TGC – Understanding Calculus II: Problems, Solutions, and Tips

You will also find these benefits beyond the fact that you can use the techniques you have learned in Calculus II are practical and interesting and Elegant, complex ideas that are elegantly simple. Because it can show real.-Calculus is a versatile tool that can be used in all kinds of life situations. and These applications blossom in full bloom Calculus II.

Understanding Calculus II: Problems, Solutions, and Tips Take this thrilling journey in 36 fully illustrated halves-Hour-long lectures covering all the major topics of second full-Year calculus course at high school, College Board Advanced Placement BC Level or a second-semester course in college. Professor Bruce H. Edwards, University of Florida, enriches his lectures by crystalizing his decades of teaching experience.-Clear explanations, frequent tips and pitfalls to avoid. and—best of all—hundreds of examples and Problems in practice that are designed to help you understand and reinforce key concepts.

Professor Edwards is a highly qualified and accessible calculus teacher who has been awarded multiple teaching awards. and Co-authored the best-Selling series of calculus textbooks. Many students who struggle to understand calculus give up. Why? A particular procedure is effective and Do not try to remember the steps of a solution. Professor Edwards is a clear example of the fundamental concepts. and This makes it much easier to learn the material.

Get behind the wheel of the “Limit Machine”

Professor Edwards opens with a trio-Lecture review of the key ideas behind calculus. He also provides brief reviews of the major concepts throughout the course. Understanding Calculus II Self-employment-This lecture series is for those who are already familiar with the main operations of calculus and differentiation. and integration. These ideas are more than just definitions and rules. and Formulas that are the focal point of first-semester calculus and These principles are applied in new and interesting ways. Take, for example:

• Differential equations This far-reaching field puts derivatives to work—modeling population growth, nuclear decay, falling objects, and Numerous other processes involve change. Professor Edwards recalls as a young mathematician that he worked for NASA during summers, solving differential equations to support aircraft in flight.
• Infinite Series: Is it possible to add infinite numbers in order to get an infinite result? Not necessarily. It may converge at a particular value or diverge to infinity. Calculus Different types of infinite series can be solved by this tool. and In surprising ways, you can represent algebraic or trigonometry functions in familiar ways.
• Vectors: The analysis of vectors is one of the many geometric applications of calculus. These are quantities like velocity that have both magnitude and quantity. and direction. In Calculus II teaches you how to evaluate the plane’s vectors, which will help you solve problems related to moving. and Accelerating objects on straight or curved paths, regardless of whether they are on a straight path or not.

Understanding Calculus II The above topics are covered in depth, with an emphasis on infinite series. This is why 11 lectures are required. Second, you also learn about other topics.-semester calculus, including

• Formulas for integration and techniques,
• Integrating areas and volumes,
• Taylor and Maclaurin polynomials,
• L’Hôpital’s rule for evaluating limits,
• evaluating improper integrals,
• Calculus applied for parametric equations and
• Calculus applied to the polar coordinates.

Each of these applications of calculus involves the fundamental idea of the limit. Professor Edwards explains that calculus could be described as a “limit machine”—a set of procedures for approaching infinitely close to a value. Calculus’ unique feature is its combination of logic and creativity with the mysterious entity of infinite. These unusual marriages yield astonishingly precise solutions to seemingly impossible problems.

Discover the Immense Wealth of Calculus

Calculus It is filled with fascinating properties and baffling paradoxes. and You will have fun solving them. There are many things you can do to help. Understanding Calculus II These are:

• Gabriel’s Horn: Rotate a simple curve about its axis and You get three-A three-dimensional shape that looks almost like an infinitely long trumpet. Called Gabriel’s Horn, this geometric figure has an unusual property: It has infinite surface area but finite volume. Calculus shows that this is true.
• Baseball: At 100 feet per second, a baseball three feet above the home plate is struck and At an angle of 45 degrees. Employ Newton’s second law of motion and The derivative of the position function is used to determine whether the ball will be a homerun, clearing a 10, or not.-Foot-High fence at 300 feet.
• Set of Cantors Take out the middle third of the line segment. Repeat the process with the other two pieces. Repeat the process ad infinitum. All the pieces will end at the same point, creating an infinite set. But how about the lengths of all the line segments? This infinite series can be summed to reveal the surprising answer.

Master Calculus Schedule Yourself

Understanding Calculus II You can enjoy this immensely rewarding experience at your own pace. Professor Edwards will often encourage you to pause the video and Test your skills by solving a problem and then asking the questioner for the answer. Engaging this way will prove to be a benefit for many. and flexible presentation include:

• Students in high school and college are currently enrolled or soon to be enrolled Calculus II who desire personal coaching from an outstanding teacher
• High school students are preparing to take the College Board Advanced Placement Test in Calculus At the BC level
• Students in higher education-Level math courses for professionals or professionals who need to review calculus. and
• anyone interested in pursuing one of life’s greatest intellectual adventures, which has been solving difficult problems for over 300 years.

Three-Professor Edwards is the University of Florida’s Teacher of Year. He knows how students can overcome obstacles and master calculus. Edwards uses a steady flow of on-demand lectures to teach this course.-screen equations, graphs, and You can also use visual aids to illustrate the steps involved in solving problems. Each lecture is reinforced with additional practice problems in the accompanying workbook. and worked-You can find solutions and lecture summaries as well tips. and pitfalls; and formulas for derivatives, integration, and Power series.

Professor Edwards’s lectures also include a feature he calls “You Be the Teacher,” in which he reverses roles, challenging you to answer a typical question posed in the classroom, design a suitable problem to illustrate a principle, or otherwise put yourself in the instructor’s shoes—an invaluable exercise in learning to think for yourself in the language of calculus.

Your Fluency will Open Doors

Calculus’s place at the end is what makes it appear like a final destination. It is only the beginning. Calculus This is a universe unto itself, an infinite world.-Expanding range of tools that can help solve the most complex problems in ingenious and Sometimes in surprising ways. Calculus is richer the deeper you get into it and The better prepared you are for advanced math courses that will open up doors for you.

Professor Edwards gives his final lecture and looks at where math studies might take him after this course. It’s exciting terrain. Imagine arriving in a foreign country equipped with the ability to speak the nation’s language. You have many opportunities to interact and explore. and There are endless possibilities for further education. That’s what Understanding Calculus II It will improve your fluency in one the greatest achievements of the human brain.