Integrated Engineering Calculus I & II

Linear Regression......Page 11
Finding the Regression Parameters......Page 14
Judging the Strength of the Relationship......Page 15
Target Practice......Page 18
Exercises......Page 20
Solutions to Target Practice......Page 23
Classes of Functions......Page 25
Linear Function......Page 26
Quadratic Function......Page 27
Other Polynomial Functions......Page 28
Exponential Function......Page 29
Sine and Cosine Functions......Page 31
Target Practice......Page 32
Exercises......Page 33
Properties of Basic Functions......Page 37
Shifts and Stretches......Page 39
Target Practice......Page 43
Exercises......Page 44
Solutions to Target Practice......Page 47
Slope and Rate of Change......Page 49
Target Practice......Page 51
Exercises......Page 52
Limits and the Derivative......Page 54
Target Practice......Page 56
The Derivative as a Function......Page 57
Target Practice......Page 58
Exercises......Page 59
Some Terminology and Notation......Page 61
Exercises......Page 62
The Derivative of a Sine Function......Page 64
Sine Functions with Different Frequencies......Page 66
Sines and Cosines......Page 67
Exercises......Page 68
Higher Order Derivatives......Page 69
More Derivatives......Page 70
Exercises......Page 71
Solutions to Target Practice......Page 72
Polynomials......Page 77
Exercises......Page 81
Extending the Power Rule......Page 83
Target Practice......Page 84
Exercises......Page 85
Derivatives of sin(x) and cos(x)......Page 86
Exercises......Page 90
Derivative of an Exponential Function......Page 91
Target Practice......Page 92
Exercises......Page 93
Derivative of a Logarithm Function......Page 94
Exercises......Page 95
Hyperbolic Functions......Page 97
Exercises......Page 99
Solutions to Target Practice......Page 101
The Chain Rule......Page 103
Exercises......Page 105
The Product Rule......Page 107
Target Practice......Page 108
The Quotient Rule......Page 109
Exercises......Page 110
Exercises......Page 114
Solutions to Target Practice......Page 116
Velocity and Displacement......Page 119
The Relationship between Velocity and Position......Page 121
Exercises......Page 122
Approximating the Area Under the Graph of a Function......Page 123
Target Practice......Page 125
The Exact Area Under the Graph of a Function......Page 126
The Definite Integral......Page 127
Exercises......Page 128
Solutions to Target Practice......Page 131
Antiderivatives......Page 133
Exercises......Page 135
Initial Value Problems......Page 136
Target Practice......Page 138
Exercises......Page 139
Differential Equations of Higher Order......Page 140
A Second Order Initial Value Problem......Page 141
Quick Introduction to Matrices......Page 142
Exercises......Page 144
Antiderivatives and the Definite Integral......Page 146
Exercises......Page 149
The Fundamental Theorems......Page 150
Piecewise-defined functions......Page 151
Airy functions......Page 153
Laguerre Polynomials......Page 154
Solutions to Target Practice......Page 155
Two Quantities Changing with Time......Page 157
Exercises......Page 160
Differentiating Implicitly......Page 162
Exercises......Page 166
Exercises......Page 168
Solutions to Target Practice......Page 170
Finding the Best Strategy......Page 173
Local Maxima and Minima......Page 175
Exercises......Page 177
Deciding Whether an Extreme Value is a Maximum or Minimum......Page 180
Exercises......Page 182
Another Type of Critical Point......Page 184
Absolute Maxima and Minima......Page 185
Exercises......Page 186
Inflection Points......Page 187
Curve Sketching......Page 188
Exercises......Page 189
Solutions to Target Practice......Page 190
Changing Variables in Integrals......Page 193
Exercises......Page 196
Solving Differential Equations Exactly......Page 199
Exercises......Page 203
Substitution in Definite Integrals......Page 206
Exercises......Page 207
Solutions to Target Practice......Page 209
Integration By Parts......Page 213
Exercises......Page 215
Integration using Trigonometric Substitution......Page 217
Exercises......Page 219
Exercises......Page 221
Integration by Partial Fractions......Page 223
Target Practice......Page 224
Exercises......Page 225
Using Tables......Page 227
Exercises......Page 229
Solutions to Target Practice......Page 230
Areas Between Curves......Page 233
Choosing the Representative Rectangle......Page 235
Exercises......Page 236
Volumes of Solid Regions......Page 237
Solids with Circular Cross Sections – The Disk Method......Page 238
Solids with Holes – The Washer Method......Page 239
Target Practice......Page 240
Exercises......Page 241
Length of a Curve......Page 243
Choosing the Correct Method......Page 246
Exercises......Page 247
Area of a Three-Dimensional Surface......Page 248
Exercises......Page 249
Applied Geometry Problems......Page 250
Exercises......Page 253
Solutions to Target Practice......Page 258
Work with a Variable Force......Page 261
Emptying a Tank......Page 264
Exercises......Page 265
Fluid Pressure......Page 268
Force Due to Fluid Pressure......Page 269
Exercises......Page 271
Improper Integrals......Page 273
Exercises......Page 276
Solutions to Target Practice......Page 279
Neverending Sums......Page 281
Sequences and Series......Page 282
Target Practice......Page 283
Exercises......Page 284
Geometric Series......Page 286
A Series with Decreasing Terms that Does Not Converge......Page 287
Exercises......Page 288
Integral Test......Page 291
Comparison Test......Page 292
Target Practice......Page 293
Exercises......Page 294
Ratio Test......Page 295
Target Practice......Page 296
exercises......Page 297
Summary of Tests for Infinite Series of the Form n=k an......Page 298
Solutions to Target Practice......Page 299
Approximating functions......Page 301
Quadratic approximations......Page 302
Cubic approximation......Page 303
Target Practice......Page 304
Exercises......Page 306
Definition of Taylor Series......Page 307
Target Practice......Page 308
Special limits......Page 309
Exercises......Page 310
Error......Page 311
Solutions to Target Practice......Page 313