About the Author |
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xi | |
Introduction |
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xv | |
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Chapter 1 Introduction to MATLAB |
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1 | (10) |
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1.1 Numerical Calculations with MATLAB |
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1 | (2) |
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1.2 Symbolic Calculations with MATLAB |
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3 | (2) |
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5 | (1) |
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1.4 General Notation. The Command Window |
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5 | (3) |
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1.5 MATLAB and Programming |
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8 | (1) |
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1.6 Translating C, FORTRAN and TEX expressions |
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9 | (2) |
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Chapter 2 Integers, Divisibility and Number Systems |
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11 | (32) |
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2.1 Arithmetic Operations in MATLAB |
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11 | (5) |
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16 | (1) |
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17 | (11) |
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28 | (4) |
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2.5 Divisibility in Z[ √n] |
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32 | (3) |
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2.6 Diophantine Equations |
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35 | (1) |
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36 | (7) |
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Chapter 3 Real and Complex Numbers |
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43 | (52) |
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43 | (8) |
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51 | (4) |
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55 | (7) |
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62 | (1) |
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63 | (1) |
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3.6 Common Functions with Real Arguments |
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63 | (3) |
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66 | (1) |
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3.8 Common Functions with Complex Arguments |
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66 | (13) |
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3.9 Divisibility in the Complex Field. The Ring of Gaussian Integers |
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79 | (6) |
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3.10 Approximation and Precision |
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85 | (4) |
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3.11 Types of Numbers and Expressions |
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89 | (3) |
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92 | (3) |
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Chapter 4 Numerical Variables, Vectors and Matrices |
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95 | (44) |
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95 | (3) |
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4.2 Variables and Special Constants |
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98 | (2) |
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4.3 Symbolic and Numeric Variables |
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100 | (5) |
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105 | (5) |
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110 | (9) |
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119 | (3) |
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122 | (4) |
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4.7.1 Arithmetic Operators |
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122 | (3) |
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4.7.2 Relational Operators |
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125 | (1) |
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126 | (1) |
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126 | (3) |
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4.9 Elementary Functions that Support Complex Matrix Arguments |
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129 | (4) |
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4.10 Elementary Functions that Support Complex Vector Arguments |
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133 | (3) |
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4.11 Vector Functions of Several Variables |
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136 | (1) |
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4.12 Functions of One Variable |
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137 | (2) |
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Chapter 5 Vectors and Matrices |
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139 | (40) |
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139 | (1) |
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5.2 Operations with Numeric Matrices |
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140 | (10) |
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5.3 Eigenvalues and Eigenvectors |
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150 | (6) |
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156 | (13) |
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5.5 Similar Matrices and Diagonalization |
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169 | (2) |
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171 | (2) |
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173 | (6) |
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179 | (32) |
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6.1 Custom Defined Functions |
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179 | (1) |
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6.2 Functions and M-files |
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179 | (4) |
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6.3 Functions and Flow Control. Loops |
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183 | (1) |
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183 | (2) |
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185 | (1) |
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6.6 IF ELSEIF ELSE END LOOP |
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186 | (1) |
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187 | (3) |
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6.8 Conditional Functions |
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190 | (3) |
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6.9 Defining Functions Directly. Evaluating Functions |
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193 | (1) |
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6.10 Functions of One Variable |
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193 | (1) |
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6.11 Functions of Several Variables |
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194 | (4) |
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198 | (6) |
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6.13 Functional Operations |
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204 | (7) |
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Chapter 7 Programming and Numerical Analysis |
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211 | (68) |
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7.1 MATLAB and Programming |
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211 | (1) |
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211 | (3) |
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214 | (3) |
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7.4 Functions and M-files. Eval and feval |
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217 | (3) |
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7.4.1 A Simple Function Definition |
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122 | (98) |
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7.5 Local and Global Variables |
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220 | (2) |
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222 | (1) |
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7.7 Flow Control: FOR, WHILE and IF ELSEIF Loops |
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223 | (1) |
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223 | (1) |
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224 | (1) |
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7.10 IF ELSEIF ELSE END Loops |
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225 | (2) |
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227 | (1) |
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228 | (1) |
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229 | (1) |
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230 | (1) |
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230 | (1) |
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231 | (1) |
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232 | (1) |
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7.18 Functions relating to Arrays of Cells |
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233 | (3) |
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7.19 Functions of Multidimensional Arrays |
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236 | (4) |
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7.20 Numerical Analysis Methods in MATLAB |
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240 | (1) |
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7.21 Zeros of Functions and Optimization |
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240 | (3) |
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7.22 Numerical Integration |
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243 | (1) |
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7.23 Numerical Differentiation |
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244 | (2) |
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7.24 Approximate Solutions of Differential Equations |
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246 | (1) |
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7.25 Ordinary Differential Equations with Initial Values |
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246 | (3) |
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7.26 Ordinary Differential Equations with Boundary Conditions |
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249 | (3) |
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7.27 Partial Differential Equations |
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252 | (27) |
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Chapter 8 Numerical Algorithms: Equations, Derivatives, Integrals and Differential Equations |
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279 | |
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8.1 Solving Non-Linear Equations |
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279 | (5) |
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8.1.1 The fixed Point Method for Solving x = g(x) |
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279 | (3) |
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8.1.2 Newton's Method for Solving the Equation f(x) = 0 |
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282 | (2) |
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8.1.3 Schroder's Method for Solving the Equation f(x)=0 |
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284 | (1) |
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8.2 Systems of Non-Linear Equations |
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284 | (4) |
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284 | (1) |
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8.2.2 The Newton-Raphson Method |
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285 | (3) |
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8.3 Interpolation Methods |
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288 | (3) |
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8.3.1 Lagrange Polynomial Interpolation |
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288 | (2) |
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8.3.2 Newton Polynomial Interpolation |
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290 | (1) |
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8.4 Numerical Derivation Methods |
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291 | (6) |
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8.4.1 Numerical Derivation via Limits |
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291 | (3) |
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8.4.2 Richardson's Extrapolation Method |
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294 | (1) |
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8.4.3 Derivation Using Interpolation (n + 1 Nodes) |
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295 | (2) |
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8.5 Numerical Integration Methods |
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297 | (5) |
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8.5.1 The Trapezium Method |
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297 | (3) |
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300 | (2) |
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8.6 Ordinary Differential Equations |
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302 | |
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302 | (1) |
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303 | (1) |
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8.6.3 The Taylor Series Method |
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304 | |