9780812098198

Calculus

by
  • ISBN13:

    9780812098198

  • ISBN10:

    0812098196

  • Format: Paperback
  • Copyright: 9/1/1997
  • Publisher: Barrons Educational Series Inc

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Summary

This general review covers equations, functions, and graphs; limits, derivatives; integrals and antiderivatives; word problems; applications of integrals to geometry; and much more. Additional features make this volume especially helpful to students working on their own. They include worked-out examples, a summary of the main points of each chapter, exercises, and where needed, background material on algebra, geometry, and reading comprehension.

Table of Contents

Introduction vii
1 Equations, Functions, and Graphs
1(16)
1.1 Equations
1(1)
1.2 Functions
2(6)
1.3 Graphs
8(5)
1.4 Summary of Main Points
13(1)
1.5 Exercises
14(3)
2 Change, and the Idea of the Derivative
17(30)
2.1 Average Rates of Change
17(6)
2.2 Instantaneous Rates of Change
23(10)
2.3 The Derivative
33(4)
2.4 The Geometric Meaning of Derivatives
37(6)
2.5 Summary of Main Points
43(1)
2.6 Exercises
44(3)
3 The Idea of Limits
47(22)
3.1 The Basic Definition
47(3)
3.2 Some Complications with the Definition of Limits
50(2)
3.3 The Problem of Division By Zero
52(4)
3.4 The Case of (0/0)
56(3)
3.5 Continuity and Differentiability
59(4)
3.6 Summary of Main Points
63(2)
3.7 Exercises
65(4)
4 Computing Some Derivatives
69(14)
4.1 Powers of x
70(3)
4.2 Fractional Expressions with the Variable in the Denominator
73(6)
4.3 Square Roots
79(1)
4.4 Some Harder Examples
80(2)
4.5 Summary of Main Points
82(1)
4.6 Exercises
82(1)
5 Formulas for Derivatives
83(20)
5.1 Derivatives of Some Particular Functions
84(2)
5.2 Derivatives of Combinations of Functions
86(7)
5.3 The Chain Rule
93(8)
5.4 Summary of Main Points
101(1)
5.5 Exercises
101(2)
6 Extreme Values, the Mean Value Theorem, and Curve Sketching
103(22)
6.1 Extreme Values
104(6)
6.2 The Mean Value Theorem
110(4)
6.3 Curve Sketching
114(7)
6.4 Summary of Main Points
121(1)
6.5 Exercises
122(3)
7 Word Problems
125(30)
7.1 A Review of Geometry
125(6)
7.2 Max-Min Word Problems
131(9)
7.3 Related Rate Word Problems
140(9)
7.4 Summary of Main Points
149(1)
7.5 Exercises
150(5)
8 The Idea of the Integral
155(34)
8.1 The Basic Idea
155(9)
8.2 Terminology and Notation
164(16)
8.3 The Definite Integral: Definition and Notation
180(3)
8.4 Summary of Main Points
183(2)
8.5 Exercises
185(4)
9 Computing Some Integrals
189(18)
9.1 Summation Rules and Formulas
189(10)
9.2 Computing Limits of Approximate Sums
199(3)
9.3 Summary of Main Points
202(2)
9.4 Exercises
204(3)
10 Formulas for Integrals: Integrals, Antiderivatives and the Fundamental Theorem of Calculus
207(28)
10.1 Introduction
207(1)
10.2 The Fundamental Theorem of Calculus--The Main Idea
207(6)
10.3 The Fundamental Theorem of Calculus--An Idea of the Proof
213(3)
10.4 Computing Some Antiderivatives
216(8)
10.5 Antiderivatives Involving the Chain Rule
224(6)
10.6 Summary of Main Points
230(2)
10.7 Exercises
232(3)
11 Geometric Applications of the Integral
235(58)
11.1 Horizontal vs. Vertical, x vs. y
235(8)
11.2 Area
243(17)
11.3 Volumes of Solids of Revolution--The Method of Cross-sectional Areas
260(15)
11.4 Volumes of Solids of Revolution--The Method of Cylindrical Shells
275(13)
11.5 Summary of Main Points
288(2)
11.6 Exercises
290(3)
12 Motion
293(12)
12.1 Simple Initial Value Problems
293(2)
12.2 Motion with Constant Acceleration
295(5)
12.3 Summary of Main Points
300(1)
12.4 Exercises
301(4)
APPENDICES 305(17)
A The Trigonometric Functions 305(10)
A.1 Definitions 305(3)
A.2 Identities 308(1)
A.3 Derivatives 309(2)
A.4 Antiderivatives 311(4)
B Exponential and Logarithmic Functions 315(7)
B.1 Definitions 315(1)
B.2 Identities 316(1)
B.3 Derivatives 317(2)
B.4 Antiderivatives 319(3)
Answers to Exercises 322(14)
Glossary 336(3)
Index 339

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