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Foundations of Mathematical And Computational Economics

by: Dadkhah, Kamran M.

Foundations of Mathematical And Computational Economics

by: Dadkhah, Kamran M.

ISBN 13:
9780324235838
ISBN 10:
0324235836
Edition: 1st
Format: Hardcover
Copyright: 01/09/2006
Publisher: Cengage Learning

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Summary

Economics doesn't have to be a mystery anymore. FOUNDATIONS OF MATHEMATICAL AND COMPUTATION ECONOMICS shows you how mathematics impacts economics and econometrics using easy-to-understand language and plenty of examples. Plus, it goes in-depth into computation and computational economics so you'll know how to handle those situations in your first economics job. Get ready for both the test and the workforce with this economics textbook.

Preface

Mathematics, Computation, and Economics

(26)

Mathematics

(12)

Philosophies of Mathematics

(3)

Women in Mathematics

(1)

How to Read a Math Book

(1)

Computation

(3)

Economics

(11)

Mathematics and Economics

(1)

Computation and Economics

(1)

Calibration

(2)

Econometrics

(3)

Empirical Work in Economics

(2)

Basic Mathematical Concepts and Methods

(54)

Sets and Set Operations

(11)

The Set of Real Numbers

(2)

Set Equality, Subsets, and Set Operations

(4)

Characteristics of Sets

(3)

Exercises

(1)

Functions

(7)

Mappings and Set Functions

(1)

Functions of Real Variables

(4)

Variety of Economic Relationships

(2)

Exercises

(1)

Series

(12)

Summation Notation Σ

(1)

Limit

(1)

Convergent and Divergent Series

(2)

Arithmetic Progression

(2)

Geometric Progression

(3)

Exercises

(1)

Permutations, Factorial, Combinations, and the Binomial Expansion

(3)

Exercises

(1)

Logarithm and Exponential Functions

(4)

Logarithm

(2)

Base of Natural Logarithm, e

(1)

Exercises

(1)

Mathematical Proof

(4)

Deduction, Mathematical Induction, and Proof by Contradiction

(2)

Computer-Assisted Mathematical Proof

(2)

Exercises

(1)

Trigonometry

(7)

Cycles and Frequencies

(1)

Exercises

(1)

Complex Numbers

(6)

Exercises

(1)

Basic Concepts and Methods of Probability Theory and Computation

(36)

Probability

(19)

Random Variables and Probability Distributions

(2)

Marginal and Conditional Distributions

(5)

The Law of Iterated Expectations

(1)

Continuous Random Variables

(3)

Correlation and Regression

(4)

Markov Chains

100

(4)

Exercises

102

(2)

Basic Concepts of Computation

104

(13)

Absolute and Relative Computation Errors

107

(2)

Efficiency of Computation

109

(2)

o and O

111

(2)

Solving an Equation

113

(2)

Exercises

115

(2)

Vectors and Matrices

117

(48)

Vectors and Vector Space

119

(13)

Vector Space

123

(2)

Norm of a Vector

125

(2)

Metric

127

(2)

Angle Between Two Vectors and the Cauchy-Schwarz Theorem

129

(2)

Exercises

131

(1)

Matrix

132

(11)

Systems of Linear Equations

138

(3)

Computation with Matrices

141

(2)

Exercises

143

(1)

The Inverse of a Matrix

143

(15)

A Number Called the Determinant

148

(5)

Rank and Trace of a Matrix

153

(1)

Another Way to Find the Inverse of a Matrix

154

(2)

Exercises

156

(2)

System of Linear Equations

158

(7)

Cramer's Rule

160

(4)

Exercises

164

(1)

Advanced Topics in Matrix Algebra

165

(48)

Quadratic Forms and Positive and Negative Definite Matrices

165

(4)

Exercises

169

(1)

Generalized Inverse of a Matrix

169

(4)

Exercises

172

(1)

Orthogonal Vectors and Matrices

173

(6)

Orthogonal Projection and Orthogonal Complement

173

(1)

Orthogonal Complement of a Matrix

174

(1)

Orthogonal Vectors

175

(1)

Gramm-Schmidt Algorithm

176

(1)

Exercises

177

(2)

Eigenvalues and Eigenvectors

179

(13)

Complex Eigenvalues

184

(1)

Repeated Eigenvalues

185

(4)

Eigenvalues and the Determinant and Trace of a Matrix

189

(2)

Exercises

191

(1)

Factorization of Symmetric Matrices

192

(9)

Some Interesting Properties of Symmetric Matrices

192

(3)

Factorization of Matrix with Real Distinct Roots

195

(2)

Factorization of a Positive Definite Matrix

197

(4)

Exercises

201

(1)

Lu Factorization of a Square Matrix

201

(7)

Cholesky Factorization

206

(2)

Exercises

208

(1)

Kronecker Product and Vec Operator

208

(5)

Vectorization of a Matrix

210

(1)

Exercises

211

(2)

Differentiation: Functions of One Variable

213

(42)

Marginal Analysis in Economics

213

(5)

Marginal Concepts and Derivatives

214

(3)

Comparative Static Analysis

217

(1)

Exercises

218

(1)

Limit and Continuity

218

(5)

Limit

219

(2)

Continuity

221

(2)

Exercises

223

(1)

Derivatives

223

(19)

Geometric Representation of Derivative

226

(1)

Differentiability

227

(3)

Rules of Differentiation

230

(3)

Properties of Derivatives

233

(8)

Exercises

241

(1)

Monotonic Functions and the Inverse Rule

242

(4)

Exercises

245

(1)

Second- and Higher-Order Derivatives

246

(2)

Exercises

248

(1)

Differential

248

(2)

Second- and Higher-Order Differentials

249

(1)

Exercises

250

(1)

Computer and Numerical Differentiation

250

(5)

Computer Differentiation

250

(1)

Numerical Differentiation

251

(2)

Exercises

253

(2)

Differentiation: Functions of Several Variables

255

(32)

Partial Differentiation

257

(8)

Second-Order Partial Derivatives

261

(1)

The Gradient and Hessian

262

(2)

Exercises

264

(1)

Differential and Total Derivative

265

(6)

Differential

265

(3)

Total Derivative

268

(2)

Exercises

270

(1)

Homogeneous Functions and the Euler Theorem

271

(3)

Exercises

274

(1)

Implicit Function Theorem

274

(5)

Exercises

279

(1)

Differentiating Systems of Equations

279

(8)

The Jacobian and Independence of Nonlinear Functions

279

(2)

Differentiating Several Functions

281

(5)

Exercises

286

(1)

The Taylor Series and Its Applications

287

(26)

The Taylor Expansion

288

(9)

Exercises

297

(1)

The Remainder and the Precision of Approximation

297

(4)

Exercises

300

(1)

Finding the Roots of an Equation

301

(6)

Iterative Methods

301

(2)

The Bisection Method

303

(1)

Newton's Method

304

(3)

Exercises

307

(1)

Taylor Expansion of Functions of Several Variables

307

(6)

Exercises

311

(2)

Static Optimization

313

(26)

Maxima and Minima of Functions of One Variable

315

(10)

Inflection Point

322

(2)

Exercises

324

(1)

Unconstrained Optima of Functions of Several Variables

325

(14)

Convex and Concave Functions

329

(3)

Quasi-convex and Quasi-concave Functions

332

(2)

Exercises

334

(1)

Numerical Optimization

334

(1)

Steepest Decent

335

(1)

Golden Section Method

335

(1)

Newton Method

336

(1)

Matlab Functions

337

(1)

Exercises

338

(1)

Constrained Optimization

339

(32)

Optimization with Equality Constraints

339

(8)

The Nature of Constrained Optima and the Significance of λ

346

(1)

Exercises

347

(1)

Value Function

347

(8)

Exercises

354

(1)

Second-Order Conditions and Comparative Static

355

(6)

Exercises

360

(1)

Inequality Constraints and Karush-Kuhn-Tucker Conditions

361

(10)

Duality

366

(3)

Exercises

369

(2)

Integration

371

(46)

The Indefinite Integral

372

(8)

Rules of Integration

373

(3)

Change of Variable

376

(2)

Integration by Part

378

(2)

Exercises

380

(1)

The Definite Integral

380

(20)

Properties of Definite Integrals

386

(4)

Rules of Integration for the Definite Integral

390

(8)

Riemann-Stieltjes Integral

398

(2)

Exercises

400

(1)

Computer and Numerical Integration

400

(11)

Computer Integration

400

(1)

Numerical Integration

401

(2)

The Trapezoid Method

403

(1)

The Lagrange Interpolation Formula

404

(3)

Newton-Cotes Method

407

(1)

Simpson's Method

408

(2)

Exercises

410

(1)

Special Functions

411

(1)

Exercises

412

(1)

The Derivative of an Integral

412

(5)

Exercises

415

(2)

Dynamic Optimization

417

(30)

Dynamic Analysis in Economics

417

(2)

The Control Problem

419

(6)

The Functional and Its Derivative

422

(3)

Calculus of Variations

425

(7)

The Euler Equation

426

(3)

Second-Order Conditions

429

(1)

Generalizing the Calculus of Variations

430

(1)

Exercises

431

(1)

Dynamic Programming

432

(5)

Exercises

437

(1)

The Maximum Principle

437

(10)

Necessary and Sufficient Conditions

445

(1)

Exercises

446

(1)

Differential Equations

447

(44)

Examples of Continuous Time Dynamic Economic Models

448

(2)

An Overview

450

(7)

Initial Value Problem

453

(2)

Existence and Uniqueness of Solutions

455

(1)

Equilibrium and Stability

456

(1)

First-Order Linear Differential Equations

457

(14)

Variable Coefficient Equations

459

(1)

Particular Integral, the Method of Undetermined Coefficients

460

(3)

Separable Equations

463

(2)

Exact Differential Equations

465

(4)

Integrating Factor

469

(1)

Exercises

470

(1)

Phase Diagram

471

(4)

Exercises

475

(1)

Second-Order Linear Differential Equations

475

(10)

Two Distinct Real Roots

476

(2)

Repeated Root

478

(2)

Complex Roots

480

(2)

Particular Integral

482

(2)

Exercises

484

(1)

Numerical Analysis of Differential Equations

485

(6)

The Euler Method

485

(3)

Runge-Kutta Methods

488

(1)

Exercises

489

(2)

Difference Equations

491

(40)

An Overview

492

(4)

Examples of Discrete Dynamic-Economic Models

496

(5)

Adaptive Expectations

496

(2)

Partial Adjustment

498

(1)

Hall's Consumption Function

499

(1)

Exercises

500

(1)

First-Order Linear Difference Equations

501

(11)

Solution of First-Order Linear Homogeneous Difference Equations

501

(4)

Solution of First-Order Nonhomogeneous Equations

505

(6)

Exercises

511

(1)

Second-Order Linear Difference Equations

511

(1)

Solution of Second-Order Linear Homogeneous Difference Equations

512

(2)

Behavior of the Solution of Second-Order Equation

514

(14)

The Lag Operator

519

(3)

Solution of Second-Order Nonhomogeneous Difference Equations

522

(5)

Exercises

527

(1)

nth-Order Difference Equations

528

(3)

Exercises

530

(1)

Dynamic Systems

531

(34)

Systems of Differential Equations

531

(7)

Equivalence of a Second-Order Linear Differential Equation and a System of Two First-Order Linear Equations

534

(2)

Linearizing Nonlinear Systems of Differential Equations

536

(2)

The Jordan Canonical Form

538

(7)

Diagonalization of a Matrix with Distinct Real Eigenvalues

539

(1)

Block Diagonal Form of a Matrix with Complex Eigenvalues

540

(1)

An Alternative Form for a Matrix with Complex Roots

541

(1)

Decomposition of a Matrix with Repeated Roots

542

(2)

Exercises

544

(1)

Exponential of a Matrix

545

(6)

Real Distinct Roots

546

(1)

Complex Roots

547

(2)

Repeated Roots

549

(2)

Exercises

551

(1)

Solution of Systems of Linear Differential Equations

551

(6)

Decoupled Systems

552

(1)

Systems with Real and Distinct Roots

553

(2)

Systems with Complex Roots

555

(1)

Systems with Repeated Roots

556

(1)

Exercises

557

(1)

Numerical Analysis of Systems of Differential Equations

557

(1)

Exercises

558

(1)

The Phase Portrait

558

(7)

Exercises

563

(2)

Solutions to Selected Exercises

565

(10)

Index

575

Amazon no longer offers textbook rentals. We do!

Foundations of Mathematical And Computational Economics

Foundations of Mathematical And Computational Economics

9780324235838

0324235836

Summary

Table of Contents

Supplemental Materials

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