21 Oct 23 Wednesday 16:00 - 17:00 Ernest Rutherford 260 23 Jul - 26 Aug 10 Sep - 21 Oct 24 Monday 15:00 - 16:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 25 Thursday 09:00 - 10:00 Jack Erskine 241 23 Jul - 26 Aug 10 Sep - 21 Oct 26 Thursday 09:00 - 10:00 Jack Erskine 235 23 Jul - 26 Aug 10 Sep - 21 Oct 27 Thursday 12:00 - 13:00 Jack Erskine 242 23 Jul - 26 Aug 10 Sep - 21 Oct 28 Thursday 13:00 - 14:00 Ernest Rutherford 141 23 Jul - 26 Aug 10 Sep - 21 Oct 29 Thursday 14:00 - 15:00 Ernest Rutherford 140 23 Jul - 26 Aug 10 Sep - 21 Oct 30 Thursday 14:00 - 15:00 Jack Erskine 121 23 Jul - 26 Aug 10 Sep - 21 Oct 31 Thursday 15:00 - 16:00 Jack Erskine 241 23 Jul - 26 Aug 10 Sep - 21 Oct 32 Thursday 15:00 - 16:00 Jack Erskine 111 23 Jul - 26 Aug 10 Sep - 21 Oct 33 Wednesday 09:00 - 10:00 Jack Erskine 443 23 Jul - 26 Aug 10 Sep - 21 Oct 34 Monday 14:00 - 15:00 West 214 23 Jul - 26 Aug 10 Sep - 21 Oct

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Monday 18:30 - 20:00 A1 Lecture Theatre (20/8)A2 Lecture Theatre (20/8)A3 Lecture Theatre (20/8)C1 Lecture Theatre (20/8)C2 Lecture Theatre (20/8)C3 Lecture Theatre (20/8)E8 Lecture Theatre (20/8)E9 Lecture Theatre (20/8) 20 Aug - 26 Aug Test B 01 Wednesday 09:00 - 09:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 02 Wednesday 09:30 - 10:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 03 Wednesday 10:00 - 10:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 04 Wednesday 10:30 - 11:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 05 Wednesday 11:00 - 11:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 06 Wednesday 11:30 - 12:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 07 Wednesday 13:00 - 13:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 08 Wednesday 13:30 - 14:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 09 Wednesday 14:00 - 14:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 10 Wednesday 14:30 - 15:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 11 Thursday 09:00 - 09:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 12 Thursday 09:30 - 10:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 13 Thursday 10:00 - 10:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 14 Thursday 10:30 - 11:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 15 Thursday 13:00 - 13:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 16 Thursday 13:30 - 14:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 17 Thursday 14:00 - 14:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 18 Thursday 14:30 - 15:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 19 Thursday 15:00 - 15:30 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct 20 Thursday 15:30 - 16:00 Jack Erskine 035 Lab 2 17 Sep - 23 Sep 8 Oct - 14 Oct

## Textbooks

Stewart, James: Calculus Early Transcendentals. 8th edition. ISBN: 9781305272378

## Indicative Fees

Domestic fee \$937.00

International fee \$5,125.00

* 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 EMTH119 Occurrences

• EMTH119-18S2 (C) Semester Two 2018