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Full Description
In order to show scientists and engineers how to apply calculus, this edition places a greater emphasis on conceptual understanding. It provides a nice balance between rigor and accessibility that will challenge them. Unique elements are integrated throughout that deepen the appreciation for calculus. Numerous nonstandard challenging exercises build better math skills. Innovative approaches on topics such as limits also help uncover new areas of learning for scientists and engineers.
Contents
1 Basics 1 1.1 Number Systems 1
1.2 Planar Coordinates and Graphing in the Pl ne 4
1.3 Lines and Their Slopes 10
1.4 Functions and Their Graphs 16
1.5 Combining Functions 21
1.6 Trigonometry 26
2 Limits 35
2.1 The Concept of Limit 35
2.2 Limit Theorems 41
2.3 Continuity 46
2.4 In nite Limits and Asymptotes 52
2.5 Limits of Sequences 57
2.6 Exponential Functions and Logarithms 60
3 The Derivative 68
3.1 Rates of Change and Tangent Lines 68
3.2 The Derivative 74
3.3 Rules for Dierentiation 80
3.4 Dierentiation of Some Basic Functions 88
3.5 The Chain Rule 93
3.6 Derivatives of Inverse Functions 99
3.7 Higher Derivatives 104
3.8 Implicit Dierentiation 109
3.9 Dierentials and Approximation of Functions 117
3.10 Other Transcendental Functions 122
4 Applications of the Derivative 130
4.1 Related Rates 130
4.2 The Mean Value Theorem 133
4.3 Maxima and Minima of Functions 139
4.4 Applied Maximum-Minimum Problems 145
4.5 Concavity 151
4.6 Graphing Functions 156
4.7 L'H^opital's Rule 162
4.8 The Newton-Raphson Method 168
4.9 Antidierentiation and Applications 172
5 The Integral 182
5.1 Introduction to Integration|The Area Problem 182
5.2 The Riemann Integral 187
5.3 Properties of the Integral 192
5.4 The Fundamental Theorem of Calculus 197
5.5 A Calculus Approach to the Logarithm and Exponential Function 202
5.6 Integration by Substitution 208
5.7 More on the Calculation of Area 216
5.8 Numerical Techniques of Integration 223
6 Techniques of Integration 239
6.1 Integration by Parts 239
6.2 Powers and Products of Trigonometric Functions 252
6.3 Trigonometric Substitution 264
6.4 Partial Fractions|Linear Factors 276
6.5 Partial Fractions|Irreducible Quadratic Factors 285
6.6 Improper Integrals|Unbounded Integrands 294
6.7 Improper Integrals|Unbounded Intervals 304
7 Applications of the Integral 325
7.1 Volumes 325
7.2 Arc Length and Surface Area 332
7.3 The Average Value of a Function 337
7.4 Center of Mass 341
7.5 Work 346
7.6 First Order Dierential Equations{Separable Equations 350
7.7 First Order Dierential Equations{Linear Equations 358
8 In nite Series 371
8.1 Series 371
8.2 The Divergence Test and the Integral Test 377
8.3 The Comparison Tests 382
8.4 Alternating Series 385
8.5 The Root and Ratio Tests 388
8.6 Introduction to Power Series 392
8.7 Representing Functions by Power Series 403
8.8 Taylor Series 411
