EMTH119-21SU2 (C) Summer Nov 2021 start

# Engineering Mathematics 1B

15 points

Details:
 Start Date: Monday, 29 November 2021 End Date: Sunday, 13 February 2022
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 12 December 2021
• Without academic penalty (including no fee refund): Friday, 21 January 2022

## 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.

Due to the condensed nature of this course, this course requires a commitment of 20 hours per week of classes and study. You must be able to attend all in-person classes as these are essential to support your learning

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 2022

Students must attend one activity from each section.

Activity Day Time Location Weeks Drop in Class A 01 Tuesday 14:00 - 16:00 Jack Erskine 443 7 Feb - 13 Feb Drop in Class B 01 Wednesday 14:00 - 16:00 Jack Erskine 443 7 Feb - 13 Feb Drop in Class C 01 Thursday 14:00 - 16:00 Jack Erskine 443 7 Feb - 13 Feb Tutorial A 01 Tuesday 10:00 - 12:00 Jack Erskine 111 10 Jan - 6 Feb 02 Tuesday 10:00 - 12:00 Jack Erskine 242 10 Jan - 6 Feb 03 Tuesday 10:00 - 12:00 Jack Erskine 244 10 Jan - 6 Feb 04 Tuesday 10:00 - 12:00 Jack Erskine 235 10 Jan - 6 Feb 05 Tuesday 10:00 - 12:00 Jack Erskine 340 10 Jan - 6 Feb 06 Tuesday 10:00 - 12:00 Jack Erskine 315 10 Jan - 6 Feb 07 Tuesday 10:00 - 12:00 Link 309 Lecture Theatre (11/1-25/1) Jack Erskine 443 (1/2) 10 Jan - 6 Feb 08 Tuesday 10:00 - 12:00 Jack Erskine 101 10 Jan - 6 Feb 09 Tuesday 10:00 - 12:00 Beatrice Tinsley 111 10 Jan - 6 Feb 10 Tuesday 10:00 - 12:00 Ernest Rutherford 465 10 Jan - 6 Feb 11 Tuesday 10:00 - 12:00 Ernest Rutherford 140 10 Jan - 6 Feb Tutorial B 01 Wednesday 13:00 - 15:00 Jack Erskine 111 10 Jan - 6 Feb 02 Wednesday 13:00 - 15:00 Jack Erskine 242 10 Jan - 6 Feb 03 Wednesday 13:00 - 15:00 Jack Erskine 244 10 Jan - 6 Feb 04 Wednesday 13:00 - 15:00 Jack Erskine 235 10 Jan - 6 Feb 05 Wednesday 13:00 - 15:00 Jack Erskine 340 10 Jan - 6 Feb 06 Wednesday 13:00 - 15:00 Jack Erskine 315 10 Jan - 6 Feb 07 Wednesday 13:00 - 15:00 Link 309 Lecture Theatre (12/1-26/1) Jack Erskine 443 (2/2) 10 Jan - 6 Feb 08 Wednesday 13:00 - 15:00 Jack Erskine 101 10 Jan - 6 Feb 09 Wednesday 13:00 - 15:00 Beatrice Tinsley 111 10 Jan - 6 Feb 10 Wednesday 13:00 - 15:00 Ernest Rutherford 465 10 Jan - 6 Feb 11 Wednesday 13:00 - 15:00 Ernest Rutherford 140 10 Jan - 6 Feb Tutorial C 07 Thursday 13:00 - 15:00 Link 309 Lecture Theatre 10 Jan - 30 Jan Tutorial D 07 Friday 10:00 - 12:00 Link 309 Lecture Theatre 10 Jan - 30 Jan

## Examination and Formal Tests

Activity Day Time Location Weeks Exam A 01 Friday 09:30 - 12:00 A1 Lecture Theatre 7 Feb - 13 Feb 02 Friday 09:30 - 12:00 A3 Lecture Theatre 7 Feb - 13 Feb 03 Friday 09:30 - 12:00 A2 Lecture Theatre 7 Feb - 13 Feb 04 Friday 09:30 - 12:00 Jack Erskine 031 Lecture Theatre 7 Feb - 13 Feb 05 Friday 09:30 - 12:00 Zoom 7 Feb - 13 Feb Test A 01 Monday 16:30 - 18:00 A2 Lecture Theatre 10 Jan - 16 Jan 02 Monday 16:30 - 18:00 A1 Lecture Theatre 10 Jan - 16 Jan

## Textbooks / Resources

#### Recommended Reading

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

## 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 .

## All EMTH119 Occurrences

• EMTH119-21SU2 (D) Summer Nov 2021 start (Distance) - Not Offered
• EMTH119-21SU2 (C) Summer Nov 2021 start
• EMTH119-22S2 (C) Semester Two 2022
• EMTH119-22S2 (D) Semester Two 2022 (Distance)