{"product_id":"introduction-to-dynamic-systems-isbn-9780471025948","title":"Introduction to Dynamic Systems","description":"Integrates the traditional approach to differential equations with the modern systems and control theoretic approach to dynamic systems, emphasizing theoretical principles and classic models in a wide variety of areas. Provides a particularly comprehensive theoretical development that includes chapters on positive dynamic systems and optimal control theory. Contains numerous problems. \u003cp\u003e\u003cb\u003e1 Introduction\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Dynamic Phenomena 1\u003c\/p\u003e \u003cp\u003e1.2 Multivariable Systems 2\u003c\/p\u003e \u003cp\u003e1.3 A Catalog of Examples 4\u003c\/p\u003e \u003cp\u003e1.4 The Stages of Dynamic System Analysis 10\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Difference And Differential Equations\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Difference Equations 14\u003c\/p\u003e \u003cp\u003e2.2 Existence and Uniqueness of Solutions 17\u003c\/p\u003e \u003cp\u003e2.3 A First-Order Equation 19\u003c\/p\u003e \u003cp\u003e2.4 Chain Letters and Amortization 21\u003c\/p\u003e \u003cp\u003e2.5 The Cobweb Model 23\u003c\/p\u003e \u003cp\u003e2.6 Linear Difference Equations 26\u003c\/p\u003e \u003cp\u003e2.7 Linear Equations with Constant Coefficients 32\u003c\/p\u003e \u003cp\u003e2.8 Differential Equations 38\u003c\/p\u003e \u003cp\u003e2.9 Linear Differential Equations 40\u003c\/p\u003e \u003cp\u003e2.10 Harmonic Motion and Beats 44\u003c\/p\u003e \u003cp\u003e2.11 Problems 47\u003cbr\u003e\u003cbr\u003e Notes and References 54\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Linear Algebra\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAlgebraic Properties\u003c\/p\u003e \u003cp\u003e3.1 Fundamentals 56\u003c\/p\u003e \u003cp\u003e3.2 Determinants 62\u003c\/p\u003e \u003cp\u003e3.3 Inverses and the Fundamental Lemma 66\u003c\/p\u003e \u003cp\u003eGeometric Properties\u003c\/p\u003e \u003cp\u003e3.4 Vector Space 69\u003c\/p\u003e \u003cp\u003e3.5 Transformations 73\u003c\/p\u003e \u003cp\u003e3.6 Eigenvectors 77\u003c\/p\u003e \u003cp\u003e3.7 Distinct Eigenvalues 80\u003c\/p\u003e \u003cp\u003e3.8 Right and Left Eigenvectors 83\u003c\/p\u003e \u003cp\u003e3.9 Multiple Eigenvalues 84\u003c\/p\u003e \u003cp\u003e3.10 Problems 86\u003c\/p\u003e \u003cp\u003eNotes and References 89\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Linear State Equations\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Systems Of First-Order Equations 90\u003c\/p\u003e \u003cp\u003e4.2 Conversion to State Form 95\u003c\/p\u003e \u003cp\u003e4.3 Dynamic Diagrams 97\u003c\/p\u003e \u003cp\u003e4.4 Homogeneous Discrete-Time Systems 99\u003c\/p\u003e \u003cp\u003e4.5 General Solution to Linear Discrete-Time Systems 108\u003c\/p\u003e \u003cp\u003e4.6 Homogeneous Continuous-Time Systems 113\u003c\/p\u003e \u003cp\u003e4.7 General Solution to Linear Continuous-Time Systems 118\u003c\/p\u003e \u003cp\u003e4.8 Embedded Statics 121\u003c\/p\u003e \u003cp\u003e4.9 Problems 124\u003c\/p\u003e \u003cp\u003eNotes and References 130\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Linear Systems With Constant Coefficients\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Geometric Sequences and Exponentials 133\u003c\/p\u003e \u003cp\u003e5.2 System Eigenvectors 135\u003c\/p\u003e \u003cp\u003e5.3 Diagonalization of a System 136\u003c\/p\u003e \u003cp\u003e5.4 Dynamics of Right and Left Eigenvectors 142\u003c\/p\u003e \u003cp\u003e5.5 Example: A Simple Migration Model 144\u003c\/p\u003e \u003cp\u003e5.6 Multiple Eigenvalues 148\u003c\/p\u003e \u003cp\u003e5.7 Equilibrium Points 150\u003c\/p\u003e \u003cp\u003e5.8 Example: Survival Theory in Culture 152\u003c\/p\u003e \u003cp\u003e5.9 Stability 154\u003c\/p\u003e \u003cp\u003e5.10 Oscillations 160\u003c\/p\u003e \u003cp\u003e5.11 Dominant Modes 165\u003c\/p\u003e \u003cp\u003e5.12 The Cohort Population Model 170\u003c\/p\u003e \u003cp\u003e5.13 The Surprising Solution to the Natchez Problem 174\u003c\/p\u003e \u003cp\u003e5.14 Problems 179\u003c\/p\u003e \u003cp\u003eNotes and References 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Positive Linear Systems\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 188\u003c\/p\u003e \u003cp\u003e6.2 Positive Matrices 190\u003c\/p\u003e \u003cp\u003e6.3 Positive Discrete-Time Systems 195\u003c\/p\u003e \u003cp\u003e6.4 Quality in a Hierarchy-The Peter Principle 199\u003c\/p\u003e \u003cp\u003e6.5 Continuous-Time Positive Systems 204\u003c\/p\u003e \u003cp\u003e6.6 Richardson's Theory of Arms Races 206\u003c\/p\u003e \u003cp\u003e6.7 Comparative Statics for Positive Systems 211\u003c\/p\u003e \u003cp\u003e6.8 Homans-Simon Model of Group Interaction 215\u003c\/p\u003e \u003cp\u003e6.9 Problems 217\u003c\/p\u003e \u003cp\u003eNotes and References 222\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Markov Chains\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Finite Markov Chains 225\u003c\/p\u003e \u003cp\u003e7.2 Regular Markov Chains and Limiting Distributions 230\u003c\/p\u003e \u003cp\u003e7.3 Classification of States 235\u003c\/p\u003e \u003cp\u003e7.4 Transient State Analysis 239\u003c\/p\u003e \u003cp\u003e7.5 Infinite Markov Chains 245\u003c\/p\u003e \u003cp\u003e7.6 Problems 248\u003c\/p\u003e \u003cp\u003eNotes and References 253\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Concepts Of Control\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Inputs, Outputs, and Interconnections 254\u003c\/p\u003e \u003cp\u003eTransform Methods\u003c\/p\u003e \u003cp\u003e8.2 z-Transforms 255\u003c\/p\u003e \u003cp\u003e8.3 Transform Solution of Difference Equations 261\u003c\/p\u003e \u003cp\u003e8.4 State Equations and Transforms 266\u003c\/p\u003e \u003cp\u003e8.5 Laplace Transforms 272\u003c\/p\u003e \u003cp\u003eState Space Methods\u003c\/p\u003e \u003cp\u003e8.6 Controllability 276\u003c\/p\u003e \u003cp\u003e8.7 Observability 285\u003c\/p\u003e \u003cp\u003e8.8 Canonical Forms 289\u003c\/p\u003e \u003cp\u003e8.9 Feedback 296\u003c\/p\u003e \u003cp\u003e8.10 Observers 300\u003c\/p\u003e \u003cp\u003e8.11 Problems 309\u003c\/p\u003e \u003cp\u003eNotes and References 314\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Analysis Of Nonlinear Systems\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 316\u003c\/p\u003e \u003cp\u003e9.2 Equilibrium Points 320\u003c\/p\u003e \u003cp\u003e9.3 Stability 322\u003c\/p\u003e \u003cp\u003e9.4 Linearization and Stability 324\u003c\/p\u003e \u003cp\u003e9.5 Example: The Principle of Competitive Exclusion 328\u003c\/p\u003e \u003cp\u003e9.6 Liapunov Functions 332\u003c\/p\u003e \u003cp\u003e9.7 Examples 339\u003c\/p\u003e \u003cp\u003e9.8 Invariant Sets 345\u003c\/p\u003e \u003cp\u003e9.9 A Linear Liapunov Function for Positive Systems 347\u003c\/p\u003e \u003cp\u003e9.10 An Integral Liapunov Function 349\u003c\/p\u003e \u003cp\u003e9.11 A Quadratic Liapunov Function for Linear Systems 350\u003c\/p\u003e \u003cp\u003e9.12 Combined Liapunov Functions 353\u003c\/p\u003e \u003cp\u003e9.13 General Summarizing Functions 354\u003c\/p\u003e \u003cp\u003e9.14 Problems 356\u003c\/p\u003e \u003cp\u003eNotes and References 363\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Some Important Dynamic Systems\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Energy in Mechanics 365\u003c\/p\u003e \u003cp\u003e10.2 Entropy in Thermodynamics 367\u003c\/p\u003e \u003cp\u003e10.3 Interacting Populations 370\u003c\/p\u003e \u003cp\u003e10.4 Epidemics 376\u003c\/p\u003e \u003cp\u003e10.5 Stability of Competitive Economic Equilibria 378\u003c\/p\u003e \u003cp\u003e10.6 Genetics 382\u003c\/p\u003e \u003cp\u003e10.7 Problems 389\u003c\/p\u003e \u003cp\u003eNotes and References 391\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Optimal Control\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Basic Optimal Control Problem 394\u003c\/p\u003e \u003cp\u003e11.2 Examples 401\u003c\/p\u003e \u003cp\u003e11.3 Problems with Terminal Constraints 405\u003c\/p\u003e \u003cp\u003e11.4 Free Terminal Time Problems 409\u003c\/p\u003e \u003cp\u003e11.5 Linear Systems with Quadratic Cost 413\u003c\/p\u003e \u003cp\u003e11.6 Discrete-Time Problems 416\u003c\/p\u003e \u003cp\u003e11.7 Dynamic Programming 419\u003c\/p\u003e \u003cp\u003e11.8 Stability and Optimal Control 425\u003c\/p\u003e \u003cp\u003e11.9 Problems 427\u003c\/p\u003e \u003cp\u003eNotes and References 435\u003c\/p\u003e \u003cp\u003eReferences 436\u003c\/p\u003e \u003cp\u003eIndex 441\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003eDAVID G. LUENBERGER\u003c\/strong\u003e is a professor in the School of Engineering at Stanford University. He has published four textbooks and over 70 technical papers. Professor Luenberger is a Fellow of the Institute of Electrical and Electronics Engineers and recipient of the 1990 Bode Lecture Award. His current research is mainly in investment science, economics, and planning.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989458632933,"sku":"NP9780471025948","price":219.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471025948.jpg?v=1761784182","url":"https:\/\/k12savings.com\/es\/products\/introduction-to-dynamic-systems-isbn-9780471025948","provider":"K12savings","version":"1.0","type":"link"}