a very brief introduction Dieter Jaksch Explain mathematical methods Vacation work Integration problem 9 Integrate by parts Here and and Integrate by parts again ID: 796842
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Slide1
Solving Tutorial Problems
a
very brief introduction
Dieter Jaksch
Slide2Explain mathematical methods
Vacation work, Integration problem 9:
Integrate by parts:
Here:
and
and
Integrate by parts again:
Explain methods clearly
Discuss assumptions
Justify approximations
Answer the question!
Slide3Explain mathematical methodsIn later work on different topics
Same problem
Similar problem
V
acation work, problem integration 9
Integrate by parts:
Explain the physicsVacation 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 positionHere 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?
Slide5Diagrams
For instance: Superposition of waves
at
e
nvelope
Axes with labels
Features of graph
Guiding curves
Integral part of answer
Need not be quantitative
Slide6SummaryExplain mathematical methods
Explain the methods you use clearly and in detailState and discuss any assumptions you make
State and justify any approximations you use
Carefully read and answer the actual question
Explain the physicsExplain your approach clearlyCheck that the answer is sensibleEnsure that you provide the full solution to the problemDiagramsAlways draw axes with labels
Discuss special features of the graphUse additional lines and curves to guide the eyeDiagrams are in important Integral part of answers
Diagrams do not need to be quantitatively correct
Slide7Maths Logo