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Mathematics of Economics and Business - Frank R. Werner

Mathematics of Economics and Business

Paperback Published: 23rd February 2006
ISBN: 9780415332811
Number Of Pages: 518

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For all students who wish to understand current economic and business literature, knowledge of mathematical methods has become a prerequisite.  Clear and concise, with precise definitions and theorems, Werner and Sotskov cover all the major topics required to gain a firm grounding in this subject including sequences, series, applications in finance, functions, differentiations, differentials and difference equations, optimizations with and without constraints, integrations and much more.

Containing exercises and worked examples, precise definitions and theorems as well as economic applications, this book provides the reader with a comprehensive understanding of the mathematical models and tools used in both economics and business.

Prefacep. ix
List of abbreviationsp. xiii
List of notationsp. xv
Introductionp. 1
Logic and propositional calculusp. 1
Propositions and their compositionp. 1
Universal and existential propositionsp. 7
Types of mathematical proofp. 9
Sets and operations on setsp. 15
Basic definitionsp. 15
Operations on setsp. 16
Combinatoricsp. 26
Real numbers and complex numbersp. 32
Real numbersp. 32
Complex numbersp. 47
Sequences; series; financep. 61
Sequencesp. 61
Basic definitionsp. 61
Limit of a sequencep. 65
Seriesp. 71
Partial sumsp. 71
Series and convergence of seriesp. 73
Financep. 80
Simple interest and compound interestp. 80
Periodic paymentsp. 85
Loan repayments, redemption tablesp. 90
Investment projectsp. 97
Depreciationp. 101
Relations; mappings; functions of a real variablep. 107
Relationsp. 107
Mappingsp. 110
Functions of a real variablep. 116
Basic notionsp. 117
Properties of functionsp. 121
Elementary types of functionsp. 126
Differentiationp. 148
Limit and continuityp. 148
Limit of a functionp. 148
Continuity of a functionp. 151
Difference quotient and the derivativep. 155
Derivatives of elementary functions; differentiation rulesp. 158
Differential; rate of change and elasticityp. 164
Graphing functionsp. 168
Monotonicityp. 168
Extreme pointsp. 169
Convexity and concavityp. 175
Limitsp. 178
Further examplesp. 181
Mean-value theoremp. 184
Taylor polynomialsp. 186
Approximate determination of zeroesp. 189
Integrationp. 197
Indefinite integralsp. 197
Integration formulas and methodsp. 198
Basic indefinite integrals and rulesp. 198
Integration by substitutionp. 200
Integration by partsp. 204
The definite integralp. 209
Approximation of definite integralsp. 215
Improper integralsp. 219
Infinite limits of integrationp. 219
Unbounded integrandsp. 220
Some applications of integrationp. 222
Present value of a continuous future income flowp. 222
Lorenz curvesp. 224
Consumer and producer surplusp. 225
Vectorsp. 230
Preliminariesp. 230
Operations on vectorsp. 233
Linear dependence and independencep. 240
Vector spacesp. 244
Matrices and determinantsp. 253
Matricesp. 253
Matrix operationsp. 258
Determinantsp. 263
Linear mappingsp. 271
The inverse matrixp. 273
An economic application: input-output modelp. 277
Linear equations and inequalitiesp. 287
Systems of linear equationsp. 287
Preliminariesp. 287
Existence and uniqueness of a solutionp. 290
Elementary transformation; solution proceduresp. 292
General solutionp. 302
Matrix inversionp. 306
Systems of linear inequalitiesp. 308
Preliminariesp. 308
Properties of feasible solutionsp. 309
A solution procedurep. 315
Linear programmingp. 328
Preliminariesp. 328
Graphical solutionp. 330
Properties of a linear programming problem; standard formp. 334
Simplex algorithmp. 339
Two-phase simplex algorithmp. 350
Duality; complementary slacknessp. 357
Dual simplex algorithmp. 363
Eigenvalue problems and quadratic formsp. 368
Eigenvalues and eigenvectorsp. 368
Quadratic forms and their signp. 376
Functions of several variablesp. 383
Preliminariesp. 383
Partial derivatives; gradientp. 387
Total differentialp. 394
Generalized chain rule; directional derivativesp. 397
Partial rate of change and elasticity; homogeneous functionsp. 402
Implicit functionsp. 405
Unconstrained optimizationp. 409
Optimality conditionsp. 409
Method of least squaresp. 419
Extreme points of implicit functionsp. 423
Constrained optimizationp. 424
Local optimality conditionsp. 424
Global optimality conditionsp. 434
Double integralsp. 436
Differential equations and difference equationsp. 444
Differential equations of the first orderp. 445
Graphical solutionp. 445
Separable differential equationsp. 447
Linear differential equations of order np. 451
Properties of solutionsp. 451
Differential equations with constant coefficientsp. 454
Systems of linear differential equations of the first orderp. 461
Linear difference equationsp. 472
Definitions and properties of solutionsp. 472
Linear difference equations of the first orderp. 474
Linear difference equations of the second orderp. 478
Selected solutionsp. 486
Literaturep. 511
Indexp. 513
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780415332811
ISBN-10: 0415332818
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 518
Published: 23rd February 2006
Publisher: Taylor & Francis Ltd
Country of Publication: GB
Dimensions (cm): 24.5 x 17.0  x 2.92
Weight (kg): 0.93
Edition Number: 1

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