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Mathematics for Economics third edition [Kietas viršelis]

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  • Formatas: Hardback, 974 pages, aukštis x plotis x storis: 229x203x48 mm, weight: 1701 g
  • Serija: The MIT Press
  • Išleidimo metai: 04-Mar-2011
  • Leidėjas: MIT Press
  • ISBN-10: 0262015072
  • ISBN-13: 9780262015073
Kitos knygos pagal šią temą:
Mathematics for Economics third editionDidesnis paveikslėlis
  • Formatas: Hardback, 974 pages, aukštis x plotis x storis: 229x203x48 mm, weight: 1701 g
  • Serija: The MIT Press
  • Išleidimo metai: 04-Mar-2011
  • Leidėjas: MIT Press
  • ISBN-10: 0262015072
  • ISBN-13: 9780262015073
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780262015073.html
Raktažodžiai:
A new edition of a comprehensive undergraduate mathematics text for economics students.

This text offers a comprehensive presentation of the mathematics required to tackle problems in economic analysis. To give a better understanding of the mathematical concepts, the text follows the logic of the development of mathematics rather than that of an economics course. The only prerequisite is high school algebra, but the book goes on to cover all the mathematics needed for undergraduate economics. It is also a useful reference for graduate students. After a review of the fundamentals of sets, numbers, and functions, the book covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics. To develop the student’s problem-solving skills, the book works through a large number of examples and economic applications.

This streamlined third edition offers an array of new and updated examples. [ Some of the lengthier proofs and examples have been moved to the book’s Web site. This combination of formats allows the authors to add content without expanding the physical size of the book. The book and the Web material are integral to each other; examples and figures on the Web are cross-referenced in the text. A student solutions manual will be available in e-book form. Instructors will be able to access online instructor’s material that includes Power Point slides.
Preface xiii
Part I Introduction and Fundamentals
Chapter 1 Introduction
3(8)
1.1 What Is an Economic Model?
3(5)
1.2 How to Use This Book
8(1)
1.3 Conclusion
9(2)
Chapter 2 Review of Fundamentals
11(50)
2.1 Sets and Subsets
11(12)
2.2 Numbers
23(8)
2.3 Some Properties of Point Sets in 1"
31(10)
2.4 Functions
41(20)
Chapter 3 Sequences, Series, and Limits
61(42)
3.1 Definition of a Sequence
61(4)
3.2 Limit of a Sequence
65(4)
3.3 Present-Value Calculations
69(10)
3.4 Properties of Sequences
79(5)
3.5 Series
84(19)
Part II Univariate Calculus and Optimization
Chapter 4 Continuity of Functions
103(24)
4.1 Continuity of a Function of One Variable
103(10)
4.2 Economic Applications of Continuous and Discontinuous Functions
113(14)
Chapter 5 The Derivative and Differential for Functions of One Variable
127(68)
5.1 Definition of a Tangent Line
127(7)
5.2 Definition of the Derivative and the Differential
134(7)
5.3 Conditions for Differentiability
141(6)
5.4 Rules of Differentiation
147(28)
5.5 Higher Order Derivatives: Concavity and Convexity of a Function
175(10)
5.6 Taylor Series Formula and the Mean-Value Theorem
185(10)
Chapter 6 Optimization of Functions of One Variable
195(40)
6.1 Necessary Conditions for Unconstrained Maxima and Minima
196(15)
6.2 Second-Order Conditions
211(9)
6.3 Optimization over an Interval
220(15)
Part III Linear Algebra
Chapter 7 Systems of Linear Equations
235(32)
7.1 Solving Systems of Linear Equations
236(14)
7.2 Linear Systems in n-Variables
250(17)
Chapter 8 Matrices
267(34)
8.1 General Notation
267(6)
8.2 Basic Matrix Operations
273(15)
8.3 Matrix Transposition
288(5)
8.4 Some Special Matrices
293(8)
Chapter 9 Determinants and the Inverse Matrix
301(46)
9.1 Defining the Inverse
301(17)
9.2 Obtaining the Determinant and Inverse of a 3 × 3 Matrix
318(6)
9.3 The Inverse of an n × n Matrix and Its Properties
324(5)
9.4 Cramer's Rule
329(18)
Chapter 10 Some Advanced Topics in Linear Algebra
347(46)
10.1 Vector Spaces
347(16)
10.2 The Eigenvalue Problem
363(15)
10.3 Quadratic Forms
378(15)
Part IV Multivariate Calculus
Chapter 11 Calculus for Functions of n-Variables
393(80)
11.1 Partial Differentiation
393(14)
11.2 Second-Order Partial Derivatives
407(8)
11.3 The First-Order Total Differential
415(21)
11.4 Curvature Properties: Concavity and Convexity
436(15)
11.5 More Properties of Functions with Economic Applications
451(13)
11.6 Taylor Series Expansion
464(9)
Chapter 12 Optimization of Functions of n-Variables
473(30)
12.1 First-Order Conditions
474(10)
12.2 Second-Order Conditions
484(7)
12.3 Direct Restrictions on Variables
491(12)
Chapter 13 Constrained Optimization
503(26)
13.1 Constrained Problems and Approaches to Solutions
504(12)
13.2 Second-Order Conditions for Constrained Optimization
516(4)
13.3 Existence. Uniqueness, and Characterization of Solutions
520(9)
Chapter 14 Comparative Statics
529(38)
14.1 Introduction to Comparative Statics
529(11)
14.2 General Comparative-Statics Analysis
540(14)
14.3 The Envelope Theorem
554(13)
Chapter 15 Concave Programming and the Kuhn-Tucker Conditions
567(18)
15.1 The Concave-Programming Problem
567(8)
15.2 Many Variables and Constraints
575(10)
Part V Integration and Dynamic Methods
Chapter 16 Integration
585(48)
16.1 The Indefinite Integral
585(8)
16.2 The Riemann (Definite) Integral
593(12)
16.3 Properties of Integrals
605(8)
16.4 Improper Integrals
613(10)
16.5 Techniques of Integration
623(10)
Chapter 17 An Introduction to Mathematics for Economic Dynamics
633(10)
17.1 Modeling Time
634(9)
Chapter 18 Linear, First-Order Difference Equations
643(22)
18.1 Linear, First-Order, Autonomous Difference Equations
643(13)
18.2 The General, Linear, First-Order Difference Equation
656(9)
Chapter 19 Nonlinear, First-Order Difference Equations
665(16)
19.1 The Phase Diagram and Qualitative Analysis
665(8)
19.2 Cycles and Chaos
673(8)
Chapter 20 Linear, Second-Order Difference Equations
681(34)
20.1 The Linear, Autonomous, Second-Order Difference Equation
681(27)
20.2 The Linear, Second-Order Difference Equation with a Variable Term
708(7)
Chapter 21 Linear, First-Order Differential Equations
715(24)
21.1 Autonomous Equations
715(16)
21.2 Nonautonomous Equations
731(8)
Chapter 22 Nonlinear, First-Order Differential Equations
739(14)
22.1 Autonomous Equations and Qualitative Analysis
739(9)
22.2 Two Special Forms of Nonlinear, First-Order Differential Equations
748(5)
Chapter 23 Linear, Second-Order Differential Equations
753(28)
23.1 The Linear, Autonomous, Second-Order Differential Equation
753(19)
23.2 The Linear, Second-Order Differential Equation with a Variable Term
772(9)
Chapter 24 Simultaneous Systems of Differential and Difference Equations
781(64)
24.1 Linear Differential Equation Systems
781(22)
24.2 Stability Analysis and Linear Phase Diagrams
803(22)
24.3 Systems of Linear Difference Equations
825(20)
Chapter 25 Optimal Control Theory
845(76)
25.1 The Maximum Principle
848(12)
25.2 Optimization Problems Involving Discounting
860(12)
25.3 Alternative Boundary Conditions on x(T)
872(14)
25.4 Infinite-Time Horizon Problems
886(13)
25.5 Constraints on the Control Variable
899(10)
25.6 Free-Terminal-Time Problems (T Free)
909(12)
Answers 921(32)
Index 953