EMTH119-21S2 (C) Semester Two 2021

# Engineering Mathematics 1B

15 points

Details:
 Start Date: Monday, 19 July 2021 End Date: Sunday, 14 November 2021
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 1 August 2021
• Without academic penalty (including no fee refund): Friday, 1 October 2021

## 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, linear algebra and probability. It includes applications of this mathematics to applied and engineering problems, and uses python to implement numerical methods. 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. Direction Fields and Euler's method. Polar form of complex numbers. Second-order ordinary differential equations with applications.
Newton-Raphson for root finding. 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.
Sets and probability. Discrete random variables. Continuous random variables. Expectation, mean, and variance.
Integration of rational functions via partial fractions. Parametrised curves. Arc length. Numerical integration including the trapezium rule.
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
- Knowing when and how to apply suitable numerical methods
• 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)

## Restrictions

MATH103, MATH109, MATH199

## Timetable 2021

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 09:00 - 10:00 C1 Lecture Theatre 19 Jul - 29 Aug 13 Sep - 24 Oct 02 Monday 11:00 - 12:00 C1 Lecture Theatre 19 Jul - 29 Aug 13 Sep - 24 Oct Lecture B 01 Wednesday 10:00 - 11:00 C1 Lecture Theatre 19 Jul - 29 Aug 13 Sep - 24 Oct 02 Wednesday 13:00 - 14:00 C1 Lecture Theatre 19 Jul - 29 Aug 13 Sep - 24 Oct Lecture C 01 Thursday 09:00 - 10:00 C1 Lecture Theatre 19 Jul - 29 Aug 13 Sep - 24 Oct 02 Thursday 12:00 - 13:00 C1 Lecture Theatre 19 Jul - 29 Aug 13 Sep - 24 Oct Lecture D 01 Friday 09:00 - 10:00 C1 Lecture Theatre 19 Jul - 29 Aug 13 Sep - 24 Oct 02 Friday 13:00 - 14:00 C1 Lecture Theatre 19 Jul - 29 Aug 13 Sep - 24 Oct Tutorial A 01 Monday 08:00 - 09:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 02 Monday 09:00 - 10:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 03 Monday 10:00 - 11:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 04 Monday 11:00 - 12:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 05 Monday 12:00 - 13:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 06 Monday 13:00 - 14:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 07 Monday 14:00 - 15:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 08 Monday 15:00 - 16:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 09 Monday 16:00 - 17:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 11 Tuesday 08:00 - 09:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 12 Tuesday 09:00 - 10:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 13 Tuesday 10:00 - 11:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 14 Tuesday 11:00 - 12:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 15 Tuesday 12:00 - 13:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 16 Tuesday 13:00 - 14:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 17 Tuesday 14:00 - 15:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 18 Tuesday 15:00 - 16:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 19 Tuesday 16:00 - 17:00 Jack Erskine 038 Lab 4 26 Jul - 29 Aug 13 Sep - 24 Oct 21 Wednesday 08:00 - 09:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 22 Wednesday 09:00 - 10:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 23 Wednesday 10:00 - 11:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 24 Wednesday 11:00 - 12:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 25 Wednesday 12:00 - 13:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 26 Wednesday 13:00 - 14:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 27 Wednesday 14:00 - 15:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 28 Wednesday 15:00 - 16:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 29 Wednesday 16:00 - 17:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 31 Monday 10:00 - 11:00 Jack Erskine 033 Lab 1 26 Jul - 29 Aug 13 Sep - 24 Oct 32 Tuesday 09:00 - 10:00 Jack Erskine 033 Lab 1 26 Jul - 29 Aug 13 Sep - 24 Oct 33 Monday 12:00 - 13:00 Jack Erskine 033 Lab 1 26 Jul - 29 Aug 13 Sep - 24 Oct 34 Monday 13:00 - 14:00 Jack Erskine 033 Lab 1 26 Jul - 29 Aug 13 Sep - 24 Oct 35 Monday 14:00 - 15:00 Jack Erskine 033 Lab 1 26 Jul - 29 Aug 13 Sep - 24 Oct 36 Tuesday 10:00 - 11:00 Jack Erskine 033 Lab 1 26 Jul - 29 Aug 13 Sep - 24 Oct 37 Tuesday 11:00 - 12:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 38 Tuesday 12:00 - 13:00 Jack Erskine 436 Computer Lab 26 Jul - 29 Aug 13 Sep - 24 Oct 39 Wednesday 11:00 - 12:00 Jack Erskine 033 Lab 1 26 Jul - 29 Aug 13 Sep - 24 Oct 41 Wednesday 15:00 - 16:00 Jack Erskine 033 Lab 1 26 Jul - 29 Aug 13 Sep - 24 Oct 44 Tuesday 15:00 - 16:00 Jack Erskine 033 Lab 1 26 Jul - 29 Aug 13 Sep - 24 Oct

## Examination and Formal Tests

Activity Day Time Location Weeks Test B 01 Wednesday 16:00 - 17:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 02 Wednesday 17:00 - 18:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 03 Wednesday 18:00 - 19:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 04 Wednesday 19:00 - 20:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 05 Thursday 16:00 - 17:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 06 Thursday 17:00 - 18:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 07 Thursday 18:00 - 19:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 08 Thursday 19:00 - 20:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 09 Friday 12:00 - 13:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 10 Friday 13:00 - 14:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 11 Friday 14:00 - 15:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 12 Friday 15:00 - 16:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 13 Friday 16:00 - 17:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 14 Friday 17:00 - 18:00 Jack Erskine 035 Lab 2 4 Oct - 10 Oct 15 Thursday 15:00 - 16:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 16 Thursday 16:00 - 17:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 17 Thursday 17:00 - 18:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 18 Thursday 18:00 - 19:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 19 Thursday 19:00 - 20:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 20 Friday 12:00 - 13:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 21 Friday 13:00 - 14:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 22 Friday 14:00 - 15:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 23 Friday 15:00 - 16:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 24 Friday 16:00 - 17:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct 25 Friday 17:00 - 18:00 Jack Erskine 033 Lab 1 4 Oct - 10 Oct

## Textbooks / Resources

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

## 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.