ENCN304-23S1 (C) Semester One 2023

# Deterministic Mathematical Methods

15 points

Details:
 Start Date: Monday, 20 February 2023 End Date: Sunday, 25 June 2023
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 5 March 2023
• Without academic penalty (including no fee refund): Sunday, 14 May 2023

## Description

Analytical and numerical methods for engineering problems. Vector calculus. Systems of linear equations. Systems of ordinary differential equations. Partial differential equations.

Deterministic Mathematical Methods is a compulsory 15 point course taught in the first semester of second professional to all civil and natural resources engineering students. It builds directly on the material taught in EMTH210. The focus of the course is on advanced deterministic mathematical methods that have application in a range of core engineering disciplines. Mathematical modelling and analysis lie at the heart of engineering analysis and this course aims to extend your skills in this area whereby you will be able to construct both analytical and numerical models that describe a range of physical problems, most particularly in the area of continuum mechanics. Solid mechanics, geomechanics and fluid mechanics all deal with dynamical systems that vary in both space and time and the description of these systems is heavily dependent on vector calculus and partial differential equations.

The course is split into two broad components, each of which is comprised of a number of sub-topics. The first component covers advanced ideas in linear algebra, ordinary differential equations and vector calculus. Both analytical and numerical solution methods are introduced for the material on linear algebra and ordinary differential equations. In many ways this first component provides the necessary tools for attacking problems that arise in the second component on partial differential equations. In this component the equations governing fundamental physical processes such as wave transmission, and unsteady and steady state diffusion are derived and solved both analytically and numerically. The three canonical partial differential equations, the wave equation, diffusion/heat equation and Laplace's equation, are covered. The analytical solutions developed for these equations are intended to provide you with some basic tools for solving these equations and gaining important insights into the physical phenomena they model, while the numerical solutions will introduce methods more generally used for solving practical engineering problems.

The concepts and techniques developed in this course will appear in a number of third professional courses, in particular those that consider fluid dynamical problems such as unsteady pipe flow and ocean waves. In addition if you are contemplating postgraduate study you will find the mathematical skills developed in this course, and those the companion ENCN305 course, which considers non-deterministic methods, to be very useful.

In both components of the course the emphasis is on the application of the mathematical tools and concepts to engineering, and civil and natural resources engineering in particular.

## Learning Outcomes

The specific aims of the course are:

- to develop analytic and numerical methods for the solution of linear algebra problems,
- to solve systems of ordinary differential equations using analytical and numerical methods,
- to introduce the key concepts of vector calculus that facilitate the description of continuum mechanics problems,
- to introduce the canonical second-order partial differential equations, the wave equation, the diffusion equation and Laplace's equation, and
- to develop analytical and numerical solutions to these equations that provide insight into the underlying physical phenomona being modelled.

ENCI302

## Timetable 2023

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 09:00 - 11:00 Meremere 108 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun 02 Monday 13:00 - 15:00 E9 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun Lecture B 01 Tuesday 08:00 - 10:00 A2 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun 02 Tuesday 13:00 - 15:00 A3 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun Tutorial A 01 Tuesday 11:00 - 12:00 Rehua 102 20 Feb - 2 Apr 24 Apr - 4 Jun 02 Tuesday 15:00 - 16:00 Rata 222 & 223 Drawing Office 20 Feb - 2 Apr 24 Apr - 4 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Friday 18:30 - 21:00 E9 Lecture Theatre 27 Mar - 2 Apr 02 Friday 18:30 - 21:00 E7 Lecture Theatre 27 Mar - 2 Apr 04 Friday 18:30 - 21:00 E5 Lecture Theatre 27 Mar - 2 Apr

## Timetable Note

Computer Lab Classes

There are four computer laboratory classes in weeks 4, 6 11, and 12, as shown in the table on the last page. These classes are specifically designed to provide you with experience in some of the numerical methods taught in lectures, and will be helpful in completing some assignments which will carry a numerical method component.

Four different lab streams will be run.  Allocation of students to streams will happen once the term is underway.

## Assessment

Assessment Due Date Percentage
exam 44%
Test 44%
weekly tutorials 12%

You cannot pass this course unless you achieve a mark of at least 40% in each of the mid-semester test and the final exam. A student who narrowly fails to achieve 40% in either the test or exam, but who performs very well in the other, may be eligible for a pass in the course.

2. The weekly tutorial component of the internal assessment will comprise completion of tutorial questions. Each week’s tutorial will be worth 1% of the final course grade (totalling 12%). The grading of each tutorial will focus on an honest attempt at the questions with marks of: 0 – not attempted; 0.5 – partial attempt; 1.0 – all questions attempted. Students must submit individual tutorial answers. Students may iteratively work on the questions with guidance before and during the tutorial sessions.

3. Students will scan their assignment solutions as a single PDF file, and submit it by the required due time on Learn. Paper copies will not be accepted. If a scanner is not available, the CamScanner app may be used to edit and combine photographs into a single PDF file. Make sure your solutions are legible.

4. You are given a total allowance of two late days for the submission of assignments of the entire course. No reason needs to be provided. Submission of an assignment at any time up to 24 hours late will result in the deduction of one entire late day, and so on.

5. Students in this course can apply for special consideration provided they have sat the mid-term
test, the final exam or both.

6. Students may apply for special consideration if their performance in an assessment is affected by extenuating circumstances beyond their control. Applications for special consideration should be submitted via the Examinations Office website within five days of the assessment. However, where an extension may be granted for an assessment, this will be decided by direct application to the Course co-ordinator and an application to the Examinations Office may not be required. Special consideration is not available for items worth less than 10% of the course.

7. Students prevented by extenuating circumstances from completing the course after the final date for withdrawing, may apply for special consideration for late discontinuation of the course. Applications must be submitted to the Examinations Office within five days of the end of the main examination period for the semester.

8. In the case of an emergency that affects the whole course, the Course Coordinator, in consultation with the Dean, may change the nature, weighting and timing of assessments, e.g. tests and examination may be replaced with assignments of the same weight or different weight at a different time and/or date (which, under certain circumstances, may be outside the prescribed course dates). The ‘Special consideration’ process will also be used for unforeseen circumstances that adversely affect the academic performance of students individually. The usual grounds for this are described in the UC policy ‘Special Consideration Procedures and Guidelines’, and personal circumstances due to a wider emergency event may also qualify.

## Textbooks / Resources

Electronic copies of all course materials will be made available through Learn.

## Indicative Fees

Domestic fee \$1,030.00

International fee \$5,750.00

* 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 Civil and Natural Resources Engineering .

## All ENCN304 Occurrences

• ENCN304-23S1 (C) Semester One 2023