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Pauls Online Math Notes

Pauls Online Math Notes
Cheat Sheets and Tables Here is list of cheat sheets and tables that I've written. Most of these are pdf files and so you will need the Adobe Viewer to view them. You can download the latest version here. Algebra Cheat Sheet - [pdf] - This is as many common algebra facts, properties, formulas, and functions that I could think of. There is also a page of common algebra errors included. Related:  Wiskundereview

Math Functions - TI-Basic Developer Calculators are built with one primary purpose: math. Programming, game playing, and everything else is secondary. Thus, you will find a number of powerful math commands. Although it may seem that they are of no use to a programmer, programs sometimes need math functions, and many math functions can be used in clever ways. Number Operations These commands deal with different ways you can manipulate the integer and fraction parts of a number, and are mostly found in the MATH-NUM menu. ►Frac, ►Dec — display a number as either a fraction or a decimal.iPart(, int(, fPart(, round( — take the integer or fractional part of a number in various ways. Probability and Combinatorics These commands are generally found in the MATH-PRB menu (except for randM(, which is in the MATRIX-MATH menu). rand, randInt(, randNorm(, randBin(, randM( — pseudorandom number generation.nPr, nCr, ! Calculus Trigonometry Complex Number Operations Operators Powers, Inverses, Exponentials, and Logarithms Miscellaneous

Toomey.org Tutoring Resources This Web page contains reference materials for my WyzAnt students. My name is Harold and I have tutored hundreds of students in math, science and engineering over the past 25 years. I worked in the BYU Math Lab to pay my way through college where I earned a Master of Science degree in Electrical and Computer Engineering with a minor in mathematics. I tutor all levels of math, from prealgebra through calculus 3 and beyond. I love teaching students that really want to learn and have set a goal, but are either behind or are not connecting with their teachers. My teaching style is to show multiple ways to solve the same problem, then how to verify the answer as being correct. In addition to math and physics I also tutor chess and the C/C++ computer programming language. I am setup for remote tutoring using LogMeIn, Skype, and iPhone FaceTime. WyzAnt - Calculus, Precalculus and Physics Tutor - McKinney, TX • My WyzAnt Tutor Profile My WyzAnt Tutoring Certifications Tutoring Resources by Subject

maps home page Down to: 6th to 15th Centuries | 16th and 19th Centuries | 1901 to World War Two | 1946 to 21st Century The Ancient World ... index of places Aegean Region, to 300 BCE Aegean Region, 185 BCE Africa, 2500 to 1500 BCE Africa to 500 CE African Language Families Alexander in the East (334 to 323 BCE) Ashoka, Empire of (269 to 232 BCE) Athenian Empire (431 BCE) China, Korea and Japan (1st to 5th century CE) China's Warring States (245 to 235 BCE) Cyrus II, Empire of (559 to 530 BCE) Delian League, 431 BCE Egyptian and Hittite Empires, 1279 BCE Europe Fertile Crescent, 9000-4500 BCE Germania (120 CE) Greece (600s to 400s BCE) Gupta Empire (320 to 550 CE) Han China, circa 100 BCE Hellespont (Battle of Granicus River, 334 BCE) India to 500 BCE Israel and Judah to 733 BCE Italy and Sicily (400 to 200 BCE) Judea, Galilee, Idumea (1st Century BCE) Mesopotamia to 2500 BCE Mesoamerica and the Maya (250 to 500 CE) Oceania Power divisions across Eurasia, 301 BCE Roman Empire, CE 12 Roman Empire, CE 150 Roman Empire, CE 500

Properties of Circles. Bradshaw-Handouts The following files are the handouts used by the Ohlone College Math Department. They are available in printed form from the Math Learning Center in Hyman Hall. Trigonometry This gives a summary of the formulas used in Trigonometry. This includes the unit circle, the ranges of the inverse trig functions and information about graphing. Precalculus This gives a summary of the formulas used in Precalculus. Calculus I and II: Integral Card This contains the introductory derivative and integral formulas. Calculus II: Series This gives a summary of the convergence tests and a list of the common Taylor expansions. Calculus II: Polar Graph Paper Polar graph paper is used for graphing polar functions. Calculus III Graphing Commands This gives the various Mathematica graphing commands used in Calculus III. Calculus III Formulas This contains the formulas from Calculus III, including projectile motion, unit tangent and normal vectors, curvature, and Green's Theorem. Differential Equations

10 Awesome Online Classes You Can Take For Free Cool, but you need iTunes for nearly everything, and that gets an 'F.' Are there really no other places to get these lessons? I was sure there are some on Academic Earth. Flagged 1. 7 of them are available via YouTube. 2. iTunes is free. 1. 2. Don't worry, we're looking out for you! While I have no personal beef with iTunes, I know that many people share your sentiments — so I actually made a concerted effort to include relevant youtube links when possible.

Trigonometric and Geometric Conversions, Sin(A + B), Sin(A - B), Sin(AB) Ratios for sum angles As the examples showed, sometimes we need angles other than 0, 30, 45, 60, and 90 degrees. In this chapter you need to learn two things: 1. Sin(A + B) is not equal to sin A + sin B. First to show that removing parentheses doesn't "work." You know that no sine (or cosine) can be more than 1. Wanted sine, cosine, or tangent, of whole angle (A + B) Finding sin(A + B) The easiest way to find sin(A + B), uses the geometrical construction shown here. Notice the little right triangle (5). Now, put it all together (9). Finding cos(A + B) A very similar construction finds the formula for the cosine of an angle made with two angles added together. Using the same construction (1), notice that the adjacent side is the full base line (for cos A), with part of it subtracted at the right. The full base line, divided by the dividing line between angles A and E, is cos A (2). Now, for the little part that has to be subtracted. Finding tan(A + B) Ratios for 75 degrees Multiple angles 1.

Online tools - maths online One of many scientific calculators on the web. It accepts brackets, functions like sin, cos, tan, exp, log, sqrt, pow, asin, acos, atan, gamma, the constants E und PI. On the calculator's web page you find a detailed description. In a cooperation between the author and maths online in the beginning of 2000, the calculator's functionality has been extended. By the way: the plot is a gif-file and can be saved on your PC by a right mouse click. This page is a bit difficult to survey: The result is a web document looking exactly like the input page. Numerical tools on linear algebra: Computer algebra systems (CAS) are able to perform symbolic and numeric computations, simplify expressions, solve equations and differential equations, plot function graphs, differentiate, integrate, and much more. Dynamical geometry on the web may be found at the following sites.

Dave's Short Trig Course Table of Contents Who should take this course? Trigonometry for you Your background How to learn trigonometry Applications of trigonometry Astronomy and geography Engineering and physics Mathematics and its applications What is trigonometry? Trigonometry as computational geometry Angle measurement and tables Background on geometry The Pythagorean theorem An explanation of the Pythagorean theorem Similar triangles Angle measurement The concept of angle Radians and arc length Exercises, hints, and answers About digits of accuracy Chords What is a chord? Ptolemy’s sum and difference formulas Ptolemy’s theorem The sum formula for sines The other sum and difference formulas Summary of trigonometric formulas Formulas for arcs and sectors of circles Formulas for right triangles Formulas for oblique triangles Formulas for areas of triangles Summary of trigonometric identities More important identities Less important identities Truly obscure identities About the Java applet.

Math Scene - Functions 2 - Lesson 6 - Inverse functions Lesson 6 Inverse functions We have already seen some functions that are the inverse of each other. The functions f(x) = x2 and g(x) = √x are the inverse of each other if we limit the x values to non - negative numbers. These functions cancel each other out in the sense that if we apply first one function and then the other to a number then it's as if nothing has happened, the number is the same as it was to begin with. Look at the following example: f(x) = x2 and g(x) = f(2) = 22 = 4 and g(4) = √4 = 2 f(g(a)) = = a g(f(a)) = It doesn't matter which of the two functions f(x) or g(x) we apply first, the result is the same. A function has an inverse only if it is one - to - one and onto. We can find the equation of an inverse function algebraically by solving the equation of the function for x. Example 1 Find the inverse of the following functions: a) f(x) = 2x + 4 y = 2x + 4 put y instead of f(x) –2x = 4 – y x = –2 + ½y We have divided through by –2 This is an equation where x is a function of y. f(

Lesson The Amazing Unit Circle: Trigonometric Identities The unit circle definition of the trigonometric functions provides a lot of information The trigonometric functions sine and cosine are defined in terms of the coordinates of points lying on the unit circle x2 + y2 = 1. Start by constructing the ray from the origin at angle θ (measured counter-clockwise from the positive x-axis). Cosine of the angle θ is defined to be the horizontal coordinate x of this point P: cos(θ) = x. Sine of the angle θ is defined to be the vertical coordinate y of P: sin(θ) = y. As θ changes so does the position of the point P and thus the values of cos(θ) = x and sin(θ) = y also change. Right away the unit circle gives us properties of the cosine and sine functions. cos(0) = cos(0°) = 1 and sin(0) = sin(0°) = 0; cos(π/2) = cos(90°) = 0 and sin(π/2) = sin(90°) = 1; cos(π) = cos(180°) = -1 and sin(π) = sin(180°) = 0; cos(3π/2) = cos(270°) = 0 and sin(3π/2) = sin(270°) = -1. 1. cos2(θ) + sin2(θ) = 1. This is called the fundamental trigonometric identity. 2. or 3. 4. 5.

Area and Volume by Keith Enevoldsen Have you memorized some of the area and volume formulas, like A = πr2, without understanding the explanation for the formulas? This is an attempt to explain all the basic area and volume formulas as simply and intuitively as possible, starting with the easy ones and building up to the more difficult formulas for the area and volume of a sphere. Areas of Plane Figures Rectangles and Parallelograms Area of a rectangle or parallelogram with base b and height h is bh. Triangles Area of a triangle with base b and height h is bh/2. Polygons Area of any polygon can be determined by breaking it into simpler areas. Circles Area of a circle is πr2. Surface Areas and Volumes of Solids Prisms (including rectangular solids) and Cylinders Lateral surface area of a right prism or cylinder with perimeter p and height h is ph. Volume of a prism or cylinder, right or oblique (slanted), with base area A and height h is Ah. Pyramids and Cones Polyhedra Spheres Surface area of a sphere is 4πr2.

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