Numerical Analysis By Shanker Rao

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INDEX 321 INDEX Absolute error 4 Adams Bash–Moulton method 230 Approximate numbers 1 Argument 62 Backward interpolation formula Newton’s 104 Bessel’s formula 137 Bisection method 22 Boole’s rule 200, 201 Central difference formulae Table 134, 135 Characteristic equation 282 convergence of Newton’s method 44 rate of 45 Cotes number 197 Diagonal difference table 61 Difference(s), finite 60 first 60 second 60, 62 table 61, 62 Divided difference 116 properties 118 table 117 Double (of higher order) integration 205, 206 Differencing interval 60 Differentiation numerical 164 Differential equation 212 Eigen value(s) 282, 283 eigen vector(s) 282, 283 Everett’s formula 139 Even digit rule 3 Errors 3 absolute 5 error, limiting relative 5, 7 general formula 10 Factorial polynomial 76 Forward interpolation, Newton’s 98 Graphical solution 20 Gaussian interpolation formulae 134, 136 Gauss elimination method 250 Gauss–Jacobi’s method 253, 254 Gauss–Seidal method 256, 257 General error formula 10 Gaussain–Legendre quadrature formula 1180 321
322 NUMERICAL ANALYSIS Iteration method 25 Newton’s 33 Integration numerical 178 Inverse interpolation 151 Jacobi’s method 253, 254 Matrix inversion 248, 249 Milne’s method 224, 225 Newton binomial expansion formula 96 Newton–Cotes formula 195, 196, 197 Newton method 36 Newton–Raphson method 33 <strong>Numerical</strong> differentiation 164 Operator difference 60 backward 166 central difference 83 displacement (shift) 69 forward 60 Predictor corrector method 224-240 Picard method 242, 243 Regression analysis 300 Rounding off numbers 2 rule 2 Runge–Kutta method 233 Romberg integration 201-203 Separation of symbols 86 Significant digits 1 Simpson’s one-third rule 181, 182 three-eighths rule 182, 183, 184 Stirling’s formula 138 Taylor’s series 213, 214 Trapezoidal rule 180, 181 Weddle’s rule 184, 185
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Copyright © 2006, 2002 New Age Int
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(xii) 3.4 The operator D 73 3.5 Bac
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(xiv) 11.2 Gauss-Elimination method
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2 NUMERICAL ANALYSIS (i) lie betwee
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4 NUMERICAL ANALYSIS F HG involves
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6 NUMERICAL ANALYSIS X 1 − + −
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8 NUMERICAL ANALYSIS Rule 5 If a nu
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10 NUMERICAL ANALYSIS First two sig
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12 NUMERICAL ANALYSIS E R ∆X ∆x
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14 NUMERICAL ANALYSIS Example 1.13
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16 NUMERICAL ANALYSIS 9. If 5 6 be
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18 NUMERICAL ANALYSIS 12. (a) 1 (b)
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20 NUMERICAL ANALYSIS Theorem 2.1 I
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22 NUMERICAL ANALYSIS 2.3 METHOD OF
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24 NUMERICAL ANALYSIS In the 4th st
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26 NUMERICAL ANALYSIS Let x n - 1 a
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28 NUMERICAL ANALYSIS F ⇒ ⋅H G
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30 NUMERICAL ANALYSIS Similarly, x
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32 NUMERICAL ANALYSIS constructing
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34 NUMERICAL ANALYSIS The above val
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36 NUMERICAL ANALYSIS The second ap
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38 NUMERICAL ANALYSIS The second ap
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40 NUMERICAL ANALYSIS 2 3 x . x 03
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42 NUMERICAL ANALYSIS Example 2.16
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44 NUMERICAL ANALYSIS 1 N 3. From t
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46 NUMERICAL ANALYSIS Solution Expa
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48 NUMERICAL ANALYSIS and f ′′
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50 NUMERICAL ANALYSIS and h ∂g
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52 NUMERICAL ANALYSIS 2.7 REGULA-FA
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54 NUMERICAL ANALYSIS We take a = 2
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56 NUMERICAL ANALYSIS (x 1 , f(x 1
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FINITE DIFFERENCES 61 ∆ 2 is call
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FINITE DIFFERENCES 63 x f(x) x + h
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FINITE DIFFERENCES 65 (d) ∆ log x
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FINITE DIFFERENCES 67 Example 3.4 B
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FINITE DIFFERENCES 69 F = H G 2 aI
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FINITE DIFFERENCES 71 ⇒ b f x + h
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FINITE DIFFERENCES 73 Using the dis
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FINITE DIFFERENCES 75 In general we
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FINITE DIFFERENCES 77 Note: 1. ∆
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FINITE DIFFERENCES 79 2 3 3 3 Examp
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FINITE DIFFERENCES 81 Example 3.22
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FINITE DIFFERENCES 83 Example 3.24
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FINITE DIFFERENCES 85 Alternative n
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FINITE DIFFERENCES 87 L N M L N M 1
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FINITE DIFFERENCES 89 n n 2n 1 2n
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FINITE DIFFERENCES 91 bg d i 1 1
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FINITE DIFFERENCES 93 ∴ From (5),
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FINITE DIFFERENCES 95 µ (iii) 14.
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INTERPOLATION WITH EQUAL INTERVALS
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INTERPOLATION WITH UNEQUAL INTERVAL
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126 NUMERICAL ANALYSIS 2. Compute f
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128 NUMERICAL ANALYSIS By interchan
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130 NUMERICAL ANALYSIS bg b gb g b
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CENTRAL DIFFERENCE INTERPOLATION FO
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7 INVERSE INTERPOLATION 7.1 INTRODU
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INVERSE INTERPOLATION 153 where a 1
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INVERSE INTERPOLATION 155 ∴ Using
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INVERSE INTERPOLATION 157 Expressio
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INVERSE INTERPOLATION 159 (d) Stirl
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INVERSE INTERPOLATION 161 We have
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INVERSE INTERPOLATION 163 x 0.45 0.
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NUMERICAL DIFFERENTIATION 165 du dx
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NUMERICAL DIFFERENTIATION 167 Now u
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NUMERICAL DIFFERENTIATION 169 Examp
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NUMERICAL DIFFERENTIATION 171 Examp
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NUMERICAL DIFFERENTIATION 173 0.012
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NUMERICAL DIFFERENTIATION 175 3. Fi
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NUMERICAL DIFFERENTIATION 177 20. D
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NUMERICAL INTEGRATION 179 9.2 GENER
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NUMERICAL INTEGRATION 181 h h h h =
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NUMERICAL INTEGRATION 183 z bg L F
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NUMERICAL INTEGRATION 185 b g b ...
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NUMERICAL INTEGRATION 187 Using Tra
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NUMERICAL INTEGRATION 189 x 1.50 1.
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NUMERICAL INTEGRATION 191 π/ z2 2
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NUMERICAL INTEGRATION 193 6. Evalua
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NUMERICAL INTEGRATION 195 z 3 1 ux
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NUMERICAL INTEGRATION 197 Note: Rep
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NUMERICAL INTEGRATION 199 I z bg b
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NUMERICAL INTEGRATION 201 z bg x +
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NUMERICAL INTEGRATION 203 A 1 A 2 A
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NUMERICAL INTEGRATION 205 Exercise
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NUMERICAL INTEGRATION 207 Example 9
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NUMERICAL INTEGRATION 209 Putting x
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NUMERICAL INTEGRATION 211 z z1 2 2
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NUMERICAL SOLUTION OF ORDINARY DIFF
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SOLUTION OF LINEAR EQUATIONS 249 th
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SOLUTION OF LINEAR EQUATIONS 251 Th
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SOLUTION OF LINEAR EQUATIONS 253 11
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SOLUTION OF LINEAR EQUATIONS 255 pu
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SOLUTION OF LINEAR EQUATIONS 257 Ex
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SOLUTION OF LINEAR EQUATIONS 259 an
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SOLUTION OF LINEAR EQUATIONS 261 Fi
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SOLUTION OF LINEAR EQUATIONS 263
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SOLUTION OF LINEAR EQUATIONS 265 2x
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SOLUTION OF LINEAR EQUATIONS 267 2.
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CURVE FITTING 269 y Pr (x r , yr) e
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Page 288 and 289: CURVE FITTING 273 The normal equati
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Page 296 and 297: CURVE FITTING 281 18. Using the met
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Page 316 and 317: REGRESSION ANALYSIS 301 If the poin
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Page 332 and 333: REGRESSION ANALYSIS 317 form the li
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Numerical Analysis By Shanker Rao

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