68038 Advanced Mathematics and Physics
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Subject handbook information prior to 2024 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 68037 Physical Modelling AND 33230 Mathematics 2
Anti-requisite(s): 37234 Complex Analysis
Description
This subject is delivered by the School of Mathematics and Physical Sciences. It is aimed at both second-year engineering and science undergraduate students. This subject provides students with the fundamental mathematical and physical knowledge required as practicing engineers and scientists. It provides an up-to-date toolbox of mathematical methods needed for the analysis of electric and magnetic fields, circuits, signal processing and theoretical and applied quantum physics. The physics section of this subject provides an introduction to quantum physics (starting from classical mechanics) through to the application of quantum physics to real-world situations such as semiconductor electronic and opto-electronic devices. Mathematics topics covered include: vector calculus; differentiation, integration and functions of a complex variable; Divergence and Stokes theorems; Cauchy-Riemann equations; Residue theorem and Laplace transforms.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 01. | Solve core mathematical problems required in the engineering discipline; |
|---|---|
| 02. | Solve problems in applied and quantum physics using a range of mathematical and practical techniques; |
| 03. | Evaluate how the quantum properties of electrons in solids can be used to develop new electronic devices; |
| 04. | Interpret how the quantum and physical properties of materials have relevance to the practice of engineers and applied scientists. |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Demonstrate coherent understanding of physics and related knowledge applied to diverse contexts. (1.1)
- Evaluate the reliability of scientific evidence and apply effective experimental design, analysis and critical thinking to predict the behaviour of real-world systems using physical models (2.1)
- Engage autonomously or in teams to derive and analyse data from instrumentation and physical models to make ethical contributions to society. (3.1)
- Apply effective and appropriate communication methods for discussing physics concepts, data and analysis with diverse audiences. (5.1)
Contribution to the development of graduate attributes
Faculty of Engineering and IT Graduate Attributes
This subject contributes to the following Faculty of Engineering and Information Technology graduate attribute:
D.1 Technically Proficient: FEIT graduates apply abstraction, mathematics and discipline fundamentals, software, tools and techniques to evaluate, implement and operate systems.
Faculty of Science Graduate Attributes
This subject primarily addresses the following graduate attributes:
GA1 Disciplinary Knowledge
Through the lectures, lab experiments, class tests and final exam, this subject will provide students with the fundamental mathematical and physical knowledge that they will require as practicing engineers. The emphasis in the mathematics strand will be on developing an understanding of the concepts and techniques of advanced calculus. We will focus in particular on concepts from vector calculus and complex integration which are relevant to many problems in physics and engineering. The physics strand will provide students with a working knowledge of the fundamental physical principles behind the design and operation of technological devices such as computer processors, mobile phones, and LEDs. [Assessments 1-3]
GA2 Research, Inquiry and Cirtical Thinking
The laboratory experiments and computer simulations will provide students with practical skills and training at a level that will be encountered when they enter the engineering workforce. In particular, the lab experiments will provide students with training in the use and basic operation of electronic equipment and the use of mathematical simulation to solve physics problems. Students will also be instructed to conduct experiments and record results in a manner that enables experiments to be accurately reproduced and interpreted by others. [Assessments 1 & 2]
GA3 Professional, ethical and social reponsibility
GA5 Communication
Both written and oral communication skills will be developed through written laboratory reports, prepared as part of a group, and presentation of these reports in class tutorials. Students will also be instructed in the effective and concise presentation of data and technical reports through the physics laboratories. These laboratories will involve the use of computer simulation software, graphical analysis packages, and data acquisition and processing software currently used in research laboratories and in engineering firms. [Assessments 1 & 2]
Teaching and learning strategies
Maths: The mathematics section consists of two hours of lectures per week. Each lecture will focus on a specific maths topic (see contents below). Tutorial problem sets will be assigned each week, these will completed and assessed online. A one-hour tutorial will also be available for students to seek help with these problems.
Physics: The physics section consists of a one hour lecture and a one hour tutorial for the first 8 weeks.
The core material will be delivered via lectures, interspersed with demonstrations and explanations delivered by the lecturers. You will supplement the lecture notes by asking questions and discussing concepts and diagrams. The aim of this is to deliver a concise set of course notes while promoting attendance, active learning and exploration in the lectures and tutorials.
Pre-learning: Prior to the lectures you will be given pre-work in the form of additional reading, problems questions and research tasks (some content will be obtained online). Some of the pre-work will also be crucial for you to complete prior to entering the subsequent classes. At the start of the lectures you will be assessed on your comprehension of the pre-learning through Q+A, quizzes and discussion. To give an example: the last century has provided diverse developments in the field of quantum mechanics. As part of the pre-learning in the physics section you will be asked to research historical developments in quantum mechanics and present the findings to the class verbally.
Group learning: During the lectures small “break-out” sessions will take place that are designed for student-focussed group learning. You will be asked to complete tasks and solve problems. The lecturer will then lead discussion and give feedback to complete the learning cycle. e.g. in the form of mathematical solutions to the given problem.
Content (topics)
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Surface integrals over vector fields;
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Divergence and Stokes’ theorems;
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Differentiation and integration of a complex variable;
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Cauchy-Riemann equations;
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Cauchy’s theorem and Cauchy’s integral formula;
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Taylor and Laurent series of functions of a complex variable;
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Residue theorem and Laplace transforms;
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Quantum phenomena;
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Separation of variables to the solution of partial differential equations with given boundary conditions;
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Wave functions and probability distributions of measurements;
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Schrödinger’s wave equation;
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Introductory semiconductor physics.
Assessment
Assessment task 1: Physics Laboratory Experiment and Report
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 03 and 04 This assessment task contributes to the development of course intended learning outcome(s): 1.1 and 2.1 |
| Type: | Laboratory/practical |
| Groupwork: | Group, individually assessed |
| Weight: | 25% |
| Criteria: | Accuracy of calculations, clarity of report, correctness of conclusions. |
Assessment task 2: Weekly Physics and Maths Problems
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 3. Professional, ethical and social responsibility 5. Communication
|
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 01, 02 and 03 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 3.1 and 5.1 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 40% |
| Criteria: | Degree to which questions have been answered correctly. |
Assessment task 3: Examination
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 01 and 02 This assessment task contributes to the development of course intended learning outcome(s): 1.1 and 2.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 35% |
| Criteria: | Degree to which questions have been answered correctly. |
Recommended texts
D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics 8th or 9th ed, Wiley.D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics 8th or 9th ed, Wiley.
J. Stewart, Calculus, 6th edition, Cengage, 2007
P. O’Neil, Advanced Engineering Mathematics, 6th edition, Cengage, 2006.
(alternate physics text)
H.D. Young and R.A. Freedman, University Physics, Addison-Wesley.
Other resources
Zill and Cullen, Advanced Engineering Mathematics, 3rd edition, Jones & Bartlett, 2006
Paul's online maths notes (see External links)
S. M. Sze and Kwok K. Ng, Physics of semiconductor devices, 3rd ed., Wiley 2007 (online access through UTS library- see External links)
Nave C.R. Hyperphysics, http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html