Physics 271: Advanced Honors Physics I
Recitations: Problem-Solving Toolbox
Fall 2017

Solving differential equations I: Check to see if it is separable (for a review of separable diff equations, see the Week 1 resources on the main page). Once you separate it, see if you can do the indefinite integrals. Then, choose the constants so that the function satisfies the initial conditions (or other given information)

Solving systems of simultaneous linear equations: Systems of two linear equations in two unknowns come up frequently and occasionally we have to solve systems of three equations in three unknowns (usually the latter are special cases that allow simpler solution by hand than the general case). You should be able to do these quickly and accurately by hand. One tip is to rewrite and organize the equations neatly together to get the solution started. Another tip, to reduce work, is to look at the problem to see what quantity or quantities are asked for, and solve by eliminating the quantity or quantities not asked for.

Solving min-max problems: If you need to find the maximum or minimum value attained by a certain quantity, and there is no obvious shortcut, you should use the procedure you learned in calculus class. First, write the quantity to be maximized as a function of the quantity that you can vary. Then compute the first derivative and set it to zero to find the extrema. Evaluate at the extrema and also at the endpoints of the domain, and choose the max (or min) value.

Check the units: After doing the algebra to express the quantity (or quantities) desired in terms of the given quantities, check that your answer has the right units. This is necessary but not sufficient for a right answer, but it's quick and can help you pick up some mistakes.

A rule to decide which direction to draw the friction force when making force diagrams: First solve the related problem in which the coefficients of friction are all zero. Then look at the relative motion you find for the surfaces with friction: the direction of the friction force will act to oppose the relative motion. This works both for static friction forces and kinetic friction forces in all the problems we have considered so far, so it is looking good as a general rule -- if you find an exception, let me know!