Undergraduate Course: Algebra and Calculus (PHYS08041)
|School||School of Physics and Astronomy
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 8 (Year 2 Undergraduate)
||Availability||Available to all students
|Summary||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.
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)
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2020/21, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 42,
Seminar/Tutorial Hours 60,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Hours & Minutes
|Main Exam Diet S1 (December)||3:00|
|Resit Exam Diet (August)||3:00|
On completion of this course, the 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.
|Mathematical Methods for Physics and Engineering|
AUTHORS: K.F. Riley, M.P. Hobson & S.J. Bence
|Graduate Attributes and Skills
|Course organiser||Dr Philip Clark
Tel: (0131 6)50 5231
|Course secretary||Mr Daniel Berger
Tel: (0131 6)51 7521