Foundations of Mathematical and Computational Economics 2nd edition

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Fundations of Mathematical and Computational Economics [Second Edition]
内容涵盖了数理经济基础和数值方法 从理论到应用 非常全面！还附有excel matlab maple操作！！

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目录如下：
Part I Basic Concepts and Methods
1 Mathematics, Computation, and Economics . . . . . . . . . . . . 3
2 Basic Mathematical Concepts and Methods . . . . . . . . . . . . . 17
3 Basic Concepts of Computation . . . . . . . . . . . . . . . . . . . 57
4 Basic Concepts and Methods of Probability Theory and Statistics 69
Part II Linear Algebra
5 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6 Matrices and Matrix Algebra . . . . . . . . . . . . . . . . . . . . 113
7 Advanced Topics in Matrix Algebra . . . . . . . . . . . . . . . . . 143
Part III Calculus
8 Differentiation: Functions of One Variable . . . . . . . . . . . . . 189
9 Differentiation: Functions of Several Variables . . . . . . . . . . . 227
10 The Taylor Series and Its Applications . . . . . . . . . . . . . . . 257
11 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

Part IV Optimization
12 Static Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 323
12.1 Maxima and Minima of Functions of One Variable . . . . . . 324
12.1.1 Inflection Point . . . . . . . . . . . . . . . . . . . . . 331
12.1.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 333
12.2 Unconstrained Optima of Functions of Several Variables . . . 334
12.2.1 Convex and Concave Functions . . . . . . . . . . . . 338
12.2.2 Quasi-convex and Quasi-concave Functions . . . . . 341
12.2.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 342
12.3 NumericalOptimization . . . . . . . . . . . . . . . . . . . . . 343
12.3.1 Steepest Descent . . . . . . . . . . . . . . . . . . . . 343
12.3.2 GoldenSectionMethod . . . . . . . . . . . . . . . . 344
12.3.3 NewtonMethod . . . . . . . . . . . . . . . . . . . . 344
xiv Contents
12.3.4 Matlab Functions . . . . . . . . . . . . . . . . . . . 345
12.3.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 346
13 Constrained Optimization . . . . . . . . . . . . . . . . . . . . . . 347
13.1 Optimization with Equality Constraints . . . . . . . . . . . . 347
13.1.1 The Nature of Constrained Optima
and the Significance of λ . . . . . . . . . . . . . . . . 354
13.1.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 354
13.2 Value Function . . . . . . . . . . . . . . . . . . . . . . . . . 355
13.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 362
13.3 Second-Order Conditions and Comparative Static . . . . . . . 362
13.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 368
13.4 Inequality Constraints and Karush-Kuhn-Tucker Conditions . . 368
13.4.1 Duality . . . . . . . . . . . . . . . . . . . . . . . . . 372
13.4.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 375
14 Dynamic Optimization . . . . . . . . . . . . . . . . . . . . . . . . 377
14.1 Dynamic Analysis in Economics . . . . . . . . . . . . . . . . 377
14.2 TheControlProblem . . . . . . . . . . . . . . . . . . . . . . 379
14.2.1 The Functional and Its Derivative . . . . . . . . . . . 381
14.3 Calculus ofVariations . . . . . . . . . . . . . . . . . . . . . . 384
14.3.1 TheEulerEquation . . . . . . . . . . . . . . . . . . 386
14.3.2 Second-Order Conditions . . . . . . . . . . . . . . . 389
14.3.3 Generalizing the Calculus of Variations . . . . . . . . 390
14.3.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 391
14.4 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . 391
14.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 396
14.5 TheMaximumPrinciple . . . . . . . . . . . . . . . . . . . . 397
14.5.1 Necessary andSufficientConditions . . . . . . . . . 405
14.5.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 405
Part V Differential and Difference Equations
15 Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . 409
15.1 Examples of Continuous Time Dynamic Economic Models . . 409
15.2 AnOverview . . . . . . . . . . . . . . . . . . . . . . . . . . 412
15.2.1 Initial Value Problem . . . . . . . . . . . . . . . . . 414
15.2.2 Existence and Uniqueness of Solutions . . . . . . . . 416
15.2.3 Equilibrium and Stability . . . . . . . . . . . . . . . 417
15.3 First-Order Linear Differential Equations . . . . . . . . . . . . 418
15.3.1 VariableCoefficientEquations . . . . . . . . . . . . 420
15.3.2 Particular Integral, the Method
of Undetermined Coefficients . . . . . . . . . . . . . 421
15.3.3 Separable Equations . . . . . . . . . . . . . . . . . . 424
15.3.4 Exact Differential Equations . . . . . . . . . . . . . . 426
15.3.5 IntegratingFactor . . . . . . . . . . . . . . . . . . . 430
15.3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 433
Contents xv
15.4 Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . 433
15.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 436
15.5 Second-Order Linear Differential Equations . . . . . . . . . . 436
15.5.1 TwoDistinctRealRoots . . . . . . . . . . . . . . . . 437
15.5.2 Repeated Root . . . . . . . . . . . . . . . . . . . . . 439
15.5.3 ComplexRoots . . . . . . . . . . . . . . . . . . . . . 442
15.5.4 Particular Integral . . . . . . . . . . . . . . . . . . . 443
15.5.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 446
15.6 ComputerSolution ofDifferentialEquations . . . . . . . . . . 447
15.7 NumericalAnalysis ofDifferentialEquations . . . . . . . . . 448
15.7.1 TheEulerMethod . . . . . . . . . . . . . . . . . . . 448
15.7.2 Runge-Kutta Methods . . . . . . . . . . . . . . . . . 450
15.7.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 452
16 Difference Equations . . . . . . . . . . . . . . . . . . . . . . . . . 453
17 Dynamic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

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