| Choosing a Product |
| Scientific WorkPlace |
| Scientific Word |
| Scientific Notebook |
| Calculus:
Concepts and Methods CD |
| Software Licenses |
Related
Products  |
| Scientific Viewer |
| Localized Products |
| Spell Checkers |
| Voice Input |
| Braille Output |
| Books |
| Free Trial Versions |
|
Carol Walker and Darel Hardy ©1997 270 pages Publisher: Brooks/Cole Publishing ISBN: 0-534-34546-8 Read more about Doing Calculus with Scientific Notebook® or about other books from MacKichan Software. |
0.1 Introduction to Scientific Notebook
0.2 Functions and Their Graphs
0.3 Types of Functions: Shifting and Scaling 21
0.4 Graphing Calculators and Computers 25
0.5 Principles of Mathematical Writing 26
1.1 The Tangent and Velocity Problems 29
1.2 The Limit of a Function 32
1.3 Calculating Limits Using the Limit Laws 36
1.4 The Precise Definition of a Limit 38
1.5 Continuity 41
1.6 Limits at Infinity; Horizontal Asymptotes 45
1.7 Tangents, Velocities, and Other Rates of Change 47
2.1 Derivatives 51
2.2 Differentiation Formulas 57
2.3 Rates of Change in the Natural and Social Sciences 58
2.4 Derivatives of Trigonometric Functions 62
2.5 The Chain Rule 64
2.6 Implicit Differentiation 66
2.7 Higher Derivatives 70
2.8 Related Rates 74
2.9 Differentials; Linear and Quadratic Approximations 77
2.10 Newton's Method 80
3.1 Exponential Functions and Their Derivatives 85
3.2 Inverse Functions 87
3.3 Logarithmic Functions 90
3.4 Derivatives of Logarithmic Functions 91
3.5 Exponential Growth and Decay 94
3.6 Inverse Trigonometric Functions 97
3.7 Hyperbolic Functions 99
3.8 Indeterminate Forms and l'Hospital's Rule 104
4.1 Maximum and Minimum Values 109
4.2 The Mean Value Theorem 111
4.3 Monotonic Functions and the First Derivative Test 114
4.4 Concavity and Points of Inflection 116
4.5 Curve Sketching 120
4.6 Graphing with Calculus and Calculators 122
4.7 Applied Maximum and Minimum Problems 130
4.8 Applications to Economics 136
4.9 Antiderivatives 139
5.1 Sigma Notation 143
5.2 Area 146
5.3 The Definite Integral 148
5.4 The Fundamental Theorem of Calculus 151
5.5 The Substitution Rule 154
5.6 The Logarithm Defined as an Integral 158
6.1 Areas Between Curves 161
6.2 Volume 163
6.3 Volumes by Cylindrical Shells 166
6.4 Work 169
6.5 Average Value of a Function 171
7.1 Integration by Parts 175
7.2 Trigonometric Integrals 177
7.3 Trigonometric Substitution 180
7.4 Integration of Rational Functions by Partial Fractions 181
7.5 Rationalizing Substitutions 185
7.6 Strategy for Integration 188
7.7 Using Tables Of Integrals and Computer Algebra Systems 189
7.8 Approximate Integration 190
7.9 Improper integrals 195
8.1 Differential Equations 199
8.2 Arc Length 201
8.3 Area of a Surface of Revolution 203
8.4 Moments and Centers of Mass 205
8.5 Hydrostatic Pressure and Force 207
8.6 Applications to Economics and Biology 209
9.1 Curves Defined by Parametric Equations 213
9.2 Tangents and Areas 216
9.3 Arc Length and Surface Area 219
9.4 Polar Coordinates 221
9.5 Areas and Lengths in Polar Coordinates 223
9.6 Conic Sections 226
9.7 Conic Sections in Polar Coordinates 229
10.1 Sequences 233
10.2 Series 241
10.3 The Integral Test and Estimates of Sums 243
10.4 The Comparison Tests 245
10.5 Alternating Series 248
10.6 Absolute Convergence and the Ratio and Root Tests 250
10.7 Strategy for Testing Series 252
10.8 Power Series 252
10.9 Representations of Functions as Power Series 255
10.10 Taylor and Maclaurin Series 257
10.11 The Binomial Series 261
10.12 Applications of Taylor Polynomials 264