Undergraduate Course: Algebra and Calculus (PHYS08041)
Course Outline
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 
SCQF Credits  20 
ECTS Credits  10 
Summary  This course is designed for prehonours 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. 
Course description 
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 deMoivre. (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)

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  Students MUST NOT also be taking
Mathematics for Physics 2 (PHYS08036) OR
Linear Algebra and Several Variable Calculus (PHYS08042)

Other requirements  Physics and Maths with A grades in Advanced Highers or Alevels (or equivalent)
This course should only be taken by new entrants starting in year 2 (Direct Entry) of the following degrees:
School of Physics and Astronomy:
Physics, Astrophysics, Comp Physics, Physics with Met, Theoretical Physics (but not Mathematical Physics).
School of Chemistry:
Chemical Physics
School of Geoscience:
Geophysics, Geophysics with Met, Geophysics with Professional Placement, Geophys with Met and PP.

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 Show fluency and confidence in elementary algebra and calculus, basic problemsolving 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 problemsolving.

Reading List
Mathematical Methods for Physics and Engineering
AUTHORS: K.F. Riley, M.P. Hobson & S.J. Bence
ISBN: 9780521679718 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  AC 
Contacts
Course organiser  Dr Jamie Cole
Tel: (0131 6)50 5999
Email: R.J.Cole@ed.ac.uk 
Course secretary  Miss Stavriana Manti
Tel: (0131 6)50 5310
Email: stavriana.manti@ed.ac.uk 

