PVB205 Classical Mechanics
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| Unit code: | PVB205 |
|---|---|
| Prerequisite(s): | (MXB106 OR PVB202 OR MZB127) and (MXB105 OR PVB200 OR MZB125 OR MXB161) and (PVB105 or PVB102) |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
| CSP student contribution | $1,164 |
| Domestic tuition unit fee | $4,968 |
| International unit fee | $5,664 |
Unit Outline: Semester 1 2025, Gardens Point, Internal
| Unit code: | PVB205 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | (MXB106 OR PVB202 OR MZB127) and (MXB105 OR PVB200 OR MZB125 OR MXB161) and (PVB105 or PVB102) |
| Assumed Knowledge: | First year calculus and algebra. |
| Coordinators: | Matthew Adams | mp.adams@qut.edu.au Aijun Du | aijun.du@qut.edu.au |
Overview
The first part of this unit focuses on vector calculus, complex functions and Fourier series, which is designed to provide strong mathematical knowledge and skills required by a physicist, to be used in this and advanced physics courses such as fluid dynamics, electromagnetism and quantum physics.
The second part of this unit applies the mathematical tools acquired in the first part to 3D Newton mechanics, and reformulate classical Newtonian mechanics into mathematically sophisticated frameworks, i.e., Lagrangian and Hamiltonian mechanics under arbitrary coordinate systems.
These tools will be used to analyze real world effects, starting from First Nations Australian's experience in mechanics, through to descriptions of planetary motion and more.
The Lagrangian and Hamiltonian formulation derived from the principle of least action using the calculus of variations generalises elegantly to modern quantum mechanics.
Learning Outcomes
On successful completion of this unit you will be able to:
- Develop skills in vector calculus, function of complex variables and Fourier series by theoretical demonstrations and problem solving activities.
- Apply Lagrangian and Hamiltonian equations to the solution of classical mechanics problems including the analysis of First Nation tools.
- Use symmetry to demonstrate the conservation laws of linear momentum, angular momentum and energy.
- Write computer code to solve simple classical mechanics problems.
- Communicate solutions to classical mechanics problems in writing, adhering to the conventions and standards of the discipline
Content
Topics to be covered in this unit include:
- Vector Calculus.
- Functions of complex variables
- Fourier series
- Coordinate Systems.
- 3D Newtonian Mechanics.
- Variational Principles.
- Lagrangian Formulations of Mechanics.
- Hamiltonian Formulations of Mechanics
- Noether’s theorem, symmetry, and conservation laws.
- Canonical transformation
- Poisson brackets.
- Python programming
Learning Approaches
As a second year unit, you are expected to take responsibility for your learning and undertake some self-directed learning. You can expect to spend between 10 - 15 hours per week on average involved in preparing for and attending all scheduled tutorials, completing assessment tasks, and undertaking your own independent study to consolidate your learning.
In this unit you will spend the first six weeks studying Vector calculus and advanced mathematics and the last six week of the unit studying Classical mechanics.
This unit engages you in your learning through an integrated lecture-tutorial program.
- Lectures: in class interactive lectures will require preparatory work by watching online videos and reading material provided via the learning platform.
- Tutorials: developing problem-solving skills and the ability to confidently apply mathematical knowledge and skills to solve actual mechanics problems.
- Computer Lab: you will work in groups to develop extra skills in computation to understand key concepts in classical mechanics and solve simple mechanics problem numerically.
Feedback on Learning and Assessment
TImely self, peer and academic feedback will be provided during semester for the problem solving task.
Feedback for the mid semester and final exam will be provided as required.
Assessment
Overview
The assessment in this unit includes a portfolio of analytical and computer based problem solving tasks, a mid semester exam and a final exam.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Portfolio
Set of problems to be solved analytically or by writing a computer program to demonstrate understanding and increase your problem solving skills across the whole unit.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Mid semester exam
Short and long answer written examination on vector calculus, functions of complex numbers and Fourier transforms.
Assessment: Final exam
Short and long answer written examination on Classical mechanics problems, including First nation experience.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Requirements to Study
Requirements
No out of the ordinary requirements.
Resources
Books and other resources
Resource Materials
Recommended text(s)
Elementary Vector Calculus and Its Applications with MATLAB Programming.
Shah, Nita H.; Panchal, Jitendra.
2022 ; 1st ed.
Aalborg : River Publishers
Complex variables and analytic functions : an illustrated introduction
Fornberg, Bengt, Piret, Cécile. Publisher: Society for Industrial and Applied Mathematics Philadelphia
2020
George B. Arfken and Hans J. Weber. Mathematical methods for physicists. Academic Press Inc., San Diego, CA
Landau, Lev D., and Evgenij M. Lifshitz. Mechanics: Course of Theoretical Physics. Vol. 1. 3rd ed. Butterworth-Heinemann, 1976. ISBN: 9780750628969.
Risk Assessment Statement
There are no out of the ordinary risks associated with is unit
Standards/Competencies
This unit is designed to support your development of the following standards\competencies.
Engineers Australia Stage 1 Competency Standard for Professional Engineer
1: Knowledge and Skill Base
Relates to: Portfolio, Mid semester exam, Final exam
Relates to: Portfolio, Mid semester exam, Final exam
Relates to: Final exam
2: Engineering Application Ability
Relates to: Portfolio
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.ST01 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO3, ULO4, Portfolio, Mid semester exam, Final exam - Recognise First Nations Peoples of Australia as the nation’s first scientists, whose knowledge and contributions are valued.
Relates to: ULO2, Portfolio, Final exam - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Portfolio, Mid semester exam, Final exam - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO1, ULO4, Portfolio, Mid semester exam - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO5, Portfolio, Final exam
SV02 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO3, ULO4, Portfolio, Mid semester exam, Final exam - Recognise First Nations Peoples of Australia as the nation’s first scientists, whose knowledge and contributions are valued.
Relates to: ULO2, Portfolio, Final exam - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Portfolio, Mid semester exam, Final exam - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO1, ULO4, Portfolio, Mid semester exam - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO5, Portfolio, Final exam