You need to know a fair amount of mathematics before embarking on a study of calculus.

Listed below are topics in mathematics that are used in calculus. Some are essential for the development of the subject. They're marked with the symbol . Others are used incidently in applications of calculus. Most of them we assume that you know and we won't review them at all, but we'll remind you a bit about a few of them as we use them. Most of the topics are used in the first semester of calculus, but a few aren't used until later.

- Topics from arithmetic. We assume you know these:
- Kinds of numbers. Fractions and decimals. We'll refer to integers (whole numbers, either positive, negative, or zero), rational and irrational numbers. The number line
- Conventions for arithmetic notation including order of operations (precedence), proper use of parentheses
- Expression manipulation. Distibutive laws, law of signs
- Exponents and laws for exponents
- Roots, laws for roots, rational exponents, rationalizing denominators
- Absolute value, order (less than, etc.), and their properties
- Factorials (e.g., 5! is the product of the integers from 1 through 5)

- Topics from geometry
- Pythagorean theorem
- Similar triangles
- Areas of triangles, circles, and other simple plane figures
- Perimeters of simple plane figures, circumference of circles
- Volumes of spheres, cones, cylinders, pyramids
- Surface areas of spheres and other simple solid figures

- Topics from algebra. We use algebra constantly. You've
*got*to know algebra well. Topics:- Translating word problems into algebra
- Expression manipulation. Addition, subtraction, and multiplication of polynomials
- Rational functions and their domains, least common denominators
- Techniques for simplifying algebraic expressions
- Factoring quadratic polynomials and other simple polynomials
- Techniques for solving linear equations in one unknown
- Solving quadratic equations in one unknown, completing the square, quadratic formula
- Solving linear equations in two or more unknowns
- Techniques for solving inequalities and both equations and inequalities involving absolute value
- The concept of function, functional notation and substitution, domain and range of a function
- Composition of functions

- Uniform motion in a straight line. When objects move with constant velocity, the relation among distance, time, and velocity
- Notation and concepts from set theory. We only use a bit of the notation from
set theory and only the most basic concepts
- Sets, membership in sets, subsets, unions, intersections, empty set
- Open and closed intervals and their notations

- Topics from analytic geometry. Mainly the basics, straight lines,
circles, a little on quadratic functions
- Coordinates of points in the plane
- Linear equations. Slope-intercept form especially, but also other forms
- Distance between two points
- Equations of circles, especially the unit circle
- Slopes of straight lines, parallel lines
- Graphs of functions. Vertical line test
- Symmetries of functions, even and odd functions. Transformation of functions
- Graph of a quadratic function is a parabola
- Graph of
*y*= 1/*x*is a rectangular hyperbola

- Topics from trigonometry. For a review of trigonometry, see
"Dave's Short Course in Trig" at
http://www.clarku.edu/~djoyce/trig/
- Angle measurement, both degrees and radians, but radians are more important in calculus. Negative angles.
- Length of an arc of a circle
- Understanding of trig functions of angles, especially sine, cosine, tangent, and secant. Trig functions and the unit circle
- Right triangles, trig functions sine, cosine, and tangent of acute angles. Values of these trig functions for standard angles of 0, π/6, π/4, π/3, π/2
- Solving right triangles
- Obtuse triangles. Law of sines, law of cosines. Solving obtuse triangles
- Basic trig identities. Pythagorean identities, trig functions in terms of sines and cosines
- Other trig identities. Double angle formulas for sine and cosine, addition formulas for sine and cosine

- Exponential functions and logarithms. Although these are topics
in algebra, they deserve to be separated for emphasis
- Exponential functions. Growth of exponential functions
- Laws for exponents. Manipulation of algebraic expressions involing exponents, solving equations involving exponents
- Logarithms and their relation to exponential functions
- Laws for logs. Manipulation of algebraic expressions involing logs, solving equations involving logs

- An understanding of mathematical proof. We'll develop more in calculus. You should be able to follow proofs like the ones you've already seen in geometry, algebra, and your other mathematics courses