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.
Modern Economic Issues [TTC Video]
31 January 2016, 07:37
Course No 5610 | AVI, XviD, 640x480 | MP3, 128 kbps, 2 Ch | 36x30 mins | 6.64GB
How do the major economic issues that dominate today's news—questions about gross domestic product or budget deficits or trade imbalances—impact the average citizen? Why are health insurance and college tuition increasingly expensive? What can be done about soaring energy prices?
In Modern Economic Issues, Professor Robert Whaples has crafted a course designed to answer just these sorts of questions—a primer in 21st-century economics for the non-economist. He first presents the results of a survey of professional economists around the country on what they consider today's most urgent economic issues—the ones all of us most need to understand. Professor Whaples then puts his award-winning teaching skills to work to shape an accessible course, explaining not only those urgent issues but also the raw data economists use to describe their shape and impact.
The result is a course that finally makes the connection between the economics you may have studied in school and the economics of the lives we experience every day.
For example, how do you make the decisions—big and small—that make up your daily life?
What factors come into play when you're deciding whether to buy this car or that one, or even commute by bus? Mow the lawn or take a nap? Grill a burger with a bubbling slice of cheese or eat a simple salad?
Most economists will tell you that you make decisions on this personal level by acting as what they would call a "rational maximizer," comparing, whether explicitly or implicitly, what you expect to gain from your decision against what you expect to give up.
You weigh comfort and convenience against the rising cost of gasoline. The need to maintain your home's "curb appeal" against your need for sleep in a much-too-busy life. Your raw craving for that burger against the realities of an expanding waistline.
Learn to See the Tradeoffs in Every Decision We Make
And make no mistake about it: There is almost always something to give up, a tradeoff that is inherent in every decision we make in life—a concept memorably expressed by Nobel Laureate Milton Friedman's famous reminder that "there's no such thing as a free lunch."
But this same kind of personal analysis is just as applicable to the major issues of public policy, where the needs and wants of a nation and its people—whether financial security, safety from terrorism, or even an available kidney for someone desperately waiting on a transplant list—involve tradeoffs. Tradeoffs that are sometimes obvious and sometimes not.
Issue by issue, Professor Whaples explains those tradeoffs, guiding you through and then past the numbers, teasing out the full range of differing societal costs and benefits that will be part and parcel of any policy option our leaders choose to implement.
What does it mean, for example, if Wal-Mart decides to open a store in your town? Should your local government be enthusiastic, or should it be concerned? Should your own feelings be the same, or are your personal priorities different? What will the presence of the world's largest corporation really mean to you as a consumer, to smaller stores worried about competing, or to your local job market?
Whether dealing with the traditional sorts of topics most of us are used to seeing in an economics course—Social Security, inflation, unemployment, immigration, taxation, and the like—or issues perhaps surprising, such as gambling, major sports franchises, and even overeating, Professor Whaples offers a steady flow of insights about how the American economy really works, and how the consequences of policy decisions can have a longer reach than we might imagine, sometimes ironically so.
For example, Americans are having far fewer children than we used to—the so-called "birth dearth"—because the Social Security safety net removed one of the reasons cited by economic historians for having large families in the first place: the need to be supported in one's later years.
The irony, of course, is that it is this very decline in births that Social Security helped bring about that has itself become a looming threat, with a dwindling number of adults in their working years now available to support the increasing number of retirees who will be dependent on the system.
Go Beyond the "What" to Explore the "Why" of Today's Most Important Economic Issues
Carefully balancing the statistical data—the "what" of each trend or issue—with insightful explorations of how those trends or issues took their present shape—the "why"—Professor Whaples repeatedly takes the numbers that have long been the bane of those intimidated by economics courses and explores their implications in very human terms.
Showing us the human side of the numbers with which economics must be unavoidably concerned is second nature to Professor Whaples, who earned degrees in both economics and history in the process of becoming an economic historian. Honored as both a scholar and a teacher, he is intimately concerned with the real-life consequences of economics for flesh-and-blood people. In fact, his 1990 doctoral dissertation on the shortening of the American workweek was written from both economic and historical perspectives, and was honored by the Economic History Association as the "Outstanding Dissertation in American Economic History" for that year.
Professor Whaples begins the course with a thorough grounding in the basics of economics and the most important measuring sticks by which professional economists gauge an economy's performance. He always moves toward the human side of the equation, letting us see the translation of basic economic forces into the realities of our own lives.
The first lecture is a typical example of his approach. Terms such as rational maximizer, marginal cost, and demand curve fall neatly into place within the real-life example of padding over to one's thermostat on a cold winter's morning to decide where to set it, gauging where the cost–benefit tradeoffs might be—a process very similar to the one being performed at the other end of this transaction, by the marketplace players that provide our heating fuel.
As Professor Whaples so brilliantly shows, tradeoffs are a fundamental part of a system of economic forces that has been in play since long before the word economics even existed, from the moment the first want had to be balanced against the first inventory of resources, forcing someone to make a choice.
Modern Economic Issues is also about the economic implications of making those choices at the level of public policy. By showing the full range of economic factors that can come into play as a result of a given policy, and how our economy works, this course can help you become an even more insightful judge of policy recommendations and of the leaders and policy makers who advocate them.
Moreover, you will understand how professional economists view the full range of tradeoffs inherent in any decision. And you may well learn to supplement your own analyses as you make the real-life economic choices each of us faces every day, becoming an even wiser consumer and manager of your own economic future.