EMTH119-20SU2 (C) Summer Nov 2020 start

# Engineering Mathematics 1B

15 points

Details:
 Start Date: Monday, 30 November 2020 End Date: Sunday, 7 February 2021
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 11 December 2020
• Without academic penalty (including no fee refund): Friday, 15 January 2021

## 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 students are expected to attend every lecture AND every tutorial.

EMTH119-20SU2 is not available for online study. You must be able to make a commitment to being on-campus for the whole course and exam before enrolling in this course.

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:
Differential equations. First-order ordinary differential equations with applications.  Second-order ordinary differential equations with applications.
Sequences and mathematical induction.  Applications of differentiation to approximation.  Approximation by Taylor polynomials. Landau’s notation and order of magnitude.
Matrices and determinants.
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.
Vector Geometry   Projections. Parallel and intersecting planes.  Intersection and distance problems.

## 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 2021

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Tuesday 09:00 - 11:00 Meremere 108 Lecture Theatre 4 Jan - 31 Jan Lecture B 01 Wednesday 13:00 - 15:00 Meremere 108 Lecture Theatre 4 Jan - 31 Jan Lecture C 01 Thursday 13:00 - 15:00 Meremere 108 Lecture Theatre 4 Jan - 31 Jan Lecture D 01 Friday 09:00 - 11:00 Meremere 108 Lecture Theatre 4 Jan - 24 Jan Drop in Class A 01 Tuesday 10:00 - 12:00 Jack Erskine 443 1 Feb - 7 Feb Drop in Class B 01 Wednesday 10:00 - 12:00 Jack Erskine 443 1 Feb - 7 Feb Drop in Class C 01 Thursday 10:00 - 12:00 Jack Erskine 315 1 Feb - 7 Feb Tutorial A 01 Tuesday 11:00 - 12:00 Jack Erskine 111 4 Jan - 31 Jan 02 Tuesday 11:00 - 12:00 Jack Erskine 101 4 Jan - 31 Jan 03 Tuesday 11:00 - 12:00 Jack Erskine 121 4 Jan - 31 Jan 04 Tuesday 11:00 - 12:00 Jack Erskine 445 4 Jan - 31 Jan 05 Tuesday 11:00 - 12:00 Jack Erskine 340 4 Jan - 31 Jan 06 Tuesday 11:00 - 12:00 Jack Erskine 446 4 Jan - 31 Jan Tutorial B 01 Wednesday 15:00 - 16:00 Jack Erskine 111 4 Jan - 31 Jan 02 Wednesday 15:00 - 16:00 Jack Erskine 101 4 Jan - 31 Jan 03 Wednesday 15:00 - 16:00 Jack Erskine 121 4 Jan - 31 Jan 04 Wednesday 15:00 - 16:00 Jack Erskine 445 4 Jan - 31 Jan 05 Wednesday 15:00 - 16:00 Jack Erskine 446 4 Jan - 31 Jan 06 Wednesday 15:00 - 16:00 Jack Erskine 443 4 Jan - 31 Jan Tutorial C 01 Thursday 15:00 - 16:00 Jack Erskine 111 4 Jan - 31 Jan 02 Thursday 15:00 - 16:00 Jack Erskine 101 4 Jan - 31 Jan 03 Thursday 15:00 - 16:00 Jack Erskine 121 4 Jan - 31 Jan 04 Thursday 15:00 - 16:00 Jack Erskine 445 4 Jan - 31 Jan 05 Thursday 15:00 - 16:00 Jack Erskine 315 4 Jan - 31 Jan 06 Thursday 15:00 - 16:00 Jack Erskine 244 4 Jan - 31 Jan Tutorial D 01 Friday 11:00 - 12:00 Jack Erskine 111 4 Jan - 24 Jan 02 Friday 11:00 - 12:00 Jack Erskine 101 4 Jan - 24 Jan 03 Friday 11:00 - 12:00 Jack Erskine 121 4 Jan - 24 Jan 04 Friday 11:00 - 12:00 Jack Erskine 445 4 Jan - 24 Jan 05 Friday 11:00 - 12:00 Jack Erskine 315 4 Jan - 24 Jan 06 Friday 11:00 - 12:00 Jack Erskine 244 4 Jan - 24 Jan

## Examination and Formal Tests

Activity Day Time Location Weeks Exam A 01 Friday 09:30 - 12:00 K1 Lecture Theatre 1 Feb - 7 Feb Test B 01 Monday 18:00 - 19:00 E8 Lecture Theatre 11 Jan - 17 Jan

## Timetable Note

The timetable runs November 2020 to February 2021.

## Assessment

Note: To obtain a clear pass (a C– or better), you must obtain at least 40% in the final examination.

## Textbooks / Resources

Anton, Howard., Bivens, Irl., Davis, Stephen; Calculus: Early Transcendentals; 10th edition; Wiley (8th or 9th edition also suitable).