Mathematics Describing the Real World: Precalculus and Trigonometry

Prepare your student or yourself for success with this course on precalculus and trigonometry by the author of one of the most widely used textbooks on the subject.
Mathematics Describing the Real World: Precalculus and Trigonometry is rated 4.6 out of 5 by 65.
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Rated 5 out of 5 by from Trust Professor Edwards and do your homework! Professor Edwards makes an excellent presentation of this precalculus course, and it's good to know that it leads into his calculus course. But, trust him when he says that you will learn the material better if you do the homework. As a late-in-life learner, it has been a genuine help to take the time to do the homework and make sure of the solutions before going on from one unit to the next.
Date published: 2021-05-31
Rated 5 out of 5 by from Perfect for a recap on the fundamentals of Maths Alongside the Algebra II course I have found this course ideal for a recap on Trigonometry, Algebra and Exponential and Logarithmic Functions. I had a lot of blind spots in my basic understanding from not paying proper attention learning first time around. You can get away with it at a lower level of Maths, but when you are looking to grasp Undergraduate and Graduate level mathematics, you really need to be totally clear on the fundamentals, and this course is a great aid in achieving that.
Date published: 2021-05-03
Rated 5 out of 5 by from Thorough and effective! I watched this series prior to taking a calculus I class this winter. With a poor mathematical and algebraic background, I can say I'd have been hopeless without this course. A lot of the concepts introduced in this course were new to me, and to get to experience them in the context of a self-paced casual study-for-enrichment environment such as this was much better than having to learn them on the fly as one enters the strange new dimensions of the calculus universe. While it will never beat the in-person interaction with a real-time professor and class, I'd recommend this to anyone following my footsteps. The content is also quite interesting in itself.
Date published: 2021-04-24
Rated 5 out of 5 by from Didn't know I'd be taught by Bill Gates himself. :)
Date published: 2021-04-11
Rated 5 out of 5 by from Inspiring He is able to both teach the concepts and tell the overall story of Trigonometry and other branches of Pre-Calculus. I look forward to his Calculus course.
Date published: 2021-04-03
Rated 5 out of 5 by from A gifted instructor makes Precalculus fun. I took this course as a refresher because I'm hoping to finally get through all of Calculus. Dr. Edwards made the review a breeze. An amiable instructor, he has a way of making the driest mathematical topics interesting and easy. I'm definitely headed to his three Calculus courses and any other topics he has classes on.
Date published: 2021-02-18
Rated 5 out of 5 by from 11/10 Bruce is an unbelievably clear and effective educator, and so deeply knowledgeable. I am extremely grateful to have stumbled across this lecture series.
Date published: 2021-02-10
Rated 5 out of 5 by from Concise, thorough, and interesting. I am half-way through the lecture series and I must say that I am satisfied with the instructor. I believe he really touches on everything in a beautiful manner with great explanations. Of course, the lectures are on 30 minutes long so you cannot expect great historical detail, but nonetheless, all the references are provided.
Date published: 2021-02-06
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Finally make sense of the mysteries of precalculus and trigonometry in the company of master educator and award-winning Professor Bruce Edwards. In the 36 intensively illustrated lectures of Mathematics Describing the Real World: Precalculus and Trigonometry, 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. The course also comes complete with a workbook featuring a wealth of additional explanations and problems.


Bruce H. Edwards
Bruce H. Edwards

I love mathematics and tried to communicate this passion to others, regardless of their mathematical backgrounds.


University of Florida

Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. After his years at Stanford, he taught mathematics at a university near Bogota, Colombia, as a Peace Corps volunteer. Professor Edwards has won many teaching awards at the University of Florida, including Teacher of the Year in the College of Liberal Arts and Sciences, Liberal Arts and Sciences Student Council Teacher of the Year, and the University of Florida Honors Program Teacher of the Year. He was selected by the Office of Alumni Affairs to be the Distinguished Alumni Professor for 1991-1993. Professor Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He has been a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has also coauthored a wide range of mathematics textbooks with Professor Ron Larson. Their textbooks have been honored with various awards from the Text and Academic Authors Association.

By This Professor

Mathematics Describing the Real World: Precalculus and Trigonometry


An Introduction to Precalculus-Functions

01: An Introduction to Precalculus-Functions

Precalculus 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 course.

31 min
Polynomial Functions and Zeros

02: Polynomial Functions and Zeros

The 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.

31 min
Complex Numbers

03: Complex Numbers

Step 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....

31 min
Rational Functions

04: Rational Functions

Investigate 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.

31 min
Inverse Functions

05: Inverse Functions

Discover 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....

32 min
Solving Inequalities

06: Solving Inequalities

You have 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.

31 min
Exponential Functions

07: Exponential Functions

Explore exponential functions-functions that 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....

32 min
Logarithmic Functions

08: Logarithmic Functions

A logarithmic function is the inverse of the exponential function, with all the characteristics of inverse functions covered in Lecture 5. 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....

30 min
Properties of Logarithms

09: Properties of Logarithms

Learn the secret of converting logarithms to any base. Then review the three major properties of logarithms, which allow simplification or expansion of logarithmic expressions-methods widely used in calculus. Close by focusing on applications, including the pH system in chemistry and the Richter scale in geology.

32 min
Exponential and Logarithmic Equations

10: Exponential and Logarithmic Equations

Practice 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.

31 min
Exponential and Logarithmic Models

11: Exponential and Logarithmic Models

Finish the algebra portion of the course 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.

31 min
Introduction to Trigonometry and Angles

12: Introduction to Trigonometry and Angles

Trigonometry 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.

30 min
Trigonometric Functions-Right Triangle Definition

13: Trigonometric Functions-Right Triangle Definition

The 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.

32 min
Trigonometric Functions-Arbitrary Angle Definition

14: Trigonometric Functions-Arbitrary Angle Definition

Trigonometric 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.

32 min
Graphs of Sine and Cosine Functions

15: Graphs of Sine and Cosine Functions

The 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.

32 min
Graphs of Other Trigonometric Functions

16: Graphs of Other Trigonometric Functions

Continue 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.

32 min
Inverse Trigonometric Functions

17: Inverse Trigonometric Functions

For a given trigonometric function, only a small part of its graph qualifies as an inverse function as defined in Lecture 5. 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.

32 min
Trigonometric Identities

18: Trigonometric Identities

An 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.

32 min
Trigonometric Equations

19: Trigonometric Equations

In 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.

31 min
Sum and Difference Formulas

20: Sum and Difference Formulas

Study 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.

31 min
Law of Sines

21: Law of Sines

Return 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.

30 min
Law of Cosines

22: Law of Cosines

Given 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.

31 min
Introduction to Vectors

23: Introduction to Vectors

Vectors 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.

32 min
Trigonometric Form of a Complex Number

24: Trigonometric Form of a Complex Number

Apply 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.

32 min
Systems of Linear Equations and Matrices

25: Systems of Linear Equations and Matrices

Embark on the first of four lectures 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.

31 min
Operations with Matrices

26: Operations with Matrices

Deepen your understanding of matrices by learning how to do simple operations: addition, scalar multiplication, and matrix multiplication. After looking at several examples, apply matrix arithmetic to a commonly encountered problem by finding the parabola that passes through three given points.

31 min
Inverses and Determinants of Matrices

27: Inverses and Determinants of Matrices

Get ready for applications involving matrices by exploring two additional concepts: the inverse of a matrix and the determinant. The algorithm for calculating the inverse of a matrix relies on Gaussian elimination, while the determinant is a scalar value associated with every square matrix.

30 min
Applications of Linear Systems and Matrices

28: Applications of Linear Systems and Matrices

Use linear systems and matrices to analyze such questions as these: How can the stopping distance of a car be estimated based on three data points? How does computer graphics perform transformations and rotations? How can traffic flow along a network of roads be modeled?

32 min
Circles and Parabolas

29: Circles and Parabolas

In the first of two lectures on conic sections, examine the properties of circles and parabolas. Learn the formal definition and standard equation for each, and solve a real-life problem involving the reflector found in a typical car headlight.

30 min
Ellipses and Hyperbolas

30: Ellipses and Hyperbolas

Continue your survey of conic sections by looking at ellipses and hyperbolas, studying their standard equations and probing a few of their many applications. For example, calculate the dimensions of the U.S. Capitol's "whispering gallery," an ellipse-shaped room with fascinating acoustical properties.

31 min
Parametric Equations

31: Parametric Equations

How do you model a situation involving three variables, such as a motion problem that introduces time as a third variable in addition to position and velocity? Discover that parametric equations are an efficient technique for solving such problems. In one application, you calculate whether a baseball hit at a certain angle and speed will be a home run.

31 min
Polar Coordinates

32: Polar Coordinates

Take a different mathematical approach to graphing: polar coordinates. With this system, a point's location is specified by its distance from the origin and the angle it makes with the positive x axis. Polar coordinates are surprisingly useful for many applications, including writing the formula for a valentine heart!...

32 min
Sequences and Series

33: Sequences and Series

Get a taste of calculus by probing infinite sequences and series-topics that lead to the concept of limits, the summation notation using the Greek letter sigma, and the solution to such problems as Zeno's famous paradox. Also investigate Fibonacci numbers and an infinite series that produces the number e....

32 min
Counting Principles

34: Counting Principles

Counting problems occur frequently in real life, from the possible batting lineups on a baseball team to the different ways of organizing a committee. Use concepts you've learned in the course to distinguish between permutations and combinations and provide precise counts for each.

30 min
Elementary Probability

35: Elementary Probability

What are your chances of winning the lottery? Of rolling a seven with two dice? Of guessing your ATM PIN number when you've forgotten it? Delve into the rudiments of probability, learning basic vocabulary and formulas so that you know the odds.

30 min
GPS Devices and Looking Forward to Calculus

36: GPS Devices and Looking Forward to Calculus

In a final application, locate a position on the surface of the earth with a two-dimensional version of GPS technology. Then close by finding the tangent line to a parabola, thereby solving a problem in differential calculus and witnessing how precalculus paves the way for the next big mathematical adventure.

31 min