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Economic Analysis Through Mathematics Tools and Techniques for Decision Making.epub
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资料名称：Economic Analysis Through Mathematics Tools and Techniques for Decision Making
Integrating Artificial Intelligence (ChatGPT) into Marketing, Economics, Business, and Finance
Part I Linear Algebra1
1 Matrices and Types of Matrices3
1.1 Review Questions14
1.2 Practice Problems14
2 Basic Matrix Operations17
2.1 Matrix Addition17
2.2 Scalar Multiplication20
2.3 Matrix Subtraction21
2.4 Scalar Product23
2.5 Matrix Multiplication27
2.6 Inverse of a Matrix35
2.7 Review Questions40
2.8 Practice Problems41
3 Determinants47
3.1 Definition and Properties of the Determinant48
3.2 Geometric Interpretation of the Determinant57
3.3 Using Determinant to Check if Matrix Is Non-singular58
3.4 Finding the Inverse by Using the Determinant61
3.5 Cramer’s System67
3.5.1 Application of Cramer’s Rule to Problems in Economics69
3.6 Review Questions77
3.7 Practice Problems78
4 Systems of Linear Equations83
4.1 Linear Dependence and Independence85
4.2 Rank92
4.3 Elementary Transformations95
4.4 Main Results on Systems of Linear Equations101
4.5 Gauss-Jordan Elimination Method105
4.6 Finding the Inverse of a Matrix Using the Gauss-Jordan Elimination Method116
4.7 Application in Economics: Input-Output Analysis120
4.8 Review Questions128
4.9 Practice Problems132
5 Vectors and Vector Spaces143
5.1 Euclidean Vector Space143
5.2 The Norm of a Vector147
5.3 Distance Between Vectors150
5.4 Review Questions151
5.5 Practice Problems152
6 Applications of Linear Algebra in Economics153
6.1 Applications in Microeconomics and Macroeconomics154
6.2 Linear Programming156
6.3 Game Theory159
6.4 Econometrics and Regression Analysis160
6.5 Dynamic Economic Models: State-Space Representation162
Part II Differential Calculus of Functions of One Real Variable163
7 Real Functions of One Real Variable165
7.1 The Concept of a Function165
7.2 Overview of Some Basic Functions169
7.2.1 Linear Function169
7.2.2 Polynomials171
7.2.3 Absolute Value Function173
7.2.4 Root Functions173
7.2.5 Rational Function175
7.2.6 Exponential Function176
7.2.7 Logarithmic Function178
7.3 Review Questions181
7.4 Practice Problems182
8 The Concept of a Limit183
8.1 Limit of a Function183
8.2 Properties of Limits187
8.3 Asymptotes196
8.4 Review Questions199
8.5 Practice Problems200
9 Continuous Functions201
9.1 Definition and Properties201
9.2 Some Application of Continuity to Problems in Economics205
9.2.1 A Salary with a Bonus Payment205
9.2.2 Income Support Program206
9.3 Review Questions208
9.4 Practice Problems208
10 Single-Variable Differentiation209
10.1 The Concept of a Derivative210
10.2 Rules of Differentiation218
10.2.1 The Chain Rule220
10.2.2 Implicit Differentiation224
10.2.3 Derivatives of Inverse Functions226
10.2.4 Logarithmic Differentiation227
10.3 L’Hospital Rule229
10.4 Higher-Order Derivatives232
10.5 Some Economic Applications234
10.6 Review Questions238
10.7 Practice Problems239
11 Approximating Functions with Polynomials and Mean Value Theorems243
11.1 Differential of a Function244
11.2 Approximating Functions of One Variable with Polynomials248
11.3 Weierstrass Theorem and the Mean Value Theorems253
11.4 Review Problems255
11.5 Practice Problems256
12 Optimization of Functions of One Variable257
12.1 The Concept of Local and Global Extrema258
12.2 Increasing and Decreasing Functions262
12.3 The First Derivative Test for Local Extrema269
12.4 Convex and Concave Functions276
12.5 Characterization of Local Extrema Using the Second Derivative285
12.6 Review Questions291
12.7 Practice Problems293
13 Some Economic Applications297
13.1 Total, Marginal, and Average Function298
13.1.1 Cost Function298
13.1.2 Revenue Function300
13.1.3 Profit Function303
13.2 Elasticity311
13.3 Review Questions319
13.4 Practice Problems321
Part III Differential Calculus of Functions of Several Variables327
14 The Concept of a Function of Several Variables329
14.1 Some Basic Functions331
14.1.1 Linear Function332
14.1.2 Polynomials333
14.2 Continuous Functions335
14.3 Review Questions337
14.4 Practice Problems337
15 Differential Calculus of Functions of Several Variables339
15.1 Partial Derivatives340
15.2 Higher-Order Partial Derivatives347
15.3 The Chain Rule for Functions of Several Variables353
15.4 The First-Order Total Differential357
15.5 Implicitly Defined Functions and Their Derivatives371
15.6 Review Questions375
15.7 Practice Problems375
16 Homogeneous Functions383
16.1 The Concept of a Homogeneous Function384
16.2 Euler’s Theorem394
16.3 Partial and Cross Elasticity395
16.4 Review Questions401
16.5 Practice Problems402
17 Convex and Concave Functions405
17.1 Basic Concepts405
17.2 Characterization of Convex and Concave Functions407
17.3 Review Questions411
17.4 Practice Problems411
18 Optimization of Functions of Several Variables413
18.1 The Concept of Local and Global Extrema413
18.2 Unconstrained Optimization of Functions of Several Variables416
18.3 Extrema of Functions of Several Variables with One Constraint in the Form of Equation437
18.3.1 Substitution Method437
18.3.2 The Lagrange Multipliers Method440
18.4 Review Questions450
18.5 Practice Problems451
19 Applications of Multivariable Calculus in Economics457
Part IV Integrals and Differential Calculus467
20 Integrals469
20.1 Indefinite Integral470
20.2 Methods of Integration475
20.2.1 Integration by Substitution475
20.2.2 Integration by Parts477
20.3 Definite Integral481
20.4 Finding the Area491
20.5 Improper Integrals501
20.6 Review Questions509
20.7 Practice Problems511
21 Differential Equations515
21.1 The Concept of Differential Equation515
21.2 Separable Differential Equations520
21.3 The Variation of Constants Method522
21.4 Review Questions525
21.5 Practice Problems526
22 Application of Integrals and Differential Equations in Economics529
Part V Mathematics of Finance537
23 Interest539
24 Simple Interest543
24.1 Review Questions552
24.2 Practice Problems552
25 Compound Interest553
25.1 Fundamental Compound Interest Formula554
25.2 Equivalent Compound Interest Rates558
25.3 Continuous Compounding568
25.4 Discounted Value570
25.5 Finding the Rate and the Time574
25.6 Equations of Value579
25.7 Review Questions582
25.8 Practice Problems583
26 Simple Annuities587
26.1 Review Questions601
26.2 Practice Problems601
27 Amortization Schedules605
27.1 Outstanding Balance606
27.2 Amortization Schedule613
27.2.1 Level Payments613
27.2.2 Equal Installments of Principal622
27.3 Review Questions625
27.4 Practice Problems626
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