Understanding Calculus Problems, Solutions, and Tips by Bruce H. Edwards
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About this book :-
Understanding Calculus Problems, Solutions, and Tips written by
Bruce H. Edwards.
The goal of this course is for you to understand and appreciate the beautiful subject of calculus. You will see how calculus plays a fundamental role in all of science and engineering, as well as business and economics. You will learn about the 2 major ideas of calculus—the derivative and the integral. Each has a rich history and many practical applications.
Calculus is often described as the mathematics of change. For instance, calculus is the mathematics of velocities, accelerations, tangent lines, slopes, areas, volumes, arc lengths, centroids, curvatures, and a variety of other concepts that have enabled scientists, engineers, and economists to model real-life situations. For example, a NASA scientist might need to know the initial velocity required for a rocket to escape Earth’s gravitational field. Calculus is required to determine this escape velocity. An engineer might need to know the volume of a spherical object with a hole drilled through the center. The integral calculus is needed to compute this volume. Calculus is an important tool for economic predictions, such as the growth of the federal debt. Similarly, 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.
Book Detail :-
Title: Understanding Calculus Problems, Solutions, and Tips
Edition:
Author(s): Bruce H. Edwards
Publisher: The great courses teaching company
Series:
Year: 2010
Pages: 223
Type: PDF
Language: English
ISBN: 1598039563,9781598039566
Country: USA
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About Author :-
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.
Other Books of Author
Professor Edwards has taught three other Great Courses:
Understanding Calculus: Problems, Solutions, and Tips;
Mathematics Describing the Real World:
Precalculus and Trigonometry; and Prove It:
Also author of many books
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Book Contents :-
Understanding Calculus Problems, Solutions, and Tips written by
Bruce H. Edwards
cover the following topics.
'
Lesson Two Review—Graphs, Models, and Functions
Lesson Three Review—Functions and Trigonometry
Lesson Four Finding Limits
Lesson Five An Introduction to Continuity
Lesson Six Infinite Limits and Limits at Infinity
Lesson Seven The Derivative and the Tangent Line Problem
Lesson Eight Basic Differentiation Rules
Lesson Nine Product and Quotient Rules
Lesson Ten The Chain Rule
Lesson Eleven Implicit Differentiation and Related Rates
Lesson Twelve Extrema on an Interval
Lesson Thirteen Increasing and Decreasing Functions
Lesson Fourteen Concavity and Points of Inflection
Lesson Fifteen Curve Sketching and Linear Approximations
Lesson Sixteen Applications—Optimization Problems, Part 1
Lesson Seventeen Applications—Optimization Problems, Part 2
Lesson Eighteen Antiderivatives and Basic Integration Rules
Lesson Nineteen The Area Problem and the Definite Integral
Lesson Twenty The Fundamental Theorem of Calculus, Part 1
Lesson Twenty-One The Fundamental Theorem of Calculus, Part 2
Lesson Twenty-Two Integration by Substitution
Lesson Twenty-Three Numerical Integration
Lesson Twenty-Four Natural Logarithmic Function—Differentiation
Lesson Twenty-Five Natural Logarithmic Function—Integration
Lesson Twenty-Six Exponential Function
Lesson Twenty-Seven Bases other than e
Lesson Twenty-Eight Inverse Trigonometric Functions
Lesson Twenty-Nine Area of a Region between 2 Curves
Lesson Thirty Volume—The Disk Method
Lesson Thirty-One Volume—The Shell Method
Lesson Thirty-Two Applications—Arc Length and Surface Area
Lesson Thirty-Three Basic Integration Rules
Lesson Thirty-Four Other Techniques of Integration
Lesson Thirty-Five Differential Equations and Slope Fields
Lesson Thirty-Six Applications of Differential Equations
Glossary
Formulas
Theorems
Review of Trigonometry
Bibliography
Solutions
Summary Sheet
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