Context
This course forms part of the Professional Skills units of the level 1 physics and astronomy courses. It is included in PHY113 Professional Skills in Physics I, PHY115 Professional Skills in Physics and Astrophysics I, PHY117 Professional Skills in Astrophysics and PHY118 Professional Skills in Physics.
Aims
The course aims to develop a systematic approach to problem solving, using a four-step process
that can be applied to any type of problem. In addition to practising this approach on a range of
problems, we will look specifically at the techniques of dimensional analysis, order-of-magnitude
estimates and scaling.
On successful completion of this course, you should be able to:
- approach physics and astrophysics problems in a systematic way;
- have confidence in your ability to tackle different types of problem;
- check that solutions to problems are likely to be correct (or at least are not obviously wrong);
- use dimensional analysis to analyse problems involving unfamiliar physics;
- use appropriate power series expansions to simplify calculations.
Syllabus
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Lecture 1: Problem Solving
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the four-step approach to problem solving:
- Model the situation, using diagrams to help you think through exactly what is happening
and what physical laws are involved.
- Formulate the problem, converting your conceptual model into equations using the appropriate
laws of physics.
- Solve the equations, first symbolically, and then inserting numbers if required.
- Check that the result makes sense!
-
Lecture 2: Dimensional Analysis and Special Values
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how to check results:
- by ensuring that they have the correct dimensions (and, for numerical results, units);
- by confirming that they behave sensibly in special cases where it is easy to see what "should" happen.
-
Lecture 3: Expansions and Estimations
-
how to use power series expansions to simplify calculations, and how to make order-of-magnitude estimates
to check numerical values.
