Astronomy 505

Homework Tips

Communicate Clearly Your submitted homework assignments should be clear, concise, and neat. First solve the problems on scratch paper, and then rewrite the solutions, filling in details as necessary and pruning dead ends. Please present your final results in CGS units. When writing up the final version, work through the following seven steps for each problem.
- State the assumptions that you are making, and give an overview of your solution.
- Draw a diagram which shows the set-up of the problem, if appropriate.
- State numerical values for constants.
- Express relevant quantities in algebraic form, defining variables as they are introduced.
- Manipulate equations, keeping as many intermediate steps as is necessary for the complete solution to be clear to the reader.
- Calculate numerical solution, with units.
- Comment on solution, as appropriate.
Draw a Picture. Diagrams are frequently a very good way to visualize the set-up of a problem, and to communicate that set-up to others. Use them whenever appropriate.
Justify your Work. Explain what you are doing, and why you are doing it. This can be particularly helpful at the beginning of each problem, as it will force you to think about the problem physically and to formulate your approach mathematically. Descriptions will help me to follow what you have done in a derivation (especially if you go off on a wild tangent!) and will also allow me to make constructive suggestions.
Show your Work. Give enough detail, and show enough mathematical steps, that a student less advanced than you could follow and understand your derivation. If you omit steps between two successive stages, be sure that you could fill in all of the gaps without hesitation and without aids. If you use a mathematical relation, cite the general form (e.g., by applying the law of cosines) and/or note the reference (e.g., as shown by Gradshteyn & Ryzhik 2.264 for the general case where R is less than unity).
Check your Units. All of your equations should be dimensionally correct. Check your work occasionally as you go through a derivation. Remember that in all physically valid solutions, the argument of all functions (e.g. trigonometric functions, exponentials, logs, hyperbolic functions) must be dimensionless.
Check the Limits. Check all of your final answers and important intermediate results to see whether they behave correctly in in the relevant limiting cases. Sometimes you will know how a general expression should behave if a particular variable is set to zero, to infinity, or to some other value. Make sure that your general expression reproduces the expected behavior!
Check for Symmetry. Symmetries are a fundamental facet of physics. Problems can exhibit symmetry about a point (spherical symmetry), a line (cylindrical or axial symmetry), or a plane (mirror symmetry). You can use them in two ways: 1) to check your final answer, or 2) to simplify your derivation. As an example, time-independent central forces (like gravity) have spherical symmetry because the force depends only on the distance from the origin. In this case, spherical symmetry means that once we find one solution (e.g. a particular ellipse for gravity), all other possible orientations of this solution in space are also solutions.
Apply Reality Checks. Develop physical insight into how the solution to a problem should look, and compare this with your derived solution. Trust your instincts! If a derived equation or numerical value looks strange, go back through the derivation and look for errors. If you can't find any, make a note of your concerns as you write up your final solution.
Collaborate. Work on the homework problems on your own first and get as far as you can on them, as this is the best way to improve your problem solving skill and to prepare for exams. But by all means, get help from other people when you are stuck! By trying the problems first, you will be able to ask more intelligent questions and to better understand the ideas that others suggest.
- Spend a minimum of 20 minutes per problem on your own, before seeking help.
- Keep your collaborative efforts balanced (give as much as you get).
- You may discuss problems with older students, but remember that all homework, quiz, and exam problems and solutions from previous years are off limits (to you, and to the people whom you consult).
- Track your level of independence with the collaborative assessment sheets every week.
Credit your Sources. If you draw heavily on material taken from a non-course text or set of notes, acknowledge this in your write-up (e.g., based on the exposition in Chapter 3, Section 2, of Landau & Lifshitz's Mechanics).
Review Assignments. When you get assignments back from me, review your work. Make sure that you could do similar problems if given the chance (say, on an exam).