Undergraduate Course: Algebra and Calculus (PHYS08041)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Credits | 20 |
| Home subject area | Undergraduate (School of Physics and Astronomy) |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This course is designed for pre-honours direct entry physics students. It covers basic and more advanced algebra, as well as basic and multivariate calculus, which are used to describe concepts in physics. The course consists of lectures to present new material, and workshops to develop understanding, familiarity and fluency. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
On completion of this course it is intended that student will be able to:
- Show fluency and confidence in elementary algebra and calculus, basic problem-solving techniques and the methods of linear algebra as they apply to physical problems.
- Interpret unfamiliar equations, e.g. through appropriate sketches (especially of graphs) and by identifying special cases.
- Present a solution to a physics problem in a clear and logical written form.
- Assess whether a solution to a given problem is physically reasonable.
- Locate and use additional sources of information (to include discussion with peers and use of computer algebra packages where appropriate) to facilitate independent problem-solving. |
Assessment Information
20% coursework
80% exam |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Basic Algebra & Calculus (20 lectures)
- Basic Algebra. Manipulating expressions. Squares. Polynomials. Factorization. Quadratic and root equations (3)
- Functions. Inequalities. Moduli. Exponentials and logarithms. Curve sketching. Series expansions. Harmonic potentials. (3)
- Geometry and trigonometry. Trig functions. Lines and circles. Conic sections. (3)
- Complex numbers. Complex algebra. Argand diagram. Euler and de-Moivre. (2)
- Derivatives. Differentiation of standard functions. Composite functions. Higher derivatives. (3)
- Elementary Ordinary Differential Equations. (3)
- Integrals. Standard integrals. Integrating by parts. Substitution. (3)
Linear Algebra & Several Variable Calculus (20 lectures)
- Vectors. Basic vector algebra. (1)
- Dot and cross products. Triple products. (3)
- Linear independence. Expansion in a basis. Change of basis. (1)
- Matrices. Matrix algebra. Orthogonal transformations. (3)
- Determinant, rank and inverse. Eigenvalues and eigenvectors. Matrix diagonalisation (4)
- Complex vectors. Hermitian and unitary matrices. (2)
- Taylor expansions. Maxima, minima and saddle points (1)
- Partial derivatives. Chain rule. Change of variables. Spherical and cylindrical polar coordinates. (3)
- Multivariate integration. (2)
|
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | AC |
Contacts
| Course organiser | Dr Richard Blythe
Tel: (0131 6)50 5105
Email: |
Course secretary | Miss Jillian Bainbridge
Tel: (0131 6)50 7218
Email: |
|
|
University Homepage