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