Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Calculus, students will enjoy the same clear, concise approach and extensive exercises to key fields they've come to expect from the series--but now within mathematics. Practice Makes Perfect: Calculus is not focused on any particular test or exam, but complementary to most calculus curricula. Because of this approach, the book can be used by struggling students needing extra help, readers who need to firm up skills for an exam, or those who are returning to the subject years after they first studied it. Its all-encompassing approach will appeal to both U.S. and international students.William Clark has contributed to Practice Makes Perfect Calculus as an author. William Clark is visiting assistant professor of history at the University of California, Los Angeles, and coeditor of "The Sciences in Enlightened Europe," also published by the University of Chicago Press.
Author(s): Dr. William Clark, Sandra McCune
Series: Practice Makes Perfect McGraw-Hill
Edition: 1
Publisher: McGraw-Hill
Year: 2010
Language: English
Pages: 160
Tags: Математика;Математический анализ;
Contents......Page 6
Preface......Page 10
I: Limits......Page 12
Limit definition and intuition......Page 14
Properties of limits......Page 15
Zero denominator limits......Page 18
Infinite limits and limits involving infinity......Page 19
Left-hand and right-hand limits......Page 20
Definition of continuity......Page 22
Properties of continuity......Page 23
Intermediate Value Theorem (IVT)......Page 24
II: Differentiation......Page 26
Definition of the derivative......Page 28
Derivative of a constant function......Page 29
Derivative of a power function......Page 30
Numerical derivatives......Page 31
Constant multiple of a function rule......Page 34
Rule for sums and differences......Page 35
Product rule......Page 36
Quotient rule......Page 37
Chain rule......Page 39
Implicit differentiation......Page 40
Derivative of the natural exponential function e[sup(x)]......Page 44
Derivatives of exponential functions for bases other than e......Page 45
Derivatives of logarithmic functions for bases other than e......Page 46
Derivatives of trigonometric functions......Page 47
Derivatives of inverse trigonometric functions......Page 48
Higher-order derivatives......Page 50
III: Integration......Page 52
Antiderivatives and the indefinite integral......Page 54
Integration of constant functions......Page 55
Integration of power functions......Page 56
Integration of exponential functions......Page 57
Integration of derivatives of trigonometric functions......Page 58
Integration of derivatives of inverse trigonometric functions......Page 59
Two useful integration rules......Page 60
Integration by substitution......Page 64
Integration by parts......Page 66
Integration by using tables of integral formulas......Page 68
Definition of the definite integral and the First Fundamental Theorem of Calculus......Page 72
Useful properties of the definite integral......Page 73
Second Fundamental Theorem of Calculus......Page 75
Mean Value Theorem for Integrals......Page 76
IV: Applications of the Derivative and the Definite Integral......Page 78
Slope of the tangent line at a point......Page 80
Instantaneous rate of change......Page 81
Differentiability and continuity......Page 83
Increasing and decreasing functions, extrema, and critical points......Page 84
Concavity and points of inflection......Page 88
Mean Value Theorem......Page 90
Area of a region under one curve......Page 94
Area of a region between two curves......Page 95
Length of an arc......Page 97
Appendix A: Basic functions and their graphs......Page 100
Appendix B: Basic differentiation formulas and rules......Page 108
Appendix C: Integral formulas......Page 110
Answer key......Page 114
Worked solutions......Page 128
