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Solving Tutorial Problems. a very brief introduction Dieter Jaksch. 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

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Solving Tutorial Problems

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## Solving Tutorial Problems

a very brief introduction

Dieter Jaksch

### 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

### Explain mathematical methods

• In later work on different topics

• Same problem

• Similar problem

Vacation work, problem integration 9

Integrate by parts:

### 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?

### Diagrams

• For instance: Superposition of wavesat

envelope

• Axes with labels

• Features of graph

• Guiding curves

• Need not be quantitative

### 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

• Explain the physics

• 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