Understanding Calculus II: Problems, Solutions, and Tips [TTC Video]
01 February 2016, 17:38
Course No 1018 | FLV, AVC, 640x360 | AAC, 64 kbps, 2 Ch | 36x30 mins | + PDF Guidebook | 13.82GB
Calculus II is the payoff for mastering Calculus I. This second course in the calculus sequence introduces you to exciting new techniques and applications of one of the most powerful mathematical tools ever invented. Equipped with the skills of Calculus II, you can solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas. Success at Calculus II also gives you a solid foundation for the further study of mathematics, and it meets the math requirement for many undergraduate majors.
But beyond these advantages, you will find that the methods you learn in Calculus II are practical, interesting, and elegant, involving ideas that are beautifully simple. Because it can model real-life situations, calculus has an amazing range of uses, and these applications come into full flower in Calculus II.
Understanding Calculus II: Problems, Solutions, and Tips takes you on this exhilarating journey in 36 intensively illustrated half-hour lectures that cover all the major topics of the second full-year calculus course in high school at the College Board Advanced Placement BC level or a second-semester course in college. Drawing on decades of teaching experience, Professor Bruce H. Edwards of the University of Florida enriches his lectures with crystal-clear explanations, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce key concepts.
Few calculus teachers are as qualified, accessible, or entertaining as Professor Edwards, who has won multiple teaching awards and coauthored a best-selling series of calculus textbooks. Many calculus students give up trying to understand why a particular procedure works and resort to memorizing the steps to a solution. With Professor Edwards, the underlying concepts are always clear and constantly reinforced, which greatly eases the path to learning the material.
Understanding Calculus: Problems, Solutions, and Tips [TTC Video]
01 February 2016, 17:12
Course No 1007 | AVI, XviD, 640x480 | MP3, 128 kbps, 2 Ch | 36x30 mins | + PDF Guidebook | 6.97GB
Calculus is the greatest mathematical breakthrough since the pioneering discoveries of the ancient Greeks. Without it, we wouldn't have spaceflight, skyscrapers, jet planes, economic modeling, accurate weather forecasting, modern medical technologies, or any of the countless other achievements we take for granted in today's world.
Indeed, calculus is so versatile and its techniques so diverse that it trains you to view problems, no matter how difficult, as solvable until proved otherwise. And the habit of turning a problem over in your mind, choosing an approach, and then working through a solution teaches you to think clearly—which is why the study of calculus is so crucial for improving your cognitive skills and why it is a prerequisite for admission to most top universities.
Understanding Calculus: Problems, Solutions, and Tips
immerses you in the unrivaled learning adventure of this mathematical field in 36 half-hour lectures that cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college. With crystal-clear explanations of the beautiful ideas of calculus, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce major concepts, this course will be your sure and steady guide to conquering calculus.
Your teacher for this intensively illustrated DVD set is Professor Bruce H. Edwards, an award-winning instructor at the University of Florida and the coauthor of a best-selling series of calculus textbooks.
Accomplish Mathematical Wonders
Calculus is one of the most powerful and astonishing tools ever invented, yet it is a skill that can be learned by anyone with an understanding of high school mathematics.
Among its many uses, calculus teaches you to
- analyze a multitude of situations involving change, whether it's an accelerating rocket, the growth of a bacterial colony, or fluctuating stock prices;
- calculate optimum values, such as the greatest volume for a box with a given surface area or the highest feasible profit from the sales of an item;
- measure complex shapes—for example, the volume of a doughnut-shaped object called a torus or the area of a plot of land bounded by a river.
Learn about Precalculus and Limits . . .
Solving many types of calculus problems usually requires employing precalculus—algebra and trigonometry—to work out a solution. For this reason, Professor Edwards devotes the first few lectures to reviewing key topics in precalculus, then he covers some basic concepts such as limits and continuity before moving on to the two simple, yet brilliant ideas behind calculus—the derivative and the integral.
Despite the apparent differences between the derivative and integral, you discover that they are inextricably linked by the surprising fundamental theorem of calculus. Throughout the course, you will discover that simplicity is one of the hallmarks of the essential ideas of calculus.
. . . the Power of the Derivative . . .
The derivative is the foundation of differential calculus, which you study through Lecture 17, exploring its many applications in science, engineering, business, and other fields.
You start with a classic problem that illustrates one of the core ideas of calculus: Can you find the tangent line to a curve at a given point? This is the same as asking if the rate of change of the curve can be measured at that point—with a host of potential applications in situations where a quantity is changing, such as the speed of an accelerating vehicle. The answer is: Yes, and with amazing simplicity! After learning the steps involved, you have solved your first calculus problem.
- study a variety of ways to find derivatives, including the power rule, the constant multiple rule, the quotient rule, the chain rule, and implicit differentiation;
- learn how to find extrema—the absolute maximum and minimum values of functions, using derivatives; and
- apply derivatives to solve a variety of real-world problems.
. . . and the Importance of the Integral
Next, you are introduced to the integral, using a classic problem in which you are asked to find the area of a plot of land bounded by curves. To solve this problem, calculus provides us with the integral—a powerful tool that allows us to calculate areas, volumes, and other characteristics of complex shapes. The balance of the course is devoted to integral calculus and its applications. You study
- arc length and surface area—two applications of calculus that are at the heart of engineering;
- integration by substitution—a method that enables you to convert a difficult problem into one that's easier to solve; and
- the formulas for continuous compound interest, radioactive decay, and a host of other real-world applications.
A Calculus Course for All
Understanding Calculus is well suited for anyone who wants to take the leap into one of history's greatest intellectual achievements, whether for the first time or for review. Those who will benefit include these learners:
- Any student now studying calculus who would like personal coaching from a professor who has spent years honing his explanations for the areas that are most challenging to students. This course is specifically designed to cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college.
- Parents of students studying calculus, a subject with which they often give up trying to help their high-school-age children—at a critical turning point in their educational careers.
- Those who have already taken calculus and who need a thorough review.
- Anyone who didn't understand calculus on the first try and wants a lucid, in-depth presentation, with lots of interesting, well-explained practice problems.
The plentiful graphs, equations, and other visual aids in these lectures are clear and well-designed, allowing you to follow each step of Professor Edwards's presentation in detail. The accompanying workbook includes lecture summaries, sample problems and worked-out solutions, tips, and pitfalls; lists of formulas and theorems; a trigonometry review sheet; a glossary; and a removable study sheet to use for quick and easy reference during the lectures.
The Ideal Calculus Teacher
Professor Edwards is the ideal calculus teacher—friendly, animated, encouraging, and witty, but also focused on presenting the material in an organized and understandable way. For anyone who feels intimidated by calculus, there is a distinct joy in being able to calculate a derivative after just a few lessons. It's easier than one might have supposed, and it opens an amazing new world of insight.
As an educator who has been honored repeatedly, both for his teaching and for his textbooks, Professor Edwards is a fount of valuable advice. He offers frequent tips for success, including guidance for those preparing for the Advanced Placement Calculus AB exam, for which he has served as a grader and for which this course is excellent preparation. Among his suggestions are these:
- Graphing calculators: While some calculus teachers prefer that their students not use graphing calculators, the Advanced Placement exam requires them. Professor Edwards points out the strengths of graphing calculators as well as the weaknesses—for example, that in certain situations they can fool you.
- Memorization: Always memorize what your teacher assigns. However, no one can memorize all the formulas in calculus. A good approach is to commit to memory the idea behind a technique—for example, that the disk method of computing the volume of a solid involves slicing it into innumerable disks.
Ever since its inception in the 17th century, calculus has spawned a continuing flood of new ideas and techniques for solving problems. It's easy to be overwhelmed by the richness of this subject, which is why many beginning students find themselves struggling.
Through Professor Edwards's exceptional teaching in Understanding Calculus, you will come away with a deep appreciation for the extraordinary power of calculus, a grasp of which methods apply to different types of problems, and, with practice, a facility for unlocking the secrets of the ceaselessly changing world around us.
Thinking about Capitalism [TTC Video]
31 January 2016, 09:32
Course No 5665 | AVI, XviD, 640x480 | MP3, 128 kbps, 2 Ch | 36x30 mins | + PDF Guidebook | 6.73GB
As the economic system under which you live, capitalism shapes the marketplaces that determine where you live and work, how much you are paid, what you can buy, what you can accumulate toward your retirement, and every other aspect of a society based on monetary exchanges for goods and services. In an era of increasing globalization, capitalism has dramatically strengthened its important role in—and its influence on—the world economy. It is the system under which a majority of the world's population lives, and it continues to strengthen the links of interdependence between the world's economies.
But capitalism's impact is about much more than money and markets. Indeed, capitalism is every bit as much a social force as an economic one. As such, its impact on noneconomic life has drawn the attention of thinkers outside of economics, as well as those inside the discipline, including some of its greatest minds.
In Thinking about Capitalism, award-winning intellectual historian and Professor Jerry Z. Muller of The Catholic University of America takes you deep inside the perspectives on this most important and pervasive force. Over 36 engaging lectures, you gain fresh insights that will strengthen your understanding of capitalism's rich history, its fascinating proponents and opponents, and its startling impact on our world.
An Exploration Beyond Economics
Drawing on his exceptional ability to frame each thinker's concerns within its historical context, Professor Muller takes you beyond economic analysis to look at how some of the greatest intellects have thought about capitalism and its moral, political, and cultural ramifications.
Covering capitalism from its 17th-century beginnings to today's era of globalization, Professor Muller explores these thinkers' insights on some wide-ranging questions:
- What effect does capitalism have on personal development? Or on our identities as individuals, as members of a group, or even as citizens of a nation?
- What about the seemingly unending variety of consumer goods made possible by capitalism? Have they made our culture better—or worse?
- Do the facts support our tendency to think about capitalism as the economic system practiced in "free" countries? Or can capitalism exist in a wide variety of political systems?
As capitalism continues to expand across geographical borders, provocative questions emerge about its overall impact. What are the short- and long-term implications of globalization? How and when should we construct economic policies to strengthen or limit its growth? Can capitalism ever undermine itself?
By placing capitalism in its full societal context, Thinking about Capitalism enhances your ability to consider, discuss, and answer these and other critical questions—whatever your point of view.
Get Insights from Three Centuries of Thinkers
For almost three centuries, some of the most interesting thinkers in history have grappled with capitalism. They have explored its key features, cultural prerequisites, and human implications with excitement, caution, or even fear.
Their writings have defended capitalism, argued against it, disagreed over how to characterize it, and questioned whether the human costs incurred in its practice can be outweighed by the obvious material benefits it brings.
These are some of the great minds you encounter in these lectures:
- Adam Smith: Although famous for The Wealth of Nations, this giant of the Enlightenment was in fact a moral philosopher and political economist whose ideas about capitalism, capitalists, and government exploded past any boundaries of "economics."
- Joseph Schumpeter: One of capitalism's most wide-ranging thinkers, Schumpeter published four books, at least three of which are considered seminal.
- Ferdinand Tönnies and Georg Simmel: Tönnies argued that modern history was moving away from tightly knit communities at emotional cost to the individual, while Simmel explored how capitalism offered new possibilities for individuality and community.
- Friedrich von Hayek: After a flirtation with reformist Socialism, Hayek embraced classical Liberalism, producing influential critiques of collectivism and the welfare state, sharing a Nobel Prize in economics, and winning broad acknowledgment for his work on the coordinating function of the marketplace.
These names only scratch the surface of the grand intellects Professor Muller discusses, who include Voltaire, Rousseau, Burke, Hamilton, De Tocqueville, Hegel, Marx, Arnold, Weber, Lenin, Schmitt, Marcuse, Gellner, Buchanan, and Olson.
Their insights can prove invaluable in every area of your life. They can surface in the decisions you make about family, work, and consumption; and they can give you a more thoughtful perspective on the ideas and behaviors of commentators, corporations, and governments.
A Fascinating Journey Led by an Ideal Teacher
An intellectual historian, Professor Muller takes you from capitalism's beginnings in commercial Holland and England to the challenges of nationalism, globalization, and contemporary varieties of capitalism.
Genial and disarming, he connects the dots from idea to idea, thinker to thinker. In Thinking about Capitalism, you can finally grasp the history and the concepts of this vital economic system, as well as its importance on the global economic stage and in your own life.