EMTH119-24S2 (C) Semester Two 2024

# Engineering Mathematics 1B

15 points

Details:
 Start Date: Monday, 15 July 2024 End Date: Sunday, 10 November 2024
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 28 July 2024
• Without academic penalty (including no fee refund): Sunday, 29 September 2024

## 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
- solve first and second order differential equations
- find Taylor approximations to functions
- calculate determinants, eigenvalues and eigenvectors
- calculate mean and variance of random variables and solve probability problems arising in engineering applications
-  evaluate integrals arising in mathematics and engineering
- 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, and random variables
- 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 2024

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 11:00 - 12:00 C1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct 02 Monday 16:00 - 17:00 C1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct Lecture B 01 Tuesday 11:00 - 12:00 C1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct 02 Tuesday 16:00 - 17:00 C1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct Lecture C 01 Wednesday 11:00 - 12:00 C1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct 02 Wednesday 16:00 - 17:00 C1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct Lecture D 01 Thursday 11:00 - 12:00 C1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct 02 Thursday 16:00 - 17:00 C1 Lecture Theatre 15 Jul - 25 Aug 9 Sep - 20 Oct Tutorial A 01 Monday 15:00 - 16:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 02 Tuesday 11:00 - 12:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 03 Wednesday 16:00 - 17:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 04 Monday 11:00 - 12:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 05 Monday 08:00 - 09:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 06 Wednesday 08:00 - 09:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 07 Wednesday 10:00 - 11:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 08 Tuesday 14:00 - 15:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 09 Tuesday 11:00 - 12:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 10 Monday 14:00 - 15:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 11 Monday 12:00 - 13:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 12 Monday 16:00 - 17:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 13 Wednesday 09:00 - 10:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 14 Tuesday 08:00 - 09:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 15 Tuesday 15:00 - 16:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 16 Wednesday 11:00 - 12:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 17 Monday 12:00 - 13:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 18 Wednesday 09:00 - 10:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 19 Wednesday 11:00 - 12:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 20 Wednesday 12:00 - 13:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 21 Tuesday 12:00 - 13:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 22 Wednesday 08:00 - 09:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 23 Wednesday 15:00 - 16:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 24 Tuesday 13:00 - 14:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 25 Monday 13:00 - 14:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 26 Monday 09:00 - 10:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 27 Monday 08:00 - 09:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 28 Wednesday 16:00 - 17:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 29 Wednesday 14:00 - 15:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 30 Tuesday 16:00 - 17:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 31 Wednesday 13:00 - 14:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 32 Tuesday 09:00 - 10:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 33 Monday 11:00 - 12:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 34 Tuesday 09:00 - 10:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 35 Wednesday 15:00 - 16:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 36 Monday 16:00 - 17:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 37 Tuesday 16:00 - 17:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 38 Tuesday 15:00 - 16:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 39 Wednesday 14:00 - 15:00 Jack Erskine 038 Lab 4 15 Jul - 25 Aug 9 Sep - 20 Oct 40 Tuesday 10:00 - 11:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 41 Monday 15:00 - 16:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 42 Monday 10:00 - 11:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 43 Tuesday 08:00 - 09:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct 44 Wednesday 10:00 - 11:00 Jack Erskine 033 Lab 1 15 Jul - 25 Aug 9 Sep - 20 Oct

## Textbooks / Resources

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