EMTH119-20S2 (C) Semester Two 2020

# Engineering Mathematics 1B

15 points

Details:
 Start Date: Monday, 13 July 2020 End Date: Sunday, 8 November 2020
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 24 July 2020
• Without academic penalty (including no fee refund): Friday, 25 September 2020

## 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)

## Restrictions

MATH103, MATH109, MATH199

## Timetable 2020

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 12:00 - 13:00 C1 Lecture Theatre 13 Jul - 23 Aug 7 Sep - 18 Oct 02 Monday 08:00 - 09:00 C3 Lecture Theatre 13 Jul - 23 Aug 7 Sep - 18 Oct Lecture B 01 Tuesday 12:00 - 13:00 C1 Lecture Theatre 13 Jul - 23 Aug 7 Sep - 18 Oct 02 Tuesday 08:00 - 09:00 A1 Lecture Theatre 13 Jul - 23 Aug 7 Sep - 18 Oct Lecture C 01 Thursday 08:00 - 09:00 C1 Lecture Theatre 13 Jul - 23 Aug 7 Sep - 18 Oct 02 Thursday 12:00 - 13:00 E8 Lecture Theatre 13 Jul - 23 Aug 7 Sep - 18 Oct Lecture D 01 Friday 08:00 - 09:00 C1 Lecture Theatre 13 Jul - 23 Aug 7 Sep - 18 Oct 02 Friday 12:00 - 13:00 C2 Lecture Theatre 13 Jul - 23 Aug 7 Sep - 18 Oct Tutorial A 01 Monday 10:00 - 11:00 Psychology - Sociology 413 20 Jul - 23 Aug 7 Sep - 18 Oct 02 Monday 11:00 - 12:00 Psychology - Sociology 456 20 Jul - 23 Aug 7 Sep - 18 Oct 03 Monday 13:00 - 14:00 Jack Erskine 240 20 Jul - 23 Aug 7 Sep - 18 Oct 04 Monday 14:00 - 15:00 Jack Erskine 235 20 Jul - 23 Aug 7 Sep - 18 Oct 05 Monday 15:00 - 16:00 Jack Erskine 121 20 Jul - 23 Aug 7 Sep - 18 Oct 06 Monday 15:00 - 16:00 Jack Erskine 111 20 Jul - 23 Aug 7 Sep - 18 Oct 07 Monday 16:00 - 17:00 Jack Erskine 121 20 Jul - 23 Aug 7 Sep - 18 Oct 08 Monday 17:00 - 18:00 Jack Erskine 121 20 Jul - 23 Aug 7 Sep - 18 Oct 09 Tuesday 09:00 - 10:00 Psychology - Sociology 411 20 Jul - 23 Aug 7 Sep - 18 Oct 10 Tuesday 10:00 - 11:00 Psychology - Sociology 411 20 Jul - 23 Aug 7 Sep - 18 Oct 11 Tuesday 12:00 - 13:00 Psychology - Sociology 411 20 Jul - 23 Aug 7 Sep - 18 Oct 12 Tuesday 13:00 - 14:00 Psychology - Sociology 411 20 Jul - 23 Aug 7 Sep - 18 Oct 13 Tuesday 14:00 - 15:00 Psychology - Sociology 411 20 Jul - 23 Aug 7 Sep - 18 Oct 14 Tuesday 15:00 - 16:00 Psychology - Sociology 411 20 Jul - 23 Aug 7 Sep - 18 Oct 15 Tuesday 16:00 - 17:00 Jack Erskine 239 20 Jul - 23 Aug 7 Sep - 18 Oct 16 Tuesday 17:00 - 18:00 Jack Erskine 241 20 Jul - 23 Aug 7 Sep - 18 Oct 17 Wednesday 08:00 - 09:00 Psychology - Sociology 213 20 Jul - 23 Aug 7 Sep - 18 Oct 18 Wednesday 09:00 - 10:00 Jack Erskine 239 20 Jul - 23 Aug 7 Sep - 18 Oct 19 Wednesday 10:00 - 11:00 Psychology - Sociology 251 20 Jul - 23 Aug 7 Sep - 18 Oct 20 Wednesday 11:00 - 12:00 Psychology - Sociology 213 20 Jul - 23 Aug 7 Sep - 18 Oct 21 Wednesday 12:00 - 13:00 Psychology - Sociology 411 20 Jul - 23 Aug 7 Sep - 18 Oct 22 Wednesday 13:00 - 14:00 Psychology - Sociology 213 20 Jul - 23 Aug 7 Sep - 18 Oct 23 Wednesday 14:00 - 15:00 Psychology - Sociology 213 20 Jul - 23 Aug 7 Sep - 18 Oct 24 Wednesday 15:00 - 16:00 Psychology - Sociology 213 20 Jul - 23 Aug 7 Sep - 18 Oct 25 Wednesday 15:00 - 16:00 Psychology - Sociology 251 20 Jul - 23 Aug 7 Sep - 18 Oct 26 Wednesday 16:00 - 17:00 Psychology - Sociology 210 20 Jul - 23 Aug 7 Sep - 18 Oct 27 Monday 10:00 - 11:00 Jack Erskine 121 20 Jul - 23 Aug 7 Sep - 18 Oct 28 Monday 11:00 - 12:00 Jack Erskine 315 20 Jul - 23 Aug 7 Sep - 18 Oct 29 Monday 12:00 - 13:00 Psychology - Sociology 456 20 Jul - 23 Aug 7 Sep - 18 Oct 30 Monday 13:00 - 14:00 Jack Erskine 315 20 Jul - 23 Aug 7 Sep - 18 Oct 31 Monday 14:00 - 15:00 Jack Erskine 240 20 Jul - 23 Aug 7 Sep - 18 Oct 32 Monday 16:00 - 17:00 Jack Erskine 235 20 Jul - 23 Aug 7 Sep - 18 Oct 33 Monday 17:00 - 18:00 Jack Erskine 241 20 Jul - 23 Aug 7 Sep - 18 Oct 34 Tuesday 09:00 - 10:00 Psychology - Sociology 213 20 Jul - 23 Aug 7 Sep - 18 Oct 35 Tuesday 10:00 - 11:00 Psychology - Sociology 213 20 Jul - 23 Aug 7 Sep - 18 Oct 36 Tuesday 11:00 - 12:00 Jack Erskine 240 20 Jul - 23 Aug 7 Sep - 18 Oct 37 Tuesday 11:00 - 12:00 Psychology - Sociology 307 20 Jul - 23 Aug 7 Sep - 18 Oct 38 Tuesday 12:00 - 13:00 Jack Erskine 242 20 Jul - 23 Aug 7 Sep - 18 Oct 39 Tuesday 13:00 - 14:00 Psychology - Sociology 307 20 Jul - 23 Aug 7 Sep - 18 Oct 40 Tuesday 14:00 - 15:00 Psychology - Sociology 307 20 Jul - 23 Aug 7 Sep - 18 Oct

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Monday 19:00 - 20:30 C1 Lecture Theatre 17 Aug - 23 Aug 02 Monday 19:00 - 20:30 C2 Lecture Theatre 17 Aug - 23 Aug 03 Monday 19:00 - 20:30 C3 Lecture Theatre 17 Aug - 23 Aug 04 Monday 19:00 - 20:30 A1 Lecture Theatre 17 Aug - 23 Aug 05 Monday 19:00 - 20:30 A2 Lecture Theatre 17 Aug - 23 Aug 06 Monday 19:00 - 20:30 A3 Lecture Theatre 17 Aug - 23 Aug 07 Monday 19:00 - 20:30 Meremere 108 Lecture Theatre 17 Aug - 23 Aug

## Textbooks / Resources

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