Deterministic Mathematical Methods

EMTH210

ENCI302

ENCN305

Timetable Note

The course topics are split into two components, the first of which plays a foundational role for the second. Each component is broken down further into a set of modules. Here is the module list together with approximate lecture times spent on each.

Field Theory, Linear Algebra and Ordinary Differential Equations:  (19 lectures)
Lecturer: Professor David Wall

Module 1: Applied linear algebra (7 lectures)
Module 2: Applied ODEs (6 lectures)
Module 3: Vector Calculus                (6 lectures)
Module 4: Ordinary Differential equations (3 lectures)
Module 5: Numerical solutions of ODEs (3 lectures)

Partial Differential Equations: (19 lectures)
Lecturer: Professor Roger Nokes

Module 1: Introduction to PDEs (1 lecture)
Module 2: Review of Fourier Series (1 lecture)
Module 3: Wave phenomena (5 lectures)
Module 4: Introduction to Diffusion        (4 lectures)
Module 5: Numerical solutions of PDEs   (4 lectures)
Module 6:   Unsteady Diffusion               (4 lectures)
Module 7:   Steady Diffusion         (3 lectures)


Course Workload

This course is primarily a lecture course with four lectures during most weeks. There is a tutorial/problems class each week that will provide you with an opportunity to work on problems with the support of a tutor. In addition the course has four two-hour computer laboratory classes in which you will get the chance to implement some of the numerical methods you have seen developed in lectures.

Your lecturer will distribute practice problems for each tutorial that will provide you with examples of problems that you will encounter in the assignments. Attendance at the tutorial is not compulsory but if you need some guidance with the tutorial problems it is certainly worth coming along. Evidence from previous years is that students who miss tutorials face a greater chance of failure than those who regularly attend.

Laboratory exercises will also be distributed ahead of the laboratory classes. It is very important that you give these laboratory exercises some thought before attending the lab classes. In the weeks when there are scheduled laboratory classes there will only be two lectures.

Mathematics is a subject that can only be learnt by doing. Unless you work consistently throughout the semester on assignments and associated problems it is unlikely that you will be able to gain the skill level required to pass the course. In mathematics “practice does make perfect”. So we encourage you to allocate a significant amount of time each week to review the lecture material and work on relevant problems.

Assessment

The assessment for this paper will comprise three components – assignments, a mid-semester test and the final exam. All of the material covered in the first component will be assessed in the mid-semester test. The second component will be tested in the final exam.


1. 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. All assignments must be submitted by the due date. Late submissions will not be accepted. If a student is unable to complete and submit an assignment by the deadline due to personal circumstances beyond their control they should discuss this with the lecturer involved as soon as possible.

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

4. All assignments can be done individually or in pairs. If done in pairs a single submission for marking is required and both students receive the same mark. It is important that both students play an equal role in completing the assessment as the internal assessment is designed to prepare you for the formal assessments.

Notes

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 field theory 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, field theory and ordinary differential equations. 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.

Indicative Fees

* 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.