Page 10 - Calculus Demystified

Contents
147
CHAPTER 6 Transcendental Functions ix
6.0 Introductory Remarks 147
6.1 Logarithm Basics 147
6.1.1 A New Approach to Logarithms 148
6.1.2 The Logarithm Function and the Derivative 150
6.2 Exponential Basics 154
6.2.1 Facts About the Exponential Function 155
6.2.2 Calculus Properties of the Exponential 156
6.2.3 The Number e 158
6.3 Exponentials with Arbitrary Bases 160
6.3.1 Arbitrary Powers 160
6.3.2 Logarithms with Arbitrary Bases 163
6.4 Calculus with Logs and Exponentials to Arbitrary Bases 166
6.4.1 Differentiation and Integration of log x and a x 166
a
6.4.2 Graphing of Logarithmic and Exponential
Functions 168
6.4.3 Logarithmic Differentiation 170
6.5 Exponential Growth and Decay 172
6.5.1 A Differential Equation 173
6.5.2 Bacterial Growth 174
6.5.3 Radioactive Decay 176
6.5.4 Compound Interest 178
6.6 Inverse Trigonometric Functions 180
6.6.1 Introductory Remarks 180
6.6.2 Inverse Sine and Cosine 180
6.6.3 The Inverse Tangent Function 185
6.6.4 Integrals in Which Inverse Trigonometric Functions
Arise 187
6.6.5 Other Inverse Trigonometric Functions 189
6.6.6 An Example Involving Inverse Trigonometric
Functions 193

CHAPTER 7 Methods of Integration 197

7.1 Integration by Parts 197
7.2 Partial Fractions 202
7.2.1 Introductory Remarks 202
7.2.2 Products of Linear Factors 203
7.2.3 Quadratic Factors 206