# Preparation for Physics

**Minimum Mathematical Background (Prerequisite: MA 106
or equivalent)
Required for PH 101-103 and PH 221-222 (with calculus)
by David G. Agresti, Professor of Physics, UAB
Bring to all classes: Scientific calculator and centimeter -based ruler and/or
triangles.**

1. Arithmetic

+ , - , × (or · ) , ÷ (or / ) , and powers

Examples: Note order!

2. Scientific Notation

Powers of 10

Examples : (both have 3 sig. digits )

3. Geometry

Drawing and properties of 2 and 3-D figures

Examples:

Properties of rectangles, triangles, cylinders, spheres, etc.

Formulas for areas , volumes, perimeters of above

Angles in triangles and intersecting lines ; degrees and radians

Compass directions; vectors and vector operations (optional)

4. Trigonometry

Relations among sides (a, b, c) and angles (α, β) in a right (90°)
triangle

Find missing information, given two sides or one side and an angle (≠90°)

Examples:

5. Graphing

2- and 3-D figures showing functional relationships and position in space

Examples:

Position coordinates in 2-D: (x, y) ; (r, θ)

Position coordinates in 3-D:

Functions of one and two variables: y = f (x); z = g (x, y)

Graphs of simple functions : etc.

6. Algebra

Manipulation of expressions with variables

Examples: Addition of polynomials

Solving quadratic equations

Solving for unknowns in one or more equations

Note two rules for equations:

Do unto one side as you do unto the other.

N unknowns require N independent equations.

7. Proportions and ratios

Change in one variable when another one changes

Examples: Suppose a = b/c . Then, assuming the other quantity is constant:

Direct proportions are: ; (read: "a is
proportional to b")

Thus, e.g., if b is doubled, then a is doubled also.

Inverse proportion is: ; ("a is inversely
proportional to c")

Thus, if c is doubled, then a is halved.

Ratios: Direct prop.: ( ratio is
constant )

Inverse prop.: ( product is constant )

8. Use of the calculator

Scientific calculator is required.

Examples of calculator operations you should be able to perform:

(optional)

9. Calculus (required only for PH 221-222)

Simple derivatives, integrals, and related concepts,

including analytic geometry, limits, slopes, and extrema

Examples:

Derivatives of simple functions:

Graphical interpretation of slope ; rate

Maxima, minima, inflection points

Antiderivatives of simple functions

Definite integrals, area, volume

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