Page 16 - Excel for Scientists and Engineers: Numerical Methods

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CONTENTS Xlll

Another Example ......................................................................................... 258
A Limitation on the Finite-Difference Method ............................................ 261
Problems ............................................................................................................. 262
Chapter 12 Partial Differential Equations 263
Elliptic. Parabolic and Hyperbolic Partial Differential Equations ..................... 263
Elliptic Partial Differential Equations ................................................................ 264
Solving Elliptic Partial Differential Equations:
Replacing Derivatives with Finite Differences ......................................... 265
An Example: Temperature Distribution in a Heated Metal Plate ................ 267
Parabolic Partial Differential Equations ............................................................. 269
Solving Parabolic Partial Differential Equations: The Explicit Method ...... 270
An Example: Heat Conduction in a Brass Rod ............................................ 272
Solving Parabolic Partial Differential Equations:
The Crank-Nicholson or Implicit Method ................................................ 274
An Example: Vapor Diffusion in a Tube ..................................................... 275
Vapor Diffusion in a Tube Revisited ........................................................... 277
Vapor Diffusion in a Tube (Again) .............................................................. 279
A Crank-Nicholson Custom Function ......................................................... 280
Vapor Diffusion in a Tube Solved by Using a Custom Function ................ 282
Hyperbolic Partial Differential Equations .......................................................... 282
Solving Hyperbolic Partial Differential Equations:
Replacing Derivatives with Finite Differences ......................................... 282
An Example: Vibration of a String .............................................................. 283
Problems ............................................................................................................. 286

Chapter 13 Linear Regression and Curve Fitting 287
Linear Regression ............................................................................................... 287
Least-Squares Fit to a Straight Line ............................................................ 288
Least-Squares Fit to a Straight Line Using the Worksheet Functions
SLOPE, INTERCEPT and RSQ ...................................................................... 289
Multiple Linear Regression ................................................................................ 291
Least-Squares Fit to a Straight Line Using LINEST ........................................ 292
Multiple Linear Regression Using LINEST ...................................................... 293
Handling Noncontiguous Ranges of known-x's in LINEST ........................... 297
A LINEST Shortcut ...................................................................................... 297
LINEST's Regression Statistics .................................................................... 297
Linear Regression Using Trendline ............................................................. 298
Limitations of Trendline .............................................................................. 301
Importing Trendline Coefficients into a Spreadsheet
by Using Worksheet Formulas ................................................................. 302
Using the Regression Tool in Analysis Tools .............................................. 303
Limitations of the Regression Tool ............................................................. 305