The Joy of Differential Calculus

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The Joy of Integral Calculus
Episode 20 of The Joy of Mathematics
Geometry and trigonometry are used to determine the areas of simple figures such as triangles and circles. But how are more complex shapes measured? Calculus comes to the rescue with a technique called integration, which adds the simple areas of many tiny quantities.
The Joy of Probability
Episode 22 of The Joy of Mathematics
Mathematics can draw detailed inferences about random events. This lecture covers major concepts in probability, such as the law of large numbers, the central limit theorem, and how to measure variance.
The Joy of Approximating with Calculus
Episode 19 of The Joy of Mathematics
Exploiting the idea of the derivative, we can approximate just about any function using simple polynomials. This lecture also shows why a formula sometimes known as "God's equation" (involving e, i, p, 1, and 0) is true, and how to calculate square roots in your head.
Derivatives of Inverse Trigonometric Functions
This program covers the important topic of Derivatives of Inverse Trigonometric Functions in Calculus. We begin by discussing what an inverse trigonometric function is, how to take its derivative, and why it is a central topic in Calculus. Next, we solve several practical calculus problems that give students practice with…
Math in Your Head!
Episode 1 of Secrets of Mental Math
Dive right into the joys of mental math. First, learn the fundamental strategies of mental arithmetic (including the value of adding from left to right, unlike what you do on paper). Then, discover how a variety of shortcuts hold the keys to rapidly solving basic multiplication problems and finding squares.
The Joy of Math - The Big Picture
Episode 1 of The Joy of Mathematics
Professor Benjamin introduces the ABCs of math appreciation: The field can be loved for its applications, its beauty and structure, and its certainty. Most of all, mathematics is a source of endless delight through creative play with numbers.
Making Use of Linear Equations
Episode 11 of Geometry
Delve deeper into the connections between algebra and geometry by looking at lines and their equations. Use the three basic assumptions from previous lectures to prove that parallel lines have the same slope and to calculate the shortest distance between a point and a line.
Mental Math and Paper
Episode 6 of Secrets of Mental Math
Sometimes we encounter math problems on paper in our daily lives. Even so, there are some rarely taught techniques to help speed up your calculations and check your answers when you are adding tall columns of numbers, multiplying numbers of any length, and more.
Geometry - An Interactive Journey to Mastery
Inscribed over the entrance of Plato's Academy were the words, "Let no one ignorant of geometry enter my doors." To ancient scholars, geometry was the gateway to knowledge. Its core skills of logic and reasoning are essential to success in school, work, and many other aspects of life. Yet sometimes…
The Joy of Trigonometry
Episode 13 of The Joy of Mathematics
Trigonometry deals with the sides and angles of triangles. This lecture defines sine, cosine, and tangent, along with their reciprocals, the cosecant, secant, and cotangent. Extending these definitions to the unit circle allows a handy measure of angle: the radian.
The Joy of Mathematics
Ready to exercise those brain cells? Humans have been having fun with mathematics for thousands of years. Along the way, they've discovered the amazing utility of this field--in science, engineering, finance, games of chance, and many other aspects of life. This course of 24 half-hour lectures celebrates the sheer joy…
The Joy of Algebra
Episode 6 of The Joy of Mathematics
Arguably the most important area of mathematics, algebra introduces the powerful idea of using an abstract variable to represent an unknown quantity. This lecture demonstrates algebra's golden rule: Do unto one side of an equation as you do unto the other.