Mathematics Describing the Real World: Precalculus and Trigonometry
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Episodes
- S1 E1 - An Introduction to Precalculus - Functions
June 16, 201131minPrecalculus is important preparation for calculus, but it's also a useful set of skills in its own right, drawing on algebra, trigonometry, and other topics. As an introduction, review the essential concept of the function, try your hand at simple problems, and hear Professor Edwards's recommendations for approaching the series. #Science & MathematicsFree trial of The Great Courses Signature Collection or buy - S1 E2 - Polynomial Functions and Zeros
June 16, 201131minThe most common type of algebraic function is a polynomial function. As examples, investigate linear and quadratic functions, probing different techniques for finding roots, or "zeros." A valuable tool in this search is the intermediate value theorem, which identifies real-number roots for polynomial functions.Free trial of The Great Courses Signature Collection or buy - S1 E3 - Complex Numbers
June 16, 201131minStep into the strange and fascinating world of complex numbers, also known as imaginary numbers, where i is defined as the square root of -1. Learn how to calculate and find roots of polynomials using complex numbers, and how certain complex expressions produce beautiful fractal patterns when graphed.Free trial of The Great Courses Signature Collection or buy - S1 E4 - Rational Functions
June 16, 201131minInvestigate rational functions, which are quotients of polynomials. First, find the domain of the function. Then, learn how to recognize the vertical and horizontal asymptotes, both by graphing and comparing the values of the numerator and denominator. Finally, look at some applications of rational functions.Free trial of The Great Courses Signature Collection or buy - S1 E5 - Inverse Functions
June 16, 201132minDiscover how functions can be combined in various ways, including addition, multiplication, and composition. A special case of composition is the inverse function, which has important applications. One way to recognize inverse functions is on a graph, where the function and its inverse form mirror images across the line y = x.Free trial of The Great Courses Signature Collection or buy - S1 E6 - Solving Inequalities
June 16, 201131minYou've already used inequalities to express the set of values in the domain of a function. Now study the notation for inequalities, how to represent inequalities on graphs, and techniques for solving inequalities, including those involving absolute value, which occur frequently in calculus.Free trial of The Great Courses Signature Collection or buy - S1 E7 - Exponential Functions
June 16, 201132minExplore exponential functions, which have a base greater than 1 and a variable as the exponent. Survey the properties of exponents, the graphs of exponential functions, and the unique properties of the natural base e. Then sample a typical problem in compound interest.Free trial of The Great Courses Signature Collection or buy - S1 E8 - Logarithmic Functions
June 16, 201130minA logarithmic function is the inverse of the exponential function, with all the characteristics of inverse functions covered earlier. Examine common logarithms (those with base 10) and natural logarithms (those with base e), and study such applications as the "rule of 70" in banking.Free trial of The Great Courses Signature Collection or buy - S1 E9 - Properties of Logarithms
June 16, 201132minLearn the secret of converting logarithms to any base. Then review the three major properties of logarithms, which allow simplification or expansion of logarithmic expressions and are widely used in calculus. Close by focusing on applications, including the pH system in chemistry and the Richter scale in geology.Free trial of The Great Courses Signature Collection or buy - S1 E10 - Exponential and Logarithmic Equations
June 16, 201131minPractice solving a range of equations involving logarithms and exponents, seeing how logarithms are used to bring exponents "down to earth" for easier calculation. Then try your hand at a problem that models the heights of males and females, analyzing how the models are put together.Free trial of The Great Courses Signature Collection or buy - S1 E11 - Exponential and Logarithmic Models
June 16, 201131minFinish the algebra portion of the series by delving deeper into exponential and logarithmic equations, using them to model real-life phenomena, including population growth, radioactive decay, SAT math scores, the spread of a virus, and the cooling rate of a cup of coffee.Free trial of The Great Courses Signature Collection or buy - S1 E12 - Introduction to Trigonometry and Angles
June 16, 201130minTrigonometry is a key topic in applied math and calculus with uses in a wide range of applications. Begin your investigation with the two techniques for measuring angles: degrees and radians. Typically used in calculus, the radian system makes calculations with angles easier.Free trial of The Great Courses Signature Collection or buy - S1 E13 - Trigonometric Functions - Right Triangle Definition
June 16, 201132minThe Pythagorean theorem, which deals with the relationship of the sides of a right triangle, is the starting point for the six trigonometric functions. Discover the close connection of sine, cosine, tangent, cosecant, secant, and cotangent, and focus on some simple formulas that are well worth memorizing.Free trial of The Great Courses Signature Collection or buy - S1 E14 - Trigonometric Functions - Arbitrary Angle Definition
June 16, 201132minTrigonometric functions need not be confined to acute angles in right triangles; they apply to virtually any angle. Using the coordinate plane, learn to calculate trigonometric values for arbitrary angles. Also see how a table of common angles and their trigonometric values has wide application.Free trial of The Great Courses Signature Collection or buy - S1 E15 - Graphs of Sine and Cosine Functions
June 16, 201132minThe graphs of sine and cosine functions form a distinctive wave-like pattern. Experiment with functions that have additional terms, and see how these change the period, amplitude, and phase of the waves. Such behavior occurs throughout nature and led to the discovery of rapidly rotating stars called pulsars in 1967.Free trial of The Great Courses Signature Collection or buy - S1 E16 - Graphs of Other Trigonometric Functions
June 16, 201132minContinue your study of the graphs of trigonometric functions by looking at the curves made by tangent, cosecant, secant, and cotangent expressions. Then bring several precalculus skills together by using a decaying exponential term in a sine function to model damped harmonic motion.Free trial of The Great Courses Signature Collection or buy - S1 E17 - Inverse Trigonometric Functions
June 16, 201132minFor a given trigonometric function, only a small part of its graph qualifies as an inverse function. However, these inverse trigonometric functions are very important in calculus. Test your skill at identifying and working with them, and try a problem involving a rocket launch.Free trial of The Great Courses Signature Collection or buy - S1 E18 - Trigonometric Identities
June 16, 201132minAn equation that is true for every possible value of a variable is called an identity. Review several trigonometric identities, seeing how they can be proved by choosing one side of the equation and then simplifying it until a true statement remains. Such identities are crucial for solving complicated trigonometric equations.Free trial of The Great Courses Signature Collection or buy - S1 E19 - Trigonometric Equations
June 16, 201131minIn calculus, the difficult part is often not the steps of a problem that use calculus but the equation that's left when you're finished, which takes precalculus to solve. Hone your skills for this challenge by identifying all the values of the variable that satisfy a given trigonometric equation.Free trial of The Great Courses Signature Collection or buy - S1 E20 - Sum and Difference Formulas
June 16, 201131minStudy the important formulas for the sum and difference of sines, cosines, and tangents. Then use these tools to get a preview of calculus by finding the slope of a tangent line on the cosine graph. In the process, you discover the derivative of the cosine function.Free trial of The Great Courses Signature Collection or buy - S1 E21 - Law of Sines
June 16, 201130minReturn to the subject of triangles to investigate the law of sines, which allows the sides and angles of any triangle to be determined, given the value of two angles and one side, or two sides and one opposite angle. Also learn a sine-based formula for the area of a triangle.Free trial of The Great Courses Signature Collection or buy - S1 E22 - Law of Cosines
June 16, 201131minGiven three sides of a triangle, can you find the three angles? Use a generalized form of the Pythagorean theorem called the law of cosines to succeed. This formula also allows the determination of all sides and angles of a triangle when you know any two sides and their included angle.Free trial of The Great Courses Signature Collection or buy - S1 E23 - Introduction to Vectors
June 16, 201132minVectors symbolize quantities that have both magnitude and direction, such as force, velocity, and acceleration. They are depicted by a directed line segment on a graph. Experiment with finding equivalent vectors, adding vectors, and multiplying vectors by scalars.Free trial of The Great Courses Signature Collection or buy - S1 E24 - Trigonometric Form of a Complex Number
June 16, 201132minApply your trigonometric skills to the abstract realm of complex numbers, seeing how to represent complex numbers in a trigonometric form that allows easy multiplication and division. Also investigate De Moivre's theorem, a shortcut for raising complex numbers to any power.Free trial of The Great Courses Signature Collection or buy - S1 E25 - Systems of Linear Equations and Matrices
June 16, 201131minEmbark on the first of four episodes on systems of linear equations and matrices. Begin by using the method of substitution to solve a simple system of two equations and two unknowns. Then practice the technique of Gaussian elimination, and get a taste of matrix representation of a linear system.Free trial of The Great Courses Signature Collection or buy
Extras
Bonus
Finally make sense of the mysteries of precalculus and trigonometry in the company of master educator and award-winning professor Bruce Edwards. In 36 intensively illustrated episodes, he takes you through all the major topics of a typical precalculus course taught in high school or college. You'll gain new insights into functions, complex numbers, matrices, and much more.
Finally make sense of the mysteries of precalculus and trigonometry in the company of master educator and award-winning professor Bruce Edwards. In 36 intensively illustrated episodes, he takes you through all the major topics of a typical precalculus course taught in high school or college. You'll gain new insights into functions, complex numbers, matrices, and much more.
Finally make sense of the mysteries of precalculus and trigonometry in the company of master educator and award-winning professor Bruce Edwards. In 36 intensively illustrated episodes, he takes you through all the major topics of a typical precalculus course taught in high school or college. You'll gain new insights into functions, complex numbers, matrices, and much more.
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