 EMTH119-17S2 (C) Semester Two 2017

# Engineering Mathematics 1B

15 points

Details:
 Start Date: Monday, 17 July 2017 End Date: Sunday, 19 November 2017
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 28 July 2017
• Without academic penalty (including no fee refund): Friday, 13 October 2017

## 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

## Assessment

Assessment Due Date Percentage
Tutorial preparation & participation 5%
Online quizzes 10%
Test 1 20%
Test 2 20%
Final Examination 45%

## Textbooks / Resources

Recommended Textbook
Anton, Bivens, Davis Calculus: Early Transcendentals. Wiley, 10th edition (the 9th edition is also suitable).