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TTC Video - Understanding Calculus II

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TTC Video - Understanding Calculus II

TTC Video - Understanding Calculus II | 13.83 GB
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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

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.
Professor Edwards begins with a three-lecture review of the fundamental ideas of calculus. He also includes brief reviews of major concepts throughout the course, which makes Understanding Calculus II a self-contained lecture series for anyone who is already familiar with the two main operations of calculus, differentiation and integration. Professor Edwards takes these ideas beyond the definitions, rules, and formulas that are the focus of first-semester calculus and applies them in intriguing ways. For example:
Infinite series: Does adding an infinite sequence of numbers give an infinite result? Not necessarily. The series may converge on a specific value, or it may diverge to infinity. Calculus can provide the answer for different types of infinite series and represent familiar functions from algebra or trigonometry in surprising ways.
Vectors: Among the geometric applications of calculus is the analysis of vectors. These are quantities, such as velocity, that have both magnitude and direction. In Calculus II, you learn techniques for evaluating vectors in the plane, allowing you to solve problems involving moving and accelerating objects, whether they are on a straight or curved path.

Understanding Calculus II covers the above subjects 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,
integrating areas and volumes,
Taylor and Maclaurin polynomials, evaluating improper integrals,
calculus applied to parametric equations, and
calculus applied to polar coordinates.
Explore the Immense Riches of Calculus

Calculus is full of fascinating properties, baffling paradoxes, and entertaining problems. Among the many you investigate in Understanding Calculus II are these:Cantor Set: Remove the middle third of a line segment. Repeat with the two pieces that remain. Repeat again ad infinitum. The end points of all the pieces will form an infinite set. But what about the total length of all the line segments? Summing this infinite series reveals the surprising answer.

Master Calculus on Your Own Schedule

Understanding Calculus II is an immensely rewarding 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 will benefit from this engaging and flexible presentation include
high school or college students currently, or about to be, enrolled 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 a rigorous review of calculus; andA three-time Teacher of the Year at the University of Florida, Professor Edwards knows how to help students surmount the stumbling blocks on their path to mastering calculus. In this course, he uses a steady stream of on-screen equations, graphs, and other visual aids to document the key steps in solving sample problems. The accompanying workbook is designed to reinforce each lecture with more practice problems and worked-out solutions, as well as lecture summaries, tips, and pitfalls; and formulas for derivatives, integration, and power series.
Open Doors with Your New Fluency

The place of calculus at the end of the high school math curriculum makes it seem like a final destination. But it is also only a beginning. Calculus is a world unto itself, an ever-expanding collection of tools that can solve the most intractable problems in ingenious and often surprising ways. The deeper you go into calculus, the richer it gets and the better you are prepared for even more advanced math courses that open doors of their own.
LECTURES
36 Lectures

1Basic Functions of Calculus and Limits
2Differentiation Warm-up
3Integration Warm-up

5Applications of Differential Equations
6Linear Differential Equations
7Areas and Volumes
8Arc Length, Surface Area, and Work
9Moments, Centers of Mass, and Centroids
10Integration by Parts
11Trigonometric Integrals
12Integration by Trigonometric Substitution
13Integration by Partial Fractions
14Indeterminate Forms and L'Hopital's Rule
15Improper Integrals
16Sequences and Limits

18Series, Divergence, and the Cantor Set

20The Comparison Tests
21Alternating Series
22The Ratio and Root Tests
23Taylor Polynomials and Approximations
24Power Series and Intervals of Convergence
25Representation of Functions by Power Series
26Taylor and Maclaurin Series
27Parabolas, Ellipses, and Hyperbolas
28Parametric Equations and the Cycloid
29Polar Coordinates and the Cardioid
30Area and Arc Length in Polar Coordinates
31Vectors in the Plane
32The Dot Product of Two Vectors
33Vector-Valued Functions
34Velocity and Acceleration
35Acceleration's Tangent and Normal Vectors
36Curvature and the Maximum Bend of a Curve

ABOUT THE PROFESSOR

TTC Video - Understanding Calculus II


Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. After his years at Stanford, he taught mathematics at a university near Bogota, Colombia, as a Peace Corps volunteer.
Professor Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He has been a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has also coauthored a wide range of mathematics textbooks with Professor Ron Larson. Their textbooks have been honored with various awards from the Text and Academic Authors Association.

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