LEADER 05788nam 2200793Ia 450 001 9911006511103321 005 20250416202448.0 010 $a9781523111268$b(electronic bk.) 010 $a1523111267 010 $a9781118343029 010 $a1118343026 010 $a9781283646093 010 $a1283646099 010 $a9781118343012 010 $a1118343018 035 $a(CKB)2670000000262608 035 $a(EBL)918264 035 $a(OCoLC)814705691 035 $a(SSID)ssj0000754604 035 $a(PQKBManifestationID)11496229 035 $a(PQKBTitleCode)TC0000754604 035 $a(PQKBWorkID)10726152 035 $a(PQKB)10323833 035 $a(MiAaPQ)EBC918264 035 $a(DLC) 2012046455 035 $a(EXLCZ)992670000000262608 100 $a19940628d2012 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApplied mathematics and modeling for chemical engineers /$fRichard G. Rice, Duong D. Do 205 $a2nd ed. 210 $aHoboken, New Jersey $cWiley$d2012 215 $a1 online resource (397 p.) 225 0 $aWiley series in chemical engineering 300 $aDescription based upon print version of record. 311 1 $a9781118024729 311 1 $a9781118024720 311 1 $a1118024729 320 $aIncludes bibliographical references and index. 327 $aAPPLIED MATHEMATICS AND MODELING FOR CHEMICAL ENGINEERS; Contents; Preface to the Second Edition; PART I; 1 Formulation of Physicochemical Problems; 1.1 Introduction; 1.2 Illustration of the Formulation Process (Cooling of Fluids); 1.2.1 Model I: Plug Flow; 1.2.2 Model II: Parabolic Velocity; 1.3 Combining Rate and Equilibrium Concepts (Packed Bed Adsorber); 1.4 Boundary Conditions and Sign Conventions; 1.5 Models with Many Variables: Vectors and Matrices; 1.6 Matrix Definition; 1.6.1 The Matrix; 1.6.2 The Vector; 1.7 Types of Matrices; 1.7.1 Square Matrix; 1.7.2 Diagonal Matrix 327 $a1.7.3 Triangular Matrix1.7.4 Tridiagonal Matrix; 1.7.5 Symmetric Matrix; 1.7.6 Sparse Matrix; 1.7.7 Diagonally Dominant Matrix; 1.8 Matrix Algebra; 1.8.1 Addition and Subtraction; 1.8.2 Multiplication; 1.8.3 Inverse; 1.8.4 Matrix Decomposition or Factorization; 1.9 Useful Row Operations; 1.9.1 Scaling; 1.9.2 Pivoting; 1.9.3 Elimination; 1.10 Direct Elimination Methods; 1.10.1 Basic Procedure; 1.10.2 Augmented Matrix; 1.10.3 Pivoting; 1.10.4 Scaling; 1.10.5 Gauss Elimination; 1.10.6 Gauss-Jordan Elimination: Solving Linear Equations; 1.10.7 LU Decomposition; 1.11 Iterative Methods 327 $a1.11.1 Jacobi Method1.11.2 Gauss-Seidel Iteration Method; 1.11.3 Successive Overrelaxation Method; 1.12 Summary of the Model Building Process; 1.13 Model Hierarchy and its Importance in Analysis; Problems; References; 2 Solution Techniques for Models Yielding Ordinary Differential Equations; 2.1 Geometric Basis and Functionality; 2.2 Classification of ODE; 2.3 First-Order Equations; 2.3.1 Exact Solutions; 2.3.2 Equations Composed of Homogeneous Functions; 2.3.3 Bernoulli's Equation; 2.3.4 Riccati's Equation; 2.3.5 Linear Coefficients; 2.3.6 First-Order Equations of Second Degree 327 $a2.4 Solution Methods for Second-Order Nonlinear Equations2.4.1 Derivative Substitution Method; 2.4.2 Homogeneous Function Method; 2.5 Linear Equations of Higher Order; 2.5.1 Second-Order Unforced Equations: Complementary Solutions; 2.5.2 Particular Solution Methods for Forced Equations; 2.5.3 Summary of Particular Solution Methods; 2.6 Coupled Simultaneous ODE; 2.7 Eigenproblems; 2.8 Coupled Linear Differential Equations; 2.9 Summary of Solution Methods for ODE; Problems; References; 3 Series Solution Methods and Special Functions; 3.1 Introduction to Series Methods 327 $a3.2 Properties of Infinite Series3.3 Method of Frobenius; 3.3.1 Indicial Equation and Recurrence Relation; 3.4 Summary of the Frobenius Method; 3.5 Special Functions; 3.5.1 Bessel's Equation; 3.5.2 Modified Bessel's Equation; 3.5.3 Generalized Bessel's Equation; 3.5.4 Properties of Bessel Functions; 3.5.5 Differential, Integral, and Recurrence Relations; Problems; References; 4 Integral Functions; 4.1 Introduction; 4.2 The Error Function; 4.2.1 Properties of Error Function; 4.3 The Gamma and Beta Functions; 4.3.1 The Gamma Function; 4.3.2 The Beta Function; 4.4 The Elliptic Integrals 327 $a4.5 The Exponential and Trigonometric Integrals 330 $aThis Second Edition of the go-to reference combines the classical analysis and modern applications of applied mathematics for chemical engineers. The book introduces traditional techniques for solving ordinary differential equations (ODEs), adding new material on approximate solution methods such as perturbation techniques and elementary numerical solutions. It also includes analytical methods to deal with important classes of finite-difference equations. The last half discusses numerical solution techniques and partial differential equations (PDEs). The reader will then be equipped to 606 $aDifferential equations 606 $aChemical processes$xMathematical models 606 $aChemical engineering$xMathematics 615 0$aDifferential equations. 615 0$aChemical processes$xMathematical models. 615 0$aChemical engineering$xMathematics. 676 $a660.01519 676 $a660.284015118 676 $a660/.284/015118 686 $a501.1$2njb/09 686 $a660/.284015118$2njb/09 701 $aDo$b Duong D$0771589 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 801 2$bOKU 906 $aBOOK 912 $a9911006511103321 996 $aApplied mathematics and modeling for chemical engineers$94390316 997 $aUNINA