Some Students Think Their Knowledge of Mathematics Disadvantages Them in Physics

Math Needed for Intro Physics

In the past, some students worried that their knowledge of mathematics might be deficient for studying physics. While it is true that the greater your mathematical proficiency the better off you will be (in most subjects, including physics) all of you should be well equipped to succeed in this course. Below is a summary of the math (beyond elementary stuff) you'll need to know for introductory physics. I don't claim this list to be exhaustive, but rather a short checklist. If you feel you don't understand any of these topics, or when and how to apply them, please seek help from me or other teachers/students.

Basic Algebra:

Solving Simultaneous Equations Suppose you have two equations with two unknowns: x + y = 1 and x - y = 5 There are many ways to go about solving these two, but perhaps the easiest is to solve one equation for one of the two unknowns and substitute this into the other equation. For example, solving the second equation for x shows that x = 5 + y. Putting this into the first equation gives (5 + y) + y = 1. Therefore 2y = 4 or y = 2. With this information we can go to either equation and show that x = 3. A word of caution: having two equations and two unknowns does not guarantee a unique solution (they must be linearly independent). Try solving x + 2y =1 and 2x + 4y = 2. We will rarely have more than three equations, however, the "unknowns" may not be as obvious (they might be F, or a, or even theta )!

Solving Quadratic Equations Given an equation of the form ax2 + bx + c = 0 the possible solutions may be found by using the quadratic formula:

 b  b 2  4ac x  2a Direct substitution into this formula will yield two answers. Both of these solutions are correct mathematically, but sometimes one of them is not appropriate or "not physical" (e.g. negative times in projectile motion).

Basic Trigonometry: Sine, Cosine, and Tangent You need to know the definition of Sine, Cosine, and Tangent. Examine the right triangle below.

 b I have labeled the three sides a, b, and c and one angle  (after all, every angle in the world is called theta.) With respect to this angle you might call a, b, and c the opposite, adjacent and hypotenuse, respectively. The trig functions are defined as follows:

a b a sin  , cos  , tan  . c c b

You may know that (sin)2 + (cos)2 = 1. Other basic geometry is useful, like determining angles from parallel lines, use of similar triangle, etc.

Some people remember the term "sohcahtoa". Each letter represents a word, so sine is opposite over hypotenous, cosine is adjacent over hypotenous, and tangent is opposite over adjacent. You may know that (sin)2 + (cos)2 = 1. Other basic geometry is useful, like determining angles from parallel lines, use of similar triangles, etc. Occasionally the law of sines and the law of cosines come in handy:

sin A sin B sin C   and c 2  a 2  b 2  2abcosC a b c

Radians are "rad"!

Lastly, your must understand the definition of a radian. A circle is said to have 360 degrees OR EQUIVALENTLY 2 radians. Thus the arclength subtended along a portion of a circle is proportional to the angle (in radians) and the radius. The following equation holds: l = r ,

where l is the arclength, r is the radius, and  is the angle.

That's about it. Not too hard. Some other advice I can give is to know (not memorize, learn) the values for sine and cosine of 0, 30, 45, 60, and 90 degrees. Also, on many problems it might be easier not to use your calculator, even if it's just to get an estimate of the answer. Lastly, always make sure your answer makes sense. I've seen many people write down numerical answers that were completely absurd for the given problem.

Keep repeating: Fizx is phun!