Applied Artificial Neural Network Methods for Engineers and Scientists: Solving Algebraic Equations

Half Title Page
Title Page
Copyright Page
Contents
Preface
Acknowledgments
Chapter 1: ANN Preliminaries
	1.1 Introduction
	1.2 ANN Architectures
	1.3 Learning Rules
		1.3.1 Backpropagation Algorithm or Delta Learning Rule
	1.4 Activation Function (or Transfer Function)
		1.4.1 Sigmoid function
		1.4.2 Tanh function
	1.5 Conclusion
Chapter 2: Mathematical Preliminaries
	2.1 Introduction
	2.2 Polynomial Equations
	2.3 Transcendental Equations
	2.4 Diophantine Equations
	2.5 Linear System of Equations (LSEs)
	2.6 Systems of Nonlinear Equations
	2.7 Eigenvalue Problems
	2.8 Nonlinear Eigenvalue Problem (NEP)
Chapter 3: Polynomial Equations with application in solving Bakery problem
	3.1 Introduction
	3.2 General model of a polynomial equation
		3.2.1 ANN procedure for solving polynomial equation
	3.3 Numerical Examples
	3.4 Bakery Problem
	3.5 Conclusion
Chapter 4: Transcendental equations in power electronics applications
	4.1 Introduction
	4.2 General model of a transcendental equation
	4.3 Numerical Examples
	4.4 Application Problem
	4.5 Conclusion
Chapter 5: Diophantine Equations in Pole placement
	5.1 Introduction
	5.2 General model of a Diophantine Equation
		5.2.1 ANN Procedure for solving Diophantine equation
	5.3 Numerical Examples
	5.4 Application Problem
	5.5 Conclusion
Chapter 6: Systems of Linear Equations with application in static structural problems
	6.1 Introduction
	6.2 ANN-based methodology
	6.3 Numerical Examples
	6.4 Static Structural Problem
	6.5 Conclusion
Chapter 7: Systems of Nonlinear Equations in Electrical Network Analysis
	7.1 Introduction
	7.2 Numerical Examples
	7.3 Application Problem
	7.4 Conclusion
Chapter 8: Eigenvalue Problems with application in structural dynamics
	8.1 Introduction
	8.2 ANN model for solving eigenvalue problems
	8.3 Numerical Examples
	8.4 Application Problem
		8.4.1 Spring mass system
		8.4.2 Multi-storey shear structure
	8.5 Conclusion
Chapter 9: Nonlinear Eigenvalue Problems with application in structural dynamics
	9.1 Introduction
	9.2 Nonlinear Eigenvalue Problem (NEP)
	9.3 Numerical Example
	9.4 Application Problem
	9.5 Conclusion
Chapter 10: Definite Integrals in the fluid force on a vertical surface
	10.1 Introduction
	10.2 Preliminaries
	10.3 ChNN Methodology
	10.4 Numerical Examples
	10.5 Application Problem
	10.6 Conclusion
Chapter 11: Inverse Problems in structural dynamics
	11.1 Introduction
	11.2 Numerical Examples
	11.3 Conclusion