Undergraduate Course: Mathematics for Physics 1 (PHYS08035)
|School||School of Physics and Astronomy
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 8 (Year 1 Undergraduate)
||Availability||Available to all students
|Summary||This course is designed for pre-honours physics students, primarily to develop their mathematical and problem solving skills in the context of basic algebra and calculus. A key element in understanding physics is the ability to apply elementary mathematics effectively in physical applications. For this, knowledge of mathematics is not enough, one also needs a deep understanding of the underlying concepts and practice in applying them to solve problems. The course is centred on problem solving workshops, and supported by lectures.
The course content is divided into six sections, each with a dedicated workbook of worked examples and exercises:
1. Solving equations and simplifying the answer: Linear and quadratic equations; arithmetic with complex numbers; expansion and factorisation; combining and decomposing fractions.
2. Functions: Definition of a function and inverse; even-odd symmetries; trigonometric functions, their inverses and reciprocals; exponential and logarithm; modulus and argument of complex numbers; Euler's formula; hyperbolic functions; trigonometric and hyperbolic identities; roots of a polynomial in the complex plane; singularities.
3. Lines and regions in the plane: equation of a straight line; conic sections; graphical representation of modulus function and polynomials; graphical representation of products and ratios of functions; algebraic and graphical representation of scaling and translation operations; relationship between regions and inequalities.
4. Differentiation. First-principles definition of a derivative and application to elementary functions; higher derivatives; product rule; chain rule; differentiating an inverse; tangent and normal to a curve; stationary points; preview of differential equations and partial derivatives.
5. Power series expansions. Power series as an approximation to a complicated function; Maclaurin and Taylor series expansion of elementary functions; ratio test for convergence; sums, products and ratios of power series; L'Hopital's rule for evaluating limits.
6. Integration. Definite and indefinite integrals. Improper integrals. Infinite range of integration. Integration by substitution and by parts. Common substitutions and other integration strategies.
Key concepts will be outlined in lectures. Students can get assistance in working through the workbooks at workshops, and a second set of workshops will be devoted to learning how to solve longer and more complex problems in groups.
Entry Requirements (not applicable to Visiting Students)
||Co-requisites|| It is RECOMMENDED that students also take
Physics 1A: Foundations (PHYS08016)
||Other requirements|| None
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 18,
Seminar/Tutorial Hours 40,
Feedback/Feedforward Hours 3,
Formative Assessment Hours 12,
Summative Assessment Hours 5,
Revision Session Hours 6,
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:
- Demonstrate awareness of foundational concepts in algebra and calculus and how these apply to physical problems
- Select an appropriate method for solving a problem, and execute it methodically
- Identify and apply a variety of strategies to check a solution is correct without referring to a given answer
- 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
- Take responsibility for learning by attending lectures and workshops, completing coursework in a timely manner, and working effectively in a collaborative group setting
K. F. Riley, M. P. Hobson and S. J. Bence. Mathematical Methods for Physics and Engineering: A Comprehensive Guide (Cambridge University Press).
K. F. Riley and M. P. Hobson. Foundation Mathematics for the Physical Sciences (Cambridge University Press, 2011). [Cheaper, cut down version of the recommended text covering the most essential material]
M. L. Boas. Mathematical Methods in the Physical Sciences (Wiley, 2006). [Covers the same content as the recommended text in a style that some students may prefer]
|Graduate Attributes and Skills
|Additional Class Delivery Information
||2 lectures and 2 out of 4 workshops.
|Course organiser||Prof Richard Blythe
Tel: (0131 6)50 5105
|Course secretary||Miss Stavriana Manti
Tel: (0131 6)50 5310