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Math Introduction to Integrals 150 150 Deborah

Math Introduction to Integrals

Overview Finding integrals, or integration, is the opposite of finding the derivative in calculus. The concept is closely connected with functions, and was independently discussed by both Newton and Leibniz in the Fundamental Theorem of Calculus. Review of Functions Suppose the values of x are {1, 2, 3, 4, 5} using set notation, and the…

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Math Introduction to Derivatives 150 150 Deborah

Math Introduction to Derivatives

Overview A derivative of a function describes its rate of change at a particular point on the function. The rate of change doesn’t have to be constant, so it can be approximated along any point of a curve. Derivatives in calculus have many applications in quantitative sciences such as physics and chemistry. Geometric Definition Not…

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Math Review of Real, Complex, and Hyperreal Numbers 150 150 Deborah

Math Review of Real, Complex, and Hyperreal Numbers

Overview Real numbers are the rational and irrational numbers that people deal with in everyday life. Hyperreal numbers include numbers that are infinitely large, infinitely small, or infinitesimal, along with the reals. Surreal numbers include the reals, the hyperreals, and other constructs in advanced mathematics that sometimes behave like numbers and sometimes do not. Rational…

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Math Review of Platonic Solids and Polyhedra 150 150 Deborah

Math Review of Platonic Solids and Polyhedra

Overview There are infinitely many regular polygons. However, there are a fixed number of regular polyhedra, called Platonic solids. Mathematicians use the definitions of the regular polygons and the characteristics of solid objects to arrive at their conclusions. Characteristics of Regular Polyhedra Regular polygons, such as equilateral triangles, squares, equilateral pentagons, hexagons, heptagons, octagons, and…

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Math Review of More Properties of Circular Functions 150 150 Deborah

Math Review of More Properties of Circular Functions

Overview The unit circle has as its center the origin point of the Cartesian coordinates x and y, and has a radius 1. The trigonometric functions are also called circular functions, because they describe relationships between angles on the unit circle. We use different ways to describe trigonometry in order to see how the relationships…

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Math Review of Applications of Circular Functions 150 150 Deborah

Math Review of Applications of Circular Functions

Overview Circular trigonometric functions can be applied to situations in physical, biological, and social sciences involving data that follows a pattern that is not linear. Many of those patterns are periodic, and can be modeled by approximations of sine, cosine, or other functions. The Sine and Cosine Waves The numerical value of t around the…

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Math Review of Angles and Circular Motion 150 150 Deborah

Math Review of Angles and Circular Motion

Overview Trigonometry is defined by the measurement of angles and their relationships. One of the ways that trigonometry can be applied is in the measurement of angles and circular motion. Angle Measure Angles in trigonometry and calculus can be measured in radians, which is a relationship of the measurement of an angle by the arc…

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Trigonometry Review of Degrees, Radians, and Measurement of Angles 150 150 Deborah

Trigonometry Review of Degrees, Radians, and Measurement of Angles

Overview Although many students are most familiar with the measurement of angles by degrees, there are other ways to measure angles. In calculus, advanced trigonometry, and applications of calculus to science, angles are measured in radians. The grad is a unit of angle measure used in surveying and as part of the metric system, and…

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Math Review of Trigonometric Identities 150 150 Deborah

Math Review of Trigonometric Identities

Overview Trigonometric identities are relationships between trigonometric ratios that define them in terms of one another. They can be used to help solve problems that involve trigonometric functions. Reciprocal Identities The reciprocal function to the sine is the cosecant, to the cosine is the secant, and to the tangent is the cotangent. In math language,…

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Trigonometry Review of Right Triangles 150 150 Deborah

Trigonometry Review of Right Triangles

Overview Right triangles have special properties that are important to determine trigonometric ratios, such as sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (csc), and cotangent (cot). Those ratios reflect the relationships between the opposite and adjacent angles of the right angle with the hypotenuse. Trigonometric Ratios Suppose a right triangle has an angle…

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