Mastering Formula Manipulation: Tips for Calculus and Physics Success"

[supernova1203]

Im going to be taking calculus soon and I am doing ok in my courses, the one thing i feel i need to work on is the ability to manipulate mathematical formulas (change a variable or 2 to find what i need)

for instance this formula

A=P(1+i)^n

can be re arranged as

P=A/(1+i)^n

also

A/P=(1+i)^n

this is a base i feel wasnt covered well enough in previous grades, its one of the most basic things, yet I am not 100% on it there must be a rulebook somewhere or something that explains what to do to variables/equations once you move them around or manipulate them to find the missing items.

Its ironic that i can do just about anything and yet i have trouble with such a simple concept, as i said I am about to take calc pretty soon and i have no trouble with the concepts and material studied so far.

I also believe this skill is needed in physics as well, any help or reference would be appreciated :)

 

[phyzguy]

The basic concept is that, since the two sides of the equation are equal, you can do pretty much anything you want to the equation, as long as you do the same thing to both sides. Since the two sides are equal to start with, if I do the same thing to both sides, the two sides will still be equal after I do whatever it is I want to do. In the example you gave, to get from your equation 1 to your equation 2, what you do is "divide both sides by (1+i)^n" . To get from your equation 1 to your equation 3, what you do is "multiply both sides by (1+i)^n" , then divide both sides by P".

From there, you just need to get an idea of where you want to go, and what manipulations you can do to move you closer to your target. The only real exception that I can think of is that you can't divide both sides by zero.

Does this help?