Course Understanding Calculus II: Problems, Solutions, and Tips. Calculus II is the result of 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 Calculus II skills, you can solve a wide variety of problems in the physical, biological and social sciences, engineering, economics, and other fields. Success in Calculus II also gives you a solid foundation for further mathematics study and fulfills the mathematics requirements of many undergraduate majors. But beyond these benefits, you’ll find that the methods you learn in Calculus II are practical, interesting, and elegant, and include ideas that are beautifully simple. Because calculus can model real-world situations, it has amazing applications, and these applications are fully on display in Calculus II.
Understanding Calculus 2: Problems, Solutions, and Tips takes you on an exciting journey in 36 half-hour, intensively illustrated lectures that cover all the core topics of the second full calculus course in high school at the Advanced Placement BC or College Board level. cover. A second semester course at the college of Professor Bruce H. Drawing on decades of teaching experience, Edwards of the University of Florida infuses his lectures with clear explanations, frequent study tips, pitfalls to avoid, and—best of all—hundreds of specially designed examples and practice problems. It enriches. To explain and reinforce key concepts. Few calculus teachers are as qualified, accessible, or entertaining as Professor Edwards, who has won numerous teaching awards and authored a series of best-selling calculus textbooks. Many calculus students give up trying to understand why a particular method works and resort to memorizing the steps of a solution. With Professor Edwards, the underlying concepts are always clear and constantly reinforced, which greatly eases the path to learning the material. Professor Edwards begins with a three-lecture review of the basic ideas of calculus. He also includes brief reviews of key concepts throughout the course, making Understanding Calculus a stand-alone lecture series for anyone already familiar with the two main calculus operations, differentiation and integration. Professor Edwards takes these ideas beyond the definitions, rules, and formulas that are central to first-semester calculus and applies them in engaging ways. For example:
- Differential Equations: This broad field employs derivatives—modeling population growth, nuclear decay, collapsing objects, and countless other processes that involve change. Professor Edwards recalls that as a young mathematician, he spent summers working for NASA, solving differential equations for airplanes in flight.
- Infinite Series: Does adding an infinite sequence of numbers produce an infinite result? It is not necessary. This series may converge to a certain value or may diverge to infinity. Calculus can provide answers to many different types of infinite series and show familiar functions from algebra or trigonometry in surprising ways.
- Vectors: One of the geometric applications of differential and integral calculus is the analysis of vectors. These are quantities, such as velocity, that have both magnitude and direction. In Calculus II, you’ll learn techniques for evaluating vectors in the plane, which will allow you to solve problems involving moving and accelerating objects, whether they’re on a straight or curved path.
Understanding Calculus II covers the above topics in considerable depth, particularly infinite series, which you explore in 11 lectures. You also study other standard topics in second semester calculus, including
- Integration formulas and techniques,
- merging areas and volumes,
- Taylor and McLaren polynomials,
- L’Hôpital’s law to evaluate limits,
- evaluation of improper integrals,
- Calculations used in parametric equations and
- Calculation used in polar coordinates
These very different applications of calculus each involve the basic idea of limit. Professor Edwards notes that calculus can be thought of as a “limiting machine” – a set of procedures for getting infinitely close to a value. One of the interesting features of calculus is its logical precision combined with its creative use of the mysterious entity of infinity. From this unusual marriage emerges surprising and precise solutions to inaccessible problems. Calculus is full of fascinating features, perplexing paradoxes, and fun problems. Among the many things you’ll examine in understanding the second account are:
- Gabriel’s Horn: Rotate a simple curve around its axis and a three-dimensional shape appears, resembling an infinitely long trumpet. This geometric shape, called Gabriel’s horn, has an unusual property: it has unlimited surface area but limited volume. See, calculus proves that this must be so.
- Exciting Baseball: A baseball is hit 3 feet above home plate at 100 feet per second at a 45 degree angle. Use Newton’s second law of motion and the derivative of the position function to determine whether the ball will be a home run, clearing a 10-foot-high fence 300 feet away.
- Cantor Set: Remove the middle third of a line segment. Repeat with the remaining two pieces. Repeat ad infinitum. The end points of all parts form an infinite set. But what about the total length of all line segments? The summation of this infinite series reveals the surprising answer.
Understanding Calculus II is a valuable experience that you can study at your own pace. Professor Edwards often encourages you to pause the video and test yourself by solving a problem before he reveals the answer. Those who benefit from this attractive and flexible offer include:
- High school or college students currently, or about to enroll in Calculus II who want personal coaching from an outstanding teacher.
- High school students preparing for the College Board Advanced Placement Test in Calculus at the BC level.
- Students in higher level math courses or professionals who want to review calculus. And
- Anyone interested in following one of life’s greatest intellectual adventures, which has been solving difficult problems for over 300 years.
A three-time Teacher of the Year at the University of Florida, Professor Edwards knows how to help students overcome obstacles on their way to mastering calculus. In this course, he uses a steady stream of on-screen equations, graphs, and other visual aids to document key steps in solving sample problems. The accompanying workbook is designed to enhance each lecture with additional practice problems and worked solutions, as well as lecture summaries, tips, and problems. and formulas for derivatives, integration and power series. Professor Edwards’ lectures also include what he calls a “you be the teacher” feature, in which he reverses the roles and challenges you to answer a typical question posed in class, an appropriate problem to illustrate. Design a principle, or otherwise make yourself available to the instructor. Shoes – a valuable exercise in learning to think for yourself in the language of calculus. Placing calculus at the end of the high school math curriculum makes it seem like the final destination. But this is just the beginning. Calculus is a world unto itself, an ever-expanding set of tools that can solve the most intractable problems in ingenious and often surprising ways. The deeper you go into calculus, the richer and better prepared you will be for the more advanced math courses that open their doors. In his final lecture, Professor Edwards looks ahead to where your mathematical studies might take you after this course. This land is exciting. Imagine entering a foreign country with the ability to speak the country’s language. Your opportunities to explore, interact and learn more are almost limitless. That’s what Understanding Calculus II does to help you master one of the greatest achievements of the human mind.
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