상세정보

CONTENTS
Preface = xi
1 Digital Computer Principles and FORTRAN IV = 1
 1.1 Introduction = 1
 1.2 Digital-Computer Components = 5
 1.3 Preparing a Digital-Computer Program = 7
 1.4 Large Computer Operating Systems = 9
 1.5 FORTRAN = 11
 1.6 The Elements of FORTRAN = 12
 1.7 Constants = 12
 1.8 Variables = 14
 1.9 Arrays = 15
 1.10 Subscripts = 16
 1.11 Arithmetic Expressions = 16
 1.12 Logical Expressions = 17
 1.13 Character Expressions (FORTRAN 77 ONLY) = 19
 1.14 FORTRAN-Supplied Mathematical Function Subprograms = 19
 1.15 FORTRAN Statements = 22
 1.16 Arithmetic-Assignment Statements = 23
 1.17 Logical-Assignment Statements = 24
 1.18 Control Statements = 24
 1.19 Input and Output Statements = 31
 1.20 Nonexecutable FORTRAN Statements = 36
 1.21 FORTRAN Statements = 36
 1.22 The DATA Initialization Statements = 52
 1.23 Specification Statements = 55
 1.24 Subprograms = 64
 1.25 The COMMON Statement = 74
 1.26 Adjustable (Object-Time) Dimensions = 78
 1.27 Subprogram Names as Arguments of Other Subprograms-the EXTERNAL and INTRINSIC Statements = 79
 1.28 The FORTRAN Source Program = 81
2 Roots of Algebraic and Transcendental Equations = 83
 2.1 Introduction = 83
 2.2 The Incremental-Search Method = 83
 2.3 The Bisection Method = 87
 2.4 The Method of False Position (Linear Interpolation) = 91
 2.5 The Secant Method = 93
 2.6 Newton-Raphson Method (Newton's Method of Tangents) = 94
 2.7 Newton's Second-Order Method = 105
 2.8 Roots of Polynomials = 108
 2.9 bairstow's Method = 111
 Problems = 127
3 Solution of Simultaneous Algebraic Equations = 146
 3.1 Introduction = 146
 3.2 Gauss's Elimination Method = 149
 3.3 Gauss-Jordan Elimination Method = 166
 3.4 Cholesky's Method = 178
 3.5 The Use of Error Equations = 185
 3.6 Matix-Inversion Method = 190
 3.7 Gauss-Seidel Method = 198
 3.8 Homogeneous Algebraic Equations-Eigenvalue Problems = 203
 3.9 Methods for Solution of Eigenvalue Problems-General = 214
 3.10 Polynomial Method-Eigenvalue Problems = 216
 3.11 Iteration Method-Eigenvalue Problems = 223
 3.12 Iteration for Intermediate Eigenvalues and Eigenvectors-Hotelling's Deflation Method = 228
 3.13 Jacobi's Simultaneous Equations = 274
 3.14 Nonlinear Simultaneous Equations = 274
 Problems = 277
4 Curve Fitting = 299
 4.1 Introduction = 299
 4.2 Method of Least-Squares = 300
 4.3 Matrix Formulation for Least-Squares Procedure for Linear Forms = 308
 4.4 Weighting for Least Squares Method = 313
 4.5 Curve Fitting Using Exponential Functions = 315
 4.6 Curve Fitting with Fourier Series = 329
 4.7 Computer Program Using Least-Squares Procedure for Linear Forms = 335
 4.8 Curve Fitting and Interpolation with a Cubic Spline = 339
 Problems = 384
5 Numerical Integration of Ordinary Differential Equations : Initial-Value Problems = 367
 5.1 Introduction = 367
 5.2 Integration by the Trapezoid Rule = 368
 5.3 Romberg Integration = 374
 5.4 Integration by Simpson's Rule = 377
 5.5 Improper integrals = 390
 5.6 Numerical Differentiation = 394
 Problems = 404
6 Numerical Integration of Ordinary Differential Equations : Initial-Value Problems = 416
 6.1 Introduction = 416
 6.2 Direct Numerical-Integration Method = 417
 6.3 Euler's Method (The Euler-Cauchy Method) = 419
 6.4 Modified Euler Methods = 430
 6.5 Runge-Kutta Methods = 461
 6.6 Solution of Simultaneous Ordinary Differential Equations by Runge-Kutta Methods = 461
 6.7 Milne's Method = 461
 6.8 Hmming's Method = 487
 6.9 Error in the Numerical Solutions of Differential Equations = 503
 6.10 Selecting a Numerical-Integration Method = 505
 Problems = 507
7 Ordinary Differential Equations : Boundary-Value Problems = 535
 7.1 Introduction = 535
 7.2 Trial-and-Error Method = 535
 7.3 Simultaneous-Equation Method = 549
 7.4 Eigenvalue Problems = 554
 Problems = 570
8 Introduction to Partial Differential Equations = 584
 8.1 Introduction = 584
 8.2 Elliptic Partial Differential Equations = 585
 8.3 Parabolic Partial Differential Equations = 599
 8.4 Hyperbolic Partial Differential Equations = 607
 Problems = 618
9 Introduction to Digital Computer Simulation Using CSMP (Continuous System Modeling Program) = 630
 9.1 Introduction = 630
 9.2 General Nature of a CSMP Program = 631
 9.3 CSMP Statements = 635
 9.4 Structure Statements = 635
 9.5 CSMP Functions = 637
 9.6 Data Statements = 645
 9.7 Model Structure = 648
 9.8 Control Statements = 649
 9.9 CSMP Examples-Run Control = 664
 9.10 FORTRAN Subprograms Used with CSMP Programs = 676
 Problems = 681
Appendixes
A International System of Units = 699
 A.1 Nomenclature of SI Units and Quantities = 699
 A.2 Conversion of U.S. Customary Units to SI Units = 700
 A.3 Prefixes = 700
B Matrix Algebra = 701
 B.1 Multiplication = 701
 B.2 Matrix Inversion = 703
 B.3 Transpose of a Matrix = 704
 B.4 Orthogonality Principle of Symmetric Matrices = 704
 B.5 Orthogonality Principle of the Form AX ＝ λBX = 705
 B.6 Proof of Convergence of the Method to the Largest Eigenvalue an Corresponding Eigenvector = 706
C Interpolating Polynomials and Application to Numerical Integration and Differentiation = 710
 C.1 Introduction to Interpolation = 710
 C.2 Definition = 712
 C.3 Polynomial Approximation and Interpolation = 719
 C.4 Other Interpolating Formulas = 728
 C.5 Inverse Interpolation = 732
 C.6 Application of Polynomial Approximation to the Derivation of Numerical Integration Formulas = 735
 C.7 Application of Polynomial Approximation to the Derivation of Numerical Differentiation Formulas = 740
Index = 743