《ANALOG AND DIGITAL COMPUTER METHODS IN ENGINEERING ANALYSIS》

1．BASIC ANALOG-COMPUTER THEORY1

1-1．Introduction1

1-2．Analog Versus Digital2

1-3．Basic Elements of the Analog Computer3

1-4．The Summing Amplifier4

1-5．The Use of Coefficient Potentiometers7

1-6．Potentiometer Calibration Corrections9

1-7．The Summing Integrator10

1-8．Symbolic Notation12

1-9．Operator Notation13

1-10．Magnitude Scaling14

1-11．A General Programming Procedure for Analog Simulation15

1-12．Compensating for Circuit Damping36

1-13．Time Scaling37

1-14．General Time-Scaling Proof43

1-15．Independent Variable Other than Time47

1-16．Solution of Simultaneous Differential Equations52

1-17．Approximate Differentiation on an Analog Computer62

1-18．Accuracy of Analog Computation63

Problems64

2．SIMULATION OF DISCONTINUOUS AND NONLINEAR PHYSICAL SYSTEMS71

2-1．Introduction71

2-2．Relays74

2-3．Diodes80

2-4．Arbitrary-Function Generators93

2-5．Function Multipliers96

2-6．Implicit Techniques of Function Generation112

Problems126

3．THE ROLE OF ANALOG COMPUTERS IN ENGINEERING ANALYSIS132

3-1．Introduction132

3-2．Analysis of a Rattrap133

3-3．Velocity Characteristics of a Paratrooper During Free Fall138

3-4．Dynamic Response of a Three-Story Building Subjected to an Earthquake145

3-5．Dynamic Response of a Thin Plate Subjected to a Blast Load153

3-6．Analysis of a Turbine Supply System162

3-7．Heat Dissipation in Space171

3-8．One-Dimensional Heat-Flow Analysis179

3-9．The Use of Dimensionless Equations in Analysis186

3-10．Real Roots of Polynomials191

Problems194

4．THE DIGITAL COMPUTER AND THE FORTRAN SYSTEM199

4-1．Introduction199

4-2．History of Digital Computers199

4-3．Digital-Computer Components201

4-4．Preparinga Digital-Computer Program203

4-5．Computer Sequence of Operations205

4-6．The FORTRAN System208

4-7．FORTRAN Statements211

4-8．The Elements of FORTRAN Language213

4-9．Constants213

4-10．Variables214

4-11．Subscripted Variables214

4-12．Operation Symbols215

4-13．Predefined Function Subroutines217

4-14．Arithmetic Statements218

4-15．Control Statements221

4-16．Input and Output Statements229

4-17．FORMAT Statements231

4-18．DIMENSION Statement236

Problems236

5．NUMERICAL METHODS FOR USE WITH THE DIGITAL COMPUTER241

5-1．Introduction241

5-2．Determining Real Roots of Algebraic and Transcendental Equations241

5-3．Solution of Simultaneous Linear Algebraic Equations262

5-4．Solution of Characteristic-Value Problems286

5-5．Numerical Integration and Differentiation303

5-6．Numerical Integration of Ordinary Differential Equations;Initial-Value Problems333

5-7．Numerical Solution of Ordinary Differential Equations;Boundary-Value Problems384

5-8．Numerical Methods for the Solution of Partial Differential Equations398

Problems432

INDEX453