## MATH374 Mathematical Physics

Second Semester |

### Paper details

This paper presents the foundation theory for two major topics in Physics. The Classical Mechanics section introduces the formal framework of classical mechanics and illustrates its application to two-body problems, rotating systems, collisions and chaos. The Special Relativity and Cosmology section covers the special theory of relativity with applications to relativistic mechanics as well as an introduction to cosmology.

Note that this paper is the same as the PHSI336 paper offered by the Physics Department. It is taught jointly by staff from both Departments.

### Potential students

The paper addresses students who are interested in the mathematical foundations of physical theories. This includes Maths students, interested in applications and Physics students interested in the formal underpinnings of Physics.

### Prerequisites

MATH203 and 36 300-level MATH or PHSI points

### Restrictions

PHSI334, PHSI336

### Lecturers

- First half: Dr Terry Scott
- Second half: Dr Jörg Hennig (Room 215), Dr Florian Beyer (Room 218)

### Lectures

- Tuesday 12 noon
- Wednesday 11 am
- Thursday 12 noon

lecture theatre: PX314

### Tutorials

- First half: See the Physics web page
- Second half: 1 hour per week, Fridays at 2-3 pm.

### Literature

See the resources webpage.

### Internal Assessment

- First half: See the Physics web page
- Second half: 5 weekly assignments

### Exam format

3 hour final exam

For other details see the Physics web page

### Final mark

Your final mark F in the paper will be calculated according to this formula:

**F = 0.6E + 0.35A + 0.05W**

where:

- E is the Exam mark
- A is the Assignments mark
- W is the Workshops mark

and all quantities are expressed as percentages.

**Minimum exam score:** To pass this paper you are required to obtain at least 30% in the final examination.

### Students must abide by the University’s Academic Integrity Policy

**Academic integrity** means being honest in your studying and assessments. It is the basis for ethical decision-making and behaviour in an academic context. Academic integrity is informed by the values of honesty, trust, responsibility, fairness, respect and courage.

**Academic misconduct** is seeking to gain for yourself, or assisting another person to gain, an academic advantage by deception or other unfair means. The most common form of academic misconduct is plagiarism.

Academic misconduct in relation to work submitted for assessment (including all course work, tests and examinations) is taken very seriously at the University of Otago.

All students have a responsibility to understand the requirements that apply to particular assessments and also to be aware of acceptable academic practice regarding the use of material prepared by others. Therefore it is important to be familiar with the rules surrounding academic misconduct at the University of Otago; they may be different from the rules in your previous place of study.

Any student involved in academic misconduct, whether intentional or arising through failure to take reasonable care, will be subject to the University’s Student Academic Misconduct Procedures which contain a range of penalties.

If you are ever in doubt concerning what may be acceptable academic practice in relation to assessment, you should clarify the situation with your lecturer before submitting the work or taking the test or examination involved.

Types of academic misconduct are as follows:

**Plagiarism**

The University makes a distinction between unintentional plagiarism (Level One) and intentional plagiarism (Level Two).

- Although not intended,
*unintentional plagiarism*is covered by the Student Academic Misconduct Procedures. It is usually due to lack of care, naivety, and/or to a lack to understanding of acceptable academic behaviour. This kind of plagiarism can be easily avoided. *Intentional plagiarism*is gaining academic advantage by copying or paraphrasing someone elses work and presenting it as your own, or helping someone else copy your work and present it as their own. It also includes self-plagiarism which is when you use your own work in a different paper or programme without indicating the source. Intentional plagiarism is treated very seriously by the University.

**Unauthorised Collaboration**

Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each students answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer..

**Impersonation**

Impersonation is getting someone else to participate in any assessment on your behalf, including having someone else sit any test or examination on your behalf.

**Falsiﬁcation**

Falsiﬁcation is to falsify the results of your research; presenting as true or accurate material that you know to be false or inaccurate.

**Use of Unauthorised Materials**

Unless expressly permitted, notes, books, calculators, computers or any other material and equipment are not permitted into a test or examination. Make sure you read the examination rules carefully. If you are still not sure what you are allowed to take in, check with your lecturer.

**Assisting Others to Commit Academic Misconduct**

This includes impersonating another student in a test or examination; writing an assignment for another student; giving answers to another student in a test or examination by any direct or indirect means; and allowing another student to copy answers in a test, examination or any other assessment.

### Calculus of Variations

The**calculus of variations**uses small variations in functions to find critical points of functionals. This can be applied in physics to obtain the

**Lagrangian formulation**of classical mechanics.

### Albert Einstein

Where would modern physics be without the genius of

**Albert Einstein**(1879-1955)? In 1905, he published four brilliant articles which contributed substantially to the foundation of modern physics and changed our views on space, time and matter. His special theory of relativity is proven to be the most accurate model of motion at any speed that we have, when gravitational effects are negligible.

### Alexander Friedmann

**Alexander Friedmann**(1888-1925) was a Russian physicist and mathematician. In 1922, he discovered cosmological models as solutions to Einstein's field equations which describe an expanding universe. Only 37 years old, Friedmann died in 1925 from typhoid fever – four years before the astronomer Edwin Hubble measured the redshifts of distant galaxies and showed that the universe is indeed expanding.