Mathematics for economics (Cambridge, 2011). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаMathematics for economics / M.Hoy, J.Livernois, C.McKenna, R.Rees, T.Stengos. - 3rd ed. - Cambridge: MIT Press, 2011. - xi, 959 p.: ill. - Ind.: p.953-959. - ISBN 978-0-262-01507-3
 

Оглавление / Contents
 
Preface ...................................................... xiii

Part I  Introduction and Fundamentals

Chapter 1  Introduction ......................................... 3
1.1  What Is an Economic Model? ................................. 3
1.2  How to Use This Book ....................................... 8
1.3  Conclusion ................................................. 9

Chapter 2  Review of Fundamentals .............................. 11
2.1  Sets and Subsets .......................................... 11
2.2  Numbers ................................................... 23
2.3  Some Properties of Point Sets in fig.1n ....................... 31
2.4  Functions ................................................. 41

Chapter 3  Sequences, Series, and Limits ....................... 61
3.1  Definition of a Sequence .................................. 61
3.2  Limit of a Sequence ....................................... 65
3.3  Present-Value Calculations ................................ 69
3.4  Properties of Sequences ................................... 79
3.5  Series .................................................... 84

Part II  Univariate Calculus and Optimization

Chapter 4  Continuity of Functions ............................ 103
4.1  Continuity of a Function of One Variable ................. 103
4.2  Economic Applications of Continuous and Discontinuous 
     Functions

Chapter 5  The Derivative and Differential for Functions of
One Variable .................................................. 127
5.1  Definition of a Tangent Line ............................. 127
5.2  Definition of the Derivative and the Differential ........ 134
5.3  Conditions for Differentiability ......................... 141
5.4  Rules of Differentiation ................................. 147
5.5  Higher Order Derivatives: Concavity and Convexity of
     a Function ............................................... 175
5.6  Taylor Series Formula and the Mean-Value Theorem ......... 185

Chapter 6  Optimization of Functions of One Variable .......... 195
6.1  Necessary Conditions for Unconstrained Maxima and 
     Minima ................................................... 196
6.2  Second-Order Conditions .................................. 211
6.3  Optimization over an Interval ............................ 220

Part III  Linear Algebra

Chapter 7  Systems of Linear Equations ........................ 235
7.1  Solving Systems of Linear Equations ...................... 236
7.2  Linear Systems in n-Variables ............................ 250

Chapter 8  Matrices ........................................... 267
8.1  General Notation ......................................... 267
8.2  Basic Matrix Operations .................................. 273
8.3  Matrix Transposition ..................................... 288
8.4  Some Special Matrices .................................... 293

Chapter 9  Determinants and the Inverse Matrix ................ 301
9.1  Defining the Inverse ..................................... 301
9.2  Obtaining the Determinant and Inverse of a 3 × 3
     Matrix ................................................... 318
9.3  The Inverse of an n × n Matrix and Its Properties ........ 324
9.4  Cramer's Rule ............................................ 329

Chapter 10 Some Advanced Topics in Linear Algebra ............. 347
10.1 Vector Spaces ............................................ 347
10.2 The Eigenvalue Problem ................................... 363
10.3 Quadratic Forms .......................................... 378

Part IV Multivariate Calculus

Chapter 11 Calculus for Functions of n-Variables .............. 393
11.1 Partial Differentiation .................................. 393
11.2 Second-Order Partial Derivatives ......................... 407
11.3 The First-Order Total Differential ....................... 415
11.4 Curvature Properties: Concavity and Convexity ............ 436
11.5 More Properties of Functions with Economic 
     Applications ............................................. 451
11.6 Taylor Series Expansion .................................. 464

Chapter 12 Optimization of Functions of n-Variables ........... 473
12.1 First-Order Conditions ................................... 474
12.2 Second-Order Conditions .................................. 484
12.3 Direct Restrictions on Variables ......................... 491

Chapter 13 Constrained Optimization ........................... 503
13.1 Constrained Problems and Approaches to Solutions ......... 504
13.2 Second-Order Conditions for Constrained Optimization ..... 516
13.3 Existence, Uniqueness, and Characterization of 
     Solutions ................................................ 520

Chapter 14 Comparative Statics ................................ 529
14.1 Introduction to Comparative Statics ...................... 529
14.2 General Comparative-Statics Analysis ..................... 540
14.3 The Envelope Theorem ..................................... 554

Chapter 15 Concave Programming and the Kuhn-Tucker 
Conditions .................................................... 567
15.1 The Concave-Programming Problem .......................... 567
15.2 Many Variables and Constraints ........................... 575

Part V Integration and Dynamic Methods

Chapter 16 Integration ........................................ 585
16.1 The Indefinite Integral .................................. 585
16.2 The Riemann (Definite) Integral .......................... 593
16.3 Properties of Integrals .................................. 605
16.4 Improper Integrals ....................................... 613
16.5 Techniques of Integration ................................ 623

Chapter 17 An Introduction to Mathematics for Economic 
Dynamics ...................................................... 633
17.1 Modeling Time ............................................ 634

Chapter 18 Linear, First-Order Difference Equations ........... 643
18.1 Linear, First-Order, Autonomous Difference Equations ..... 643
18.2 The General, Linear, First-Order Difference Equation ..... 656

Chapter 19 Nonlinear, First-Order Difference Equations ........ 665
19.1 The Phase Diagram and Qualitative Analysis ............... 665
19.2 Cycles and Chaos ......................................... 673

Chapter 20 Linear, Second-Order Difference Equations .......... 681
20.1 The Linear, Autonomous, Second-Order Difference 
     Equation ................................................. 681
20.2 The Linear, Second-Order Difference Equation with
     a Variable Term .......................................... 708

Chapter 21 Linear, First-Order Differential Equations ......... 715
21.1 Autonomous Equations ..................................... 715
21.2 Nonautonomous Equations .................................. 731

Chapter 22 Nonlinear, First-Order Differential Equations ...... 739
22.1 Autonomous Equations and Qualitative Analysis ............ 739
22.2 Two Special Forms of Nonlinear, First-Order 
     Differential Equations ................................... 748

Chapter 23 Linear, Second-Order Differential Equations ........ 753
23.1 The Linear, Autonomous, Second-Order Differential
     Equation ................................................. 753
23.2 The Linear, Second-Order Differential Equation with
     a Variable Term .......................................... 772

Chapter 24 Simultaneous Systems of Differential and 
Difference Equations .......................................... 781
24.1 Linear Differential Equation Systems ..................... 781
24.2 Stability Analysis and Linear Phase Diagrams ............. 803
24.3 Systems of Linear Difference Equations ................... 825

Chapter 25 Optimal Control Theory ............................. 845
25.1 The Maximum Principle .................................... 848
25.2 Optimization Problems Involving Discounting .............. 860
25.3 Alternative Boundary Conditions on x(T) .................. 872
25.4 Infinite-Time Horizon Problems ........................... 886
25.5 Constraints on the Control Variable ...................... 899
25.6 Free-Terminal-Time Problems (T Free) ..................... 909

Answers ....................................................... 921
Index ......................................................... 953


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