Mathematics Describing the Real World: Precalculus and Trigonometry

Rated 5 out of 5 by from Excellent Pace for the variety in precalculus Professor Edwards provided understandable examples and the graph explanations were well constructed.
Date published: 2020-09-08
Rated 5 out of 5 by from A Bridge Mix of Math Complex numbers, rational functions, exponential functions, all of the trig functions, conic sections, matrices, logs, into to linear systems, graphing everything, polar co-ordinates, and even an into to probability. And more. Professor Edwards in 36 lectures delivers a diverse, but interrelated set of topics as preparation for the calculus. And he does it without either talking down to students about things that should already be known, while at the same time ensuring that he fully explains the topic at hand. Even though he covers many areas, this is decidedly not a survey course. The course material has a workbook with plenty of problems that reinforce the lectures. Dr. Edwards is most insistent that those taking the course, also do the homework. As he puts it, “math is not a spectator sport.” Further, if you are going to do the work, a graphing calculator is a must. The lectures move along quite rapidly, usually beginning with some definitions and a couple of easy examples that get us ready for what to understand the subject more deeply. Frequently there are a couple of “real world” problems that demonstrate the usefulness of the topic. Of course these are not really of the real world, something that Professor Edwards acknowledges, often contrasting his chosen examples with the number of variables and ugly data that the real world provides. I thought his lecture approach to be straightforward and logical. Professor Edwards does not waste time in going over the details of solving many of the equations he sets up, assuming that we can do the algebra involved. Another time saver is when he suggests that some of the common radian values of the trig functions be memorized; in later lectures he assumes that we indeed know the sine of π/3 is √3/2. But don’t be fooled that his lecture style is all dusty and dry. Professor Edwards will throw in the odd joke and has the occasional personal anecdote. His delivery is clear and easy to understand, so much so that I was occasionally fooled into thinking that I understood more than I really did and had to back up to see what I had missed (my fault, not his). I’m not really sure as to who is the target audience for this course. Perhaps a few like myself who are just reliving the past and a few more wish to do some college prep work or just supplement some classroom instruction. But whatever the reason that one is interested in the topic, I recommend this course.
Date published: 2020-08-23
Rated 5 out of 5 by from Pretty good I’ve been playing these dvds still class at a time when I can. I work the night shift plus overtime. So far so good.It’s great. Thanks!
Date published: 2020-05-10
Rated 5 out of 5 by from Serious students should use Dr. Edwards' text book I enjoy Dr. Edwards' lectures and think he did a great job at distilling the essential points of each topic into 30 minutes. However, for a serious student who may be preparing to test out of a pre-calculus course or who needs more practice with more difficult exercises, I recommend that they buy a 5th edition of Precalculus with Limits--a Graphing Approach (by Larson, Hostetler and Edwards). Theses lectures are based upon the sequencing in this textbook, which gives you more detail and dozens more problems in each lesson of the kind you'd be given in a college class. (Answers to the odd-numbered exercises are given in the back of the book, but there is also an available solutions manual that shows the steps to those answers.) The text also has a free online study center where you can find instructions on calculator usage for the various topics. These additions to the lectures are relatively inexpensive and recommended for users who feel the need for beefing up the course experience.
Date published: 2020-03-02
Rated 5 out of 5 by from Genius Teacher, brilliant content! I am going back to college, and have to take university calculus. Mr. Edwards communicates with clarity the pre-calculus skills any student will need to refresh and excel to the calculus goal. He provides the contextual composition of the mathematical processes necessary to be proficient in pre-calculus.
Date published: 2020-01-25
Rated 5 out of 5 by from EXCELLENT PRESENTATION For anyone teaching, tutoring, or just wanting to know more about upper level mathematics, Dr. Edwards' presentation is both logical and thorough. Several precalculus topics are covered in detail making for a solid introduction and foundation to a beginning calculus course.
Date published: 2020-01-06
Rated 5 out of 5 by from precal & trig Great way to learn without leaving the house r going to class.
Date published: 2019-12-12
Rated 5 out of 5 by from Precalculus Made Easy My son took precalc in high school and wanted to review before starting college. I bought this for him, and he loves it. He said this instructor makes it so easy to understand that he requested the next in the series.
Date published: 2019-09-29
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Mathematics Describing the Real World: Precalculus and Trigonometry
Course Trailer
An Introduction to Precalculus-Functions
1: 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
2: 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
3: 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
4: 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
5: 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
6: 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
7: 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
8: 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
9: 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
Bruce H. Edwards

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


Dartmouth College


University of Florida

About Bruce H. Edwards

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.

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