POLLUTION: ENGINEERING AND SCIENTIFIC SOLUTIONS

By LINDA RODRIGUEZ

1 Fourier Analysis 1 11 Introduction 1 12 Fourier Series 4 121 Functions with the fundamental period T = 2? 4 122 Functions with the fundamental period T = 2? 38 13 Fourier Integral 51 14 Fourier Transform 57 2 Ordinary Differential Equations 67 21 Introduction 67 22 First-Order Differential Equations 72 23 Higher-Order Differential Equations 104 24 Systems of Differential Equations 133 3 Difference Equations 139 31 Introduction 139 32 First-Order Linear Difference Equations 143 33 Second-Order Linear Difference Equations 148 34 Special Sequences 169 35 Nonlinear and Higher-Order Linear Difference Equations 181 36 Generating Functions and z-Transforms 187 4 Laplace Transformation 203 41 Introduction 203 42 Properties of Laplace Transformation 204 43 Laplace Transformation 209 431 Transforms 209 432 Inverses 227 433 Convolution 233 44 Equations 238 441 Linear differential equations 238 442 Systems of linear differential equations 249 443 Integral equations 255 5 Vector Analysis 259 51 Introduction 259 52 Vector Functions, Curves, and Surfaces 265 53 Gradient, Divergence, and Curl 271 54 Line Integrals 288 55 Surface Integrals 298 56 Green’s Theorem 306 57 Divergence Theorem 310 58 Stokes’ Theorem 321 References 333