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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:- Apply analytic and numerical methods for the solution of linear algebra problems (Washington Accord WA1) (UC EIE3)- Solve systems of ordinary differential equations using analytical and numerical methods. (Washington Accord WA1, WA5) (UC EIE3, EIE4)- Explain the key concepts of vector calculus that facilitate the description of continuum mechanics problems (Washington Accord WA2), (UC EIE3)- Explain the canonical second-order partial differential equations, the wave equation, the diffusion equation and Laplace's equation.(Washington Accord WA2), (UC EIE3)- Apply analytical and numerical solutions to these equations that provide insight into the underlying physical phenomena being modelled. (Washington Accord WA3, WA5), (UC EIE3, EIE4)
EMTH210
ENCI302
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. Four different lab streams will be run. Allocation of students to streams will happen once the term is underway.
David Dempsey
Reagan Chandramohan
1. The mid-semester test will cover all materials taught in Term 1 (first 6 weeks). The final exam will cover all the materials taught in Term 2 (last 6 weeks). 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 homework component of the internal assessment will comprise the completion of tutorial questions. Each week’s homework will be worth 0.5% of the final course grade (totalling 6%). The grading of each tutorial will focus on an honest attempt at the questions with marks of: 0 – not attempted; 0.25 – partial attempt; 0.5 – all questions attempted. Students must submit individual tutorial answers and Python code as required. 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. Code files may be required separately. Paper copies are not accepted. If a scanner is not available, the CamScanner or Adobe Scan apps may be used to edit and combine photographs into a single PDF file. Make sure your solutions are legible.4. Over the entire course, you are given a total allowance of two late days for the submission of weekly homework. No reason needs to be provided and you do not need to notify the late submission. 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. The weekly quiz component of the internal assessment will comprise a short assessment of revision or foundational material covered in recorded videos. The videos and quizzes will be released one week in advance of the lectures in which they are relevant. The expectation is that students will come prepared for each week’s lectures having watched the videos and completed the associated quiz.6. Each quiz is worth 0.5%. While you have unlimited attempts to complete each weekly quiz, a brief stand-down period will be imposed after each failed attempt to give you a chance to re-review the material. Quizzes can only be completed prior to the week for which they are relevant (excluding Week 1). If you fail to complete a quiz prior to that week’s lectures, you will have foregone the 0.5% credit associated with it.7. We recognize that illness or outside obligations can impact the completion of regular homework and quizzes. Therefore, you can drop any ONE homework assignment AND any ONE quiz without penalty throughout the semester. You do not need to apply for this exemption, it will be applied automatically at the end of the semester. This is in addition to the late allowance described in Note 4 (the late allowance applies to homework only).Special Considerations Any student who has been impaired by significant exceptional and/or unforeseeable circumstances that have prevented them from completing any major assessment items, or that have impaired their performance such that the results are not representative of their true level of mastery of the course material, may apply for special consideration through the formal university process. The applicability and academic remedy/action associated with the special consideration process are listed for each assessment item below. Please refer to the University Special Consideration Regulations and Special Consideration Policies and Procedures documents for more information on the acceptable grounds for special consideration and the application process. https://www.canterbury.ac.nz/study/study-support-info/study-topics/special-consideration Special Consideration for Weekly Homework AssignmentsDue to their smaller contribution to total course grade, weekly homework assignments are handled informally by the course coordinator. Please refer to notes 4 and 5 in Section 7 for course policies to accommodate disruptions. No additional extensions or exemptions will be granted beyond these.Special Consideration for Midterm TestsModerate/Serious/Severe Impact: Students will be offered an equivalent alternative test that will replace their original test mark. The original test mark will not be revealed to the student prior to taking the resit.Special Consideration for Final ExamModerate/Serious/Severe Impact: Students will be offered an equivalent alternative exam that will replace their original exam mark. The original exam mark will not be revealed to the student prior to taking the resit.The resit test will be held on a date early in Term 2. Resit exams will be held during the week of July 7, 2025. Students must be available to take the resit test or exam in person. Students with pending Special Consideration applications are advised to take the resit, but will not benefit from it unless their application is eventually approved at the appropriate level of severity. All communication associated with the arrangement of equivalent alternative tests/exams will be conducted using official UC email accounts. Students will have a clearly specified amount of time to respond to the offer to sit the alternative assessment. Failure to respond will be interpreted as a declined offer. If the offer is declined or no response is received in the specified time frame, the original assessment mark will be used to compute the course grade.
This course does not have a required text and instead provides notes and other resources on LEARN. Furthermore, a number of articles will be posted on the class LEARN site as recommended reading. Please note that all lecture recordings, made available through LEARN, are copyrighted and are not for public dissemination.
Generative AI use in this courseIt is not practical to regulate the use of Generative AI (e.g., ChatGPT) for internal assessments on this course – weekly homework and quiz assignments. Students are allowed to use these tools in whichever manner they see fit. However, you should be aware of the risks, which are described below.Research clearly shows that the unrestricted use of ChatGPT by students during mathematical education leads to decreased performance on external assessment (which happens to comprise most of your grade in this course). For instance, this study showed a 17% reduction in test performance, more than three grade points. The primary mechanisms leading to adverse outcomes appear to be (1) shallow learning, where AI prevents you spending sufficient time with the material to obtain a deep understanding of it, and (2) AI dependency, where overuse of the tool leads to an inability to apply methods or think critically once it is taken away.If you intend to use Generative AI on this course, consider prompting with some basic guardrails to prevent the above impacts on your learning:“You are a math tutor helping me with a homework problem. Please suggest one (and only one) next step for me to consider on the following problem. Don’t complete the problem for me. **paste your problem**.”“You are a coding tutor helping me with a homework problem. Here is some code I have written and the error that I am getting. Please give me some hints about how I can fix this. Do not give me the corrected code though. **paste your code and error message**.”Even with the guardrails, a helpful Generative AI will frequently just give you the solution to a problem, cheating you of the opportunity to learn it yourself.Code of Behaviour and Academic IntegrityAll students are expected to be familiar with the University’s codes, policies, and procedures including but not limited to the Student Code of Conduct, Campus Drug and Alcohol Policy, Copyright Policy, Disability and Impairment Policy, and Equity and Diversity Policy. It is the responsibility of each student to be familiar with the definitions, policies and procedures concerning academic misconduct/dishonest behaviour. More information on UC’s policies and academic integrity can be found in the undergraduate handbook as well as at:https://www.canterbury.ac.nz/about-uc/corporate-information/policies https://www.canterbury.ac.nz/about-uc/what-we-do/teaching/academic-integrity
Domestic fee $1,122.00
International fee $6,238.00
* 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 .