Accessible to non-mathematics professionals as well as college seniors and graduates, this text examines linear and nonlinear transformations; nonlinear algebraic and transcendental equations; nonlinear optimization; nonlinear programming and systems of inequalities; nonlinear ordinary differential euqations and much more. Exercises included. 1964 edition.

Contenuti

Preface 1. Linear and Nonlinear Transformations 1.1 Introduction 1.2 Vector Spaces; Linear Transformations 1.3 Eigenvalues; Eigenvectors 1.4 Inner-product Spaces 1.5 Self-adjoint Transformations 1.6 The Infinite-dimensional Case 1.7 Operators 1.8 Applications 1.9 Banach Spaces and Linear Functionals 1.10 Fixed-point Theorems and Applications 1.11 Lebesgue Integration, a Survey 2. Nonlinear Algebraic and Transcendental Equations 2.1 Introduction 2.2 The Newton-Raphson Method 2.3 The Method of Steepest Descent 2.4 Saddle-point Method or Steepest-descent Method of Complex Integration 3. Nonlinear Optimization; Nonlinear Programming and Systems of Inequalities 3.1 Introduction 3.2 Maxima, Minima, Quadratic Forms, and Convex Functions 3.3 Nonlinear Programming 3.4 Linear Programming 3.5 Characterization of the Optimum on the Boundary; Saddle Points; Duality 3.6 Construction of Solutions 3.7 Optimization Problems with Infinitely Many Constraints 4. Nonlinear Ordinary Differential Equations 4.1 Introduction 4.2 Some Nonlinear Equations 4.3 Existence and Uniqueness for First-order Systems 4.4 Linear Equations--Oscillatory Motion, Stability 4.5 Nonlinear Equations--Perturbation Method 4.6 Phase-plane Analysis--Stability Behavior in the Small (Systems of Two Equations) 4.7 Limit Cycles--Stability Behavior in the Large (Systems of Two Equations) 4.8 Topological Considerations: Indices and the Existence of Limit Cycles (Systems of Two Equations) 4.9 Periodic Solutions of Systems with Periodic Coefficients 4.10 Periodic Solutions of Nonlinear Systems with Periodic Coefficients 4.11 Lyapunov Stability 4.12 General Methods of Solution 5. Introduction to Automatic Control and the Pontryagin Principle 5.1 Introduction 5.2 Stability and a Class of Control Equations 5.3 Pontryagin's Maximum Principle 5.4 Functional Analysis and Optimum Control 6. Linear and Nonlinear Prediction Theory 6.1 Introduction 6.2 The Discrete Stationary Case 6.3 Construction of the Discrete-case Estimate 6.4 The Discrete Prediction Problem 6.5 The Prediction Error 6.6 The Special Case of Rational Densities 6.7 The Continuous Stationary Case 6.8 Construction of the Continuous-case Estimate 6.9 The Continuous Prediction Problem 6.10 Examples 6.11 Conditional Expectation 6.12 The General Estimation Problem 6.13 Polynomial Estimation 6.14 The Karhunen-Loeve Expansion 6.15 Dynamical Systems with Control Variables Appendix; Index

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