Solving Tutorial Problems

1. Solving Tutorial Problems a very brief introduction Dieter Jaksch

2. Explain mathematical methods • Vacation work, Integration problem 9: Integrate by parts again: Integrate by parts: • Here: and • and • Explain methods clearly • Discuss assumptions • Justify approximations • Answer the question!

3. Explain mathematical methods • In later work on different topics • Same problem • Similar problem Vacation work, problem integration 9 Integrate by parts:

4. Explain the physics • Vacation work, mechanics problem 1: A car accelerates uniformly from rest to 80km per hour in 10s. How far has the car travelled? The position of the car is related to its speed by and the acceleration is given by . Since is constant in time we can integrate this equation and find Here is the constant of integration. Since the car is at rest initially . We thus have at We now integrate to obtain the car’s position Here is another constant of integration describing the initial position. We are interested in how far the car has travelled from its initial position and so the distance travelled is • Explain approach clearly • Check that the answer is sensible • Is this the full solution to the problem?

5. Diagrams • For instance: Superposition of wavesat envelope • Axes with labels • Features of graph • Guiding curves • Integral part of answer • Need not be quantitative

6. Summary • Explain mathematical methods • Explain the methods you use clearly and in detail • State and discuss any assumptions you make • State and justify any approximations you use • Carefully read and answer the actual question • Explain the physics • Explain your approach clearly • Check that the answer is sensible • Ensure that you provide the full solution to the problem • Diagrams • Always draw axes with labels • Discuss special features of the graph • Use additional lines and curves to guide the eye • Diagrams are in important Integral part of answers • Diagrams do not need to be quantitatively correct

7. Maths Logo