EMTH119-23S2 (C) Semester Two 2023

# Engineering Mathematics 1B

15 points

Details:
 Start Date: Monday, 17 July 2023 End Date: Sunday, 12 November 2023
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 30 July 2023
• Without academic penalty (including no fee refund): Sunday, 1 October 2023

## 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. Landauâ€™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)

## Restrictions

MATH103, MATH109, MATH199

## Timetable 2023

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 08:00 - 09:00 C1 Lecture Theatre 17 Jul - 27 Aug 11 Sep - 22 Oct 02 Monday 12:00 - 13:00 C1 Lecture Theatre 17 Jul - 27 Aug 11 Sep - 22 Oct Lecture B 01 Tuesday 08:00 - 09:00 C1 Lecture Theatre 17 Jul - 27 Aug 11 Sep - 22 Oct 02 Tuesday 12:00 - 13:00 C1 Lecture Theatre 17 Jul - 27 Aug 11 Sep - 22 Oct Lecture C 01 Wednesday 08:00 - 09:00 C1 Lecture Theatre 17 Jul - 27 Aug 11 Sep - 22 Oct 02 Wednesday 12:00 - 13:00 C1 Lecture Theatre 17 Jul - 27 Aug 11 Sep - 22 Oct Lecture D 01 Thursday 08:00 - 09:00 C1 Lecture Theatre 17 Jul - 27 Aug 11 Sep - 22 Oct 02 Thursday 12:00 - 13:00 C1 Lecture Theatre 17 Jul - 27 Aug 11 Sep - 22 Oct Tutorial A 01 Monday 09:00 - 10:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 02 Monday 09:00 - 10:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 03 Monday 10:00 - 11:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 04 Monday 10:00 - 11:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 05 Monday 11:00 - 12:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 06 Monday 11:00 - 12:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 07 Monday 12:00 - 13:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 08 Monday 13:00 - 14:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 09 Monday 13:00 - 14:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 10 Monday 14:00 - 15:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 11 Monday 14:00 - 15:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 12 Monday 15:00 - 16:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 13 Monday 15:00 - 16:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 15 Monday 16:00 - 17:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 17 Tuesday 09:00 - 10:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 18 Tuesday 09:00 - 10:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 19 Tuesday 10:00 - 11:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 20 Tuesday 10:00 - 11:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 21 Tuesday 11:00 - 12:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 22 Wednesday 16:00 - 17:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 23 Tuesday 12:00 - 13:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 24 Tuesday 13:00 - 14:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 25 Tuesday 13:00 - 14:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 26 Tuesday 14:00 - 15:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 27 Tuesday 14:00 - 15:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 28 Tuesday 15:00 - 16:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 29 Tuesday 15:00 - 16:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 30 Wednesday 09:00 - 10:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 32 Wednesday 10:00 - 11:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 33 Wednesday 10:00 - 11:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 34 Wednesday 11:00 - 12:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 35 Wednesday 11:00 - 12:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 36 Wednesday 12:00 - 13:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 37 Wednesday 13:00 - 14:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 38 Wednesday 13:00 - 14:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 39 Wednesday 14:00 - 15:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 41 Wednesday 15:00 - 16:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 42 Wednesday 15:00 - 16:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct 43 Tuesday 16:00 - 17:00 Jack Erskine 038 Lab 4 24 Jul - 27 Aug 11 Sep - 22 Oct 44 Wednesday 16:00 - 17:00 Jack Erskine 033 Lab 1 24 Jul - 27 Aug 11 Sep - 22 Oct

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Monday 14:00 - 15:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 02 Monday 15:00 - 16:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 03 Monday 16:00 - 17:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 04 Monday 17:00 - 18:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 05 Monday 18:00 - 19:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 06 Monday 19:00 - 20:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 07 Tuesday 10:00 - 11:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 08 Tuesday 14:00 - 15:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 09 Tuesday 17:00 - 18:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 10 Tuesday 18:00 - 19:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 11 Tuesday 19:00 - 20:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 12 Wednesday 15:00 - 16:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 13 Wednesday 16:00 - 17:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 14 Wednesday 17:00 - 18:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 15 Wednesday 18:00 - 19:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 16 Wednesday 19:00 - 20:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 17 Thursday 17:00 - 18:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 18 Thursday 18:00 - 19:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 19 Thursday 19:00 - 20:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 21 Monday 09:00 - 10:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 22 Monday 10:00 - 11:00 Jack Erskine 035 Lab 2 21 Aug - 27 Aug 23 Thursday 19:00 - 20:00 Jack Erskine 033 Lab 1 21 Aug - 27 Aug 24 Tuesday 17:00 - 18:00 Jack Erskine 035 Lab 2 11 Sep - 17 Sep 25 Wednesday 16:00 - 17:00 Jack Erskine 035 Lab 2 11 Sep - 17 Sep

## Textbooks / Resources

Stewart, James; Calculus : early transcendentals ; Eighth edition; Cengage Learning, 2016.

## Indicative Fees

Domestic fee \$1,030.00

International fee \$5,750.00

* 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 EMTH119 Occurrences

• EMTH119-23SU2 (C) Summer Nov 2023 start
• EMTH119-23S2 (D) Semester Two 2023 (Distance) - Not Offered - see department for alternatives
• EMTH119-23S2 (C) Semester Two 2023