Understanding Calculus II: Problems, Solutions, and Tips by Bruce H. Edwards
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About this book :-
Understanding Calculus II: Problems, Solutions, and Tips written by
Bruce H. Edwards, Ph.D., Professor of Mathematics, University of Florida.
The goal of this course is to further your understanding and appreciation of calculus. Just as in Understanding Calculus: Problems, Solutions, and Tips, you will see how calculus plays a fundamental role in all of science and engineering.
In the first third of the course, you’ll use the tools of derivatives and integrals that you learned in calculus I to solve some of the great detective stories of mathematics—differential equations. The middle portion of the course will take you to the beautiful world of infinite series and their connection to the functions you have learned about in your studies of precalculus and calculus. Finally, the third part of the course will lead to a solid understanding of key concepts from physics, including particle motion, velocity, and acceleration. Calculus is often described as the mathematics of change. The concepts of calculus—including velocities, accelerations, tangent lines, slopes, areas, volumes, arc lengths, centroids, curvatures, and work—have enabled scientists, engineers, and economists to model a host of real-life situations.
For example, a physicist might need to know the work required for a rocket to escape Earth’s gravitational field. You will see how calculus allows the calculation of this quantity. An engineer might need to know the balancing point, or center of mass, of a planar object. The integral calculus is needed to compute this balancing point. A biologist might want to calculate the growth rate of a population of bacteria, or a geologist might want to estimate the age of a fossil using carbon dating. In each of these cases, calculus is needed to solve the problem. Although precalculus mathematics (geometry, algebra, and trigonometry) also deals with velocities, accelerations, tangent lines, slopes, and so on, there is a fundamental difference between precalculus mathematics and calculus. Precalculus mathematics is more static, whereas calculus is more dynamic.
Book Detail :-
Title: Understanding Calculus II: Problems, Solutions, and Tips
Author(s): Bruce H. Edwards
Publisher: The great courses teaching company
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About Author :-
The author of this book Professor Bruce H. Edwards has been a Professor of Mathematics at the University of Florida since 1976. He received his B.S. in Mathematics from Stanford University in 1968 and his Ph.D. in Mathematics from Dartmouth College in 1976. From 1968 to 1972, he was a Peace Corps volunteer in Colombia, where he taught mathematics (in Spanish) at Universidad Pedag�gica y Tecnol�gica de Colombia.
Professor Edwards�s early research interests were in the broad area of pure mathematics called algebra. His dissertation in quadratic forms was titled �Induction Techniques and Periodicity in Clifford Algebras.� Beginning in 1978, Professor Edwards became interested in applied mathematics while working summers for NASA at the Langley Research Center in Virginia. This work led to his research in numerical analysis and the solution of differential equations. During his sabbatical year, 1984 to 1985, he worked on two-point boundary value problems with Professor Leo Xanthis at the Polytechnic of Central London. Professor Edwards�s current research is focused on the algorithm called CORDIC that is used in computers and graphing calculators for calculating function values.
Professor Bruce H. Edwards has coauthored a number of mathematics textbooks with Professor Ron Larson of Penn State Erie, The Behrend College. Together, they have published leading texts in calculus, applied calculus, linear algebra, finite mathematics, algebra, trigonometry, and precalculus.
Over the years, Professor Edwards has received many teaching awards at the University of Florida. He was named Teacher of the Year in the College of Liberal Arts and Sciences in 1979, 1981, and 1990. In addition, he was named the College of Liberal Arts and Sciences Student Council Teacher of the Year and the University of Florida Honors Program Teacher of the Year in 1990. He also served as the Distinguished Alumni Professor for the UF Alumni Association from 1991 to 1993. The winners of this two-year award are selected by graduates of the university. The Florida Section of the Mathematical Association of America awarded Professor Edwards the Distinguished Service Award in 1995 for his work in mathematics education for the state of Florida. His textbooks have been honored with various awards from the Text and Academic Authors Association.
Professor Edwards has taught a wide range of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He particularly enjoys teaching calculus to freshman because of the beauty of the subject and the enthusiasm of the students. Professor Edwards has been a frequent speaker at both research conferences and meetings of the National Council of Teachers of Mathematics. He has spoken on issues relating to the Advanced Placement calculus examination, especially on the use of graphing calculators.
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Book Contents :-
Understanding Calculus II: Problems, Solutions, and Tips written by
Bruce H. Edwards
cover the following topics.
1. Basic Functions of Calculus and Limits
2. Differentiation Warm-Up
3. Integration Warm-Up
4. Differential Equations—Growth and Decay
5. Applications of Differential Equations
6. Linear Differential Equations
7. Areas and Volumes
8. Arc Length, Surface Area, and Work
9. Moments, Centers of Mass, and Centroids
10. Integration by Parts
11. Trigonometric Integrals
12. Integration by Trigonometric Substitution
13. Integration by Partial Fractions
14. Indeterminate Forms and L’Hôpital’s Rule
15. Improper Integrals
16. Sequences and Limits
17. Infinite Series—Geometric Series
18. Series, Divergence, and the Cantor Set
19. Integral Test—Harmonic Series, p-Series
20. The Comparison Tests
21. Alternating Series
22. The Ratio and Root Tests
23. Taylor Polynomials and Approximations
24. Power Series and Intervals of Convergence
25. Representation of Functions by Power Series
26. Taylor and Maclaurin Series
27. Parabolas, Ellipses, and Hyperbolas
28. Parametric Equations and the Cycloid
29. Polar Coordinates and the Cardioid
30. Area and Arc Length in Polar Coordinates
31. Vectors in the Plane
32. The Dot Product of Two Vectors
33. Vector-Valued Functions
34. Velocity and Acceleration
35. Acceleration’s Tangent and Normal Vectors
36. Curvature and the Maximum Bend of a Curve
Summary of Differentiation Formulas
Summary of Integration Formulas
Power Series for Elementary Functions
Summary of Tests for Convergence and Divergence
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