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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.
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.
Students must attend one activity from each section.
Computer Lab ClassesThere 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. Three different lab streams will be run. Allocation of students to streams will happen once the term is underway.
Notes: 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. 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. Students will submit their tutorials by 5pm each Friday in the homework boxes. Worked solutions to tutorials will be provided at the end of each week. This internal assessment approach places an emphasis on the approach to problem solving (as opposed to a focus on the exact answer), and a responsibility on students to use worked solutions to confirm their understanding of the material. No late solutions will be accepted. If a student is unable to complete and submit a tutorial by the deadline due to personal circumstances beyond their control they should discuss this with the lecturer involved as soon as possible (preferably prior to the due date) and refer to points 4 and 5 below. Students in this course can apply for special consideration provided they have sat the mid-term test, the final exam or both. 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. 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.
Domestic fee $975.00
International fee $5,500.00
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see
Civil and Natural Resources Engineering.