Introduction to mathematics for economics with R:
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| Language: | English |
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[2022]
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxix, 853 Seiten Diagramme |
| ISBN: | 9783031052019 |
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| 245 | 1 | 0 | |a Introduction to mathematics for economics with R |c Massimiliano Porto |
| 264 | 1 | |a Cham |b Springer |c [2022] | |
| 300 | |a xxix, 853 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Quantitative Economics | |
| 650 | 4 | |a Econometrics | |
| 650 | 4 | |a Statistics in Business, Management, Economics, Finance, Insurance | |
| 650 | 4 | |a Econometrics | |
| 650 | 4 | |a Statistics | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-05202-6 |
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| adam_text | Contents 1 Introduction to R........................................................................................ 1.1 Installing R......................................................................................... 1.2 Installing RStudio............................................................................... 1.3 Introduction to RStudio...................................................................... 1.3.1 Launching a New Project ................................................... 1.3.2 Opening an R Script........................................................... 1.4 Packages to Install............................................................................... 1.4.1 How to Install a Package..................................................... 1.4.2 How to Load a Package...................................................... 1.5 Good Practice and Notation................................................................ 1.5.1 How to Read the Code ........................................................ 1.6 8 Key-Points Regarding R................................................................. 1.6.1 The Assignment Operator................................................... 1.6.2 The Class of Objects............................................................ 1.6.3 Case Sensitiveness............................................................... 1.6.4 The c() Function.................................................................. 1.6.5 Square Bracket Operator [ ] ............................................ 1.6.6 Loop and
Vectorization........................................................ 1.6.7 Functions.............................................................................. 1.6.8 Errors..................................................................................... 1.7 An Example with R............................................................................ 1.8 Exercise................................................................................................ 1.8.1 Exercise 1............................................................................. 1.8.2 Exercise 2............................................................................. Part I 2 1 1 2 2 3 6 7 8 8 9 11 12 12 13 14 15 16 20 24 27 32 50 50 51 Introduction to Mathematics for Static Economics Linear Algebra ........................................................................................... 2.1 Set, Group, Ring, Field: Short Overview.......................................... 2.2 Vectors................................................................................................. 2.2.1 VectorSpace........................................................................ 55 55 59 59 XV
xvi 3 Contents 2.2.2 Vector Representation in Two and Three Dimensions .... 2.2.3 Inner Product.......................................................................... 2.2.4 Outer Product........................................................................ 2.2.5 Component Form, Magnitude and Unit Vector................. 2.2.6 Parallel and Orthogonal Vectors.......................................... 2.2.7 Vector Projection.................................................................. 2.2.8 Linear Independence............................................................ 2.3 Matrices................................................................................................ 2.3.1 Matrix Operations................................................................ 2.3.2 Symmetric Matrix................................................................ 2.3.3 Diagonal Matrix and Identity Matrix.................................. 2.3.4 Triangular Matrix.................................................................. 2.3.5 Idempotent Matrix................................................................. 2.3.6 The Inverse of a Matrix......................................................... 2.3.7 System of Linear Equations................................................. 2.3.8 Determinant........................................................................... 2.3.9 Eigenvalues and Eigenvectors.............................................. 2.3.10 Partitioned Matrix............................................................... 2.3.11 Kronecker
Product................................................................. 2.3.12 Definiteness of Matrices...................................................... 2.3.13 Decomposition....................................................................... 2.4 Applications in Economics................................................................. 2.4.1 BudgetSet ............................................................................. 2.4.2 Applying Cramer’s Rule to the IS-LM Model ................... 2.4.3 Leontief Input-Output Model............................................... 2.4.4 Network Analysis................................................................... 2.4.5 Linear Model and the Dummy Variable Trap..................... 2.5 Exercises................................................................................................ 2.5.1 Exercise 1 ............................................................................. 2.5.2 Exercise 2............................................................................. 2.5.3 Exercise3............................................................................... 2.5.4 Exercise 4............................................................................. 2.5.5 Exercise 5............................................................................. 2.5.6 Exercise 6............................................................................. 2.5.7 Exercise 7.............................................................................. 62 71 72 73 76 76 78 82 84 90 91 94 95 96 100 125 160 177 183 187 196 213 213 218
220 226 231 236 236 237 237 238 239 239 240 Functions of One Variable......................................................................... 3.1 What is a Function?........................................................................... 3.1.1 Domain and Range.............................................................. 3.1.2 Monotonicity, Boundednessand Extrema........................... 3.1.3 Convex and Concave Functions........................................... 3.1.4 Function Operations............................................................. 3.2 Linear Function................................................................................... 3.2.1 Slope of Linear Function..................................................... 3.2.2 Applications in Economics.................................................. 243 243 246 248 249 249 250 251 258
xvii Contents Quadratic Function............................................................................. 3.3.1 Roots and Vertex................................................................... 3.3.2 The Graph of the Quadratic Function................................. 3.3.3 Discriminant......................................................................... 3.3.4 Applications in Economics.................................................. Cubic Function................................................................................... 3.4.1 How to Solve Cubic Equations .......................................... 3.4.2 Applications in Economics.................................................. Polynomials of Degree Greater Than Three.................................... Logarithmic and Exponential Functions.......................................... 3.6.1 What is a Logarithm?........................................................... 3.6.2 Logarithms and Exponents.................................................. 3.6.3 The Natural Logarithm........................................................ 3.6.4 The Natural Logarithmic Function .................................... 3.6.5 Applications in Economics.................................................. 3.6.6 Exponential Function........................................................... 3.6.7 Applications in Economics.................................................. Radical Function............................................................................... 3.7.1 How to Solve Radical
Equation........................................... 3.7.2 Find the Domain of a Radical Function............................. 3.7.3 Radicals and Rational Exponents........................................ 3.7.4 Applications in Economics.................................................. Rational Function .............................................................................. 3.8.1 Intercepts and Asymptotes.................................................. 3.8.2 Applications in Economics.................................................. Exercises............................................................................................. 3.9.1 Exercise 1............................................................................. 3.9.2 Exercise 2............................................................................. 3.9.3 Exercise 3............................................................................. 3.9.4 Exercise 4............................................................................. 3.9.5 Exercise 5............................................................................. 266 269 271 278 284 287 289 295 297 300 300 301 304 304 309 317 323 331 335 337 338 339 341 342 344 348 348 348 349 349 349 Differential Calculus.................................................................................. 4.1 What is the Meaning of Derivatives?................................................ 4.2 The Limit of a Function...................................................................... 4.3 Limits, Derivatives and
Slope............................................................. 4.3.1 Newton-Raphson Method................................................... 4.4 Notation of Derivatives ...................................................................... 4.5 Differentials ........................................................................................ 4.6 Rules of Differentiation..................................................................... 4.6.1 Power Rule........................................................................... 4.6.2 Product Rule........................................................................ 4.6.3 Quotient Rule....................................................................... 4.6.4 Chain Rule............................................................................ 4.6.5 Radicals Differentiation...................................................... 351 351 352 358 361 368 370 371 371 373 373 374 376 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4
xviii Conienis 4.6.6 Logarithmic Differentiation................................................. 4.6.7 Exponential Differentiation................................................. 4.6.8 Derivatives of Elementary Functions.................................. Derivatives andInverse Functions....................................................... Tangent Line to the Function............................................................. Points of Minimum, Maximum and Inflection................................ Taylor Expansion............................................................................... 4.10.1 Nth-Derivative Test.............................................................. 4.10.2 Newton-Raphson Method.................................................. L’Hôpital Theorem............................................................................ Derivatives with R.............................................................................. Taylor Expansion with R................................................................... Applications in Economics............................................................... 4.14.1 Marginal Cost...................................................................... 4.14.2 Marginal Cost and Average Cost ...................................... 4.14.3 Profit Maximization........................................................... 4.14.4 Elasticity............................................................................. Exercise...............................................................................................
4.15.1 Exercise 1............................................................................. 4.15.2 Exercise 2............................................................................. 4.15.3 Exercise3............................................................................. 376 378 380 381 382 391 399 407 408 408 409 411 412 412 418 419 429 437 437 437 439 5Integral Calculus............................................................................................... 5.1 Indefinite Integrals ............................................................................. 5.1.1 Anti-derivative Process....................................................... 5.2 Definite Integrals................................................................................ 5.2.1 Area Under a Curve............................................................ 5.2.2 Area Between Two Lines..................................................... 5.3 Fundamental Theorem of Calculus.................................................... 5.4 Improper Integrals and Convergence................................................. 5.4.1 Case 1 : Convergence........................................................... 5.4.2 Case 2: Divergence.............................................................. 5.5 Integration with R............................................................................... 5.6 Applications in Economics ................................................................ 5.6.1 Marginal Cost and Cost Function........................................ 5.6.2 Example: A
Problem............................................................ 5.6.3 The Surplus of Consumerand Producer.............................. 5.7 Exercise................................................................................................ 441 441 442 461 461 466 471 472 472 476 477 479 479 480 481 484 6 485 485 491 501 501 505 508 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 Multivariable Calculus............................................................................... 6.1 Functions of Several Variables........................................................... 6.1.1 Applications in Economics.................................................. 6.2 Partial and Total Derivatives.............................................................. 6.2.1 Partial Derivatives............................................................... 6.2.2 Total Derivatives................................................................... 6.2.3 Derivatives with R................................................................
Contents 6.2.4 Applications in Economies.................................................. Unconstrained Optimization.............................................................. 6.3.1 First Order Condition........................................................... 6.3.2 Second Order Condition....................................................... 6.3.3 Optimization with R............................................................. 6.3.4 Applications in Economics.................................................. Integration with Multiple Variables .................................................. Exercises.............................................................................................. 6.5.1 Exercise 1 ............................................................................. 6.5.2 Exercise 2.............................................................................. 510 512 513 515 519 521 527 529 529 530 Constrained Optimization......................................................................... 7.1 Equality Constraints........................................................................... 7.1.1 First-Order Condition .......................................................... 7.1.2 Multiple Equality Constraints.............................................. 7.1.3 Lagrange Multiplier............................................................. 7.1.4 Second-Order Conditions.................................................... 7.2 Inequality Constraints......................................................................... 7.2.1 Kuhn-Tucker
Conditions..................................................... 7.3 Constrained Optimization with R ..................................................... 7.4 Applications in Economics................................................................ 7.4.1 Utility Maximization Problem............................................ 7.4.2 Firm s Cost Minimization Problem.................................... 7.4.3 Transportation Problem....................................................... 7.4.4 CGE Model with R.............................................................. 7.5 Exercise................................................................................................ 531 532 532 534 537 542 547 548 554 562 562 567 570 575 581 6.3 6.4 6.5 7 xix Part II Introduction to Mathematics for Dynamic Economics 8 Trigonometry................................................................................................. 8.1 Right Triangles and Angles............................................................... 8.2 Trigonometric Functions................................................................... 8.3 Sum and Differences of Angles........................................................ 8.4 Derivatives of Trigonometric Functions.......................................... 585 585 588 596 596 9 Complex Numbers........................................................................................ 9.1 Set of Complex Numbers................................................................. 9.2 Complex Numbers: Real Part and Imaginary Part........................... 9.3
Arithmetic Operations......................................................................... 9.4 Geometric Interpretation and Polar Form......................................... 9.5 Exponential Form ............................................................................... 599 599 599 601 602 604 Difference Equations.................................................................................. 10.1 First-Order Linear Difference Equations.......................................... 10.1.1 Solution by Iteration........................................................... 10.1.2 Solution by General Method............................................. 10.1.3 Time Path and Equilibrium................................................. 609 610 611 614 623 10
Contents XX 10.2 10.3 10.4 10.5 10.6 11 Second-Order Linear Difference Equations...................................... 10.2.1 Solution to Second-Order Linear Homogeneous Difference Equation.............................................. 10.2.2 Solution to Second-Order Linear Nonhomogeneous Difference Equation .............. 10.2.3 Time Path and Equilibrium.................................................. System of Linear Difference Equations............................................. 10.3.1 Equilibrium.......................................................................... 10.3.2 Solution with the Powers of a Matrix................................. 10.3.3 Eigenvalues Method............................................................ 10.3.4 Graphing Trajectory of a Discrete System ........................ Transforming High-Order DifferenceEquations .............................. Applications in Economics................................................................ 10.5.1 A Problem with Interest Rate............................................. 10.5.2 The Cobweb Model.............................................................. 10.5.3 The Harrod-Domar Growth Model.................................... 10.5.4 Law of Motion for Public Debt.......................................... 10.5.5 Linear Difference Equations and Autoregressive Process Exercises.............................................................................................. 10.6.1 Exercise 1.......................................................................... 10.6.2 Exercise
2............................................................................... 10.6.3 Exercise 3............................................................................... Differential Equations................................................................................. 11.1 On the Solution of Differential Equations ....................................... 11.1.1 Existence and Uniqueness................................................... 11.1.2 Implicit and Explicit S olutions........................................... 11.1.3 Complementary and Particular Solutions.......................... 11.1.4 Verification of the Solution................................................. 11.1.5 Initial Value Problem.......................................................... 11.1.6 Analytical Solution and Numerical Solution.................... 11.1.7 Geometric Interpretation.................................................... 11.2 Methods to Solve First-Order Differential Equations .................... 11.2.1 Separation of Variables....................................................... 11.2.2 Substitution Method for Homogeneous-Type Equations . 11.2.3 Integrating Factor................................................................ 11.2.4 Exact Equations................................................................... 11.2.5 Reduction to Linearity: Bernoulli Equation...................... 11.3 Time Path and Equilibrium................................................................ 11.4 Second-Order Linear Differential Equations.................................... 11.4.1
Solution to Second-Order Linear Homogeneous Differential Equation............................................ 11.4.2 Solution to Second-Order Linear Nonhomogeneous Differential Equation............ 11.4.3 The Dynamic Stability of the Equilibrium....................... 626 627 635 637 638 639 640 642 658 664 668 668 671 676 678 683 688 688 688 689 691 692 692 693 693 694 695 696 706 709 709 711 714 717 720 723 729 730 737 741
Contents xxi 11.4.4 Method of Undetermined Coefficients .............................. System of Linear Differential Equations......................................... 11.5.1 Eigenvalues Method............................................................ 11.5.2 Equilibrium.......................................................................... Transforming High-Order Differential Equations.......................... Differential Equations with R............................................................ Applications in Economics................................................................ 11.8.1 A Problem with Interest Rate............................................ 11.8.2 Advertising Model............................................................... 11.8.3 The Harrod-Domar Growth Model................................... 11.8.4 The Solow Growth Model.................................................. Exercises.............................................................................................. 741 744 745 752 767 771 781 781 784 788 790 798 A Packages Used in Chapters........................................................................ 801 В Appendix to Chap. 2.................................................................................... 803 C Appendix to Chap. 3.................................................................................... 807 D Appendix to Chap. 4.................................................................................... 811 E Appendix to Chap.
5.................................................................................... 817 F Appendix to Chap. 7.................................................................................... 823 G Appendix to Chap. 8.................................................................................... 827 H Appendix to Chap. 9.................................................................................... 833 I Appendix to Chap. 10................................................................................. 835 J AppendixtoChap.il ................................................................................. 839 Bibliography......................................................................................................... 843 11.5 11.6 11.7 11.8 11.9 Index....................................................................................................................... 847
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Contents 1 Introduction to R. 1.1 Installing R. 1.2 Installing RStudio. 1.3 Introduction to RStudio. 1.3.1 Launching a New Project . 1.3.2 Opening an R Script. 1.4 Packages to Install. 1.4.1 How to Install a Package. 1.4.2 How to Load a Package. 1.5 Good Practice and Notation. 1.5.1 How to Read the Code . 1.6 8 Key-Points Regarding R. 1.6.1 The Assignment Operator. 1.6.2 The Class of Objects. 1.6.3 Case Sensitiveness. 1.6.4 The c() Function. 1.6.5 Square Bracket Operator [ ] . 1.6.6 Loop and
Vectorization. 1.6.7 Functions. 1.6.8 Errors. 1.7 An Example with R. 1.8 Exercise. 1.8.1 Exercise 1. 1.8.2 Exercise 2. Part I 2 1 1 2 2 3 6 7 8 8 9 11 12 12 13 14 15 16 20 24 27 32 50 50 51 Introduction to Mathematics for Static Economics Linear Algebra . 2.1 Set, Group, Ring, Field: Short Overview. 2.2 Vectors. 2.2.1 VectorSpace. 55 55 59 59 XV
xvi 3 Contents 2.2.2 Vector Representation in Two and Three Dimensions . 2.2.3 Inner Product. 2.2.4 Outer Product. 2.2.5 Component Form, Magnitude and Unit Vector. 2.2.6 Parallel and Orthogonal Vectors. 2.2.7 Vector Projection. 2.2.8 Linear Independence. 2.3 Matrices. 2.3.1 Matrix Operations. 2.3.2 Symmetric Matrix. 2.3.3 Diagonal Matrix and Identity Matrix. 2.3.4 Triangular Matrix. 2.3.5 Idempotent Matrix. 2.3.6 The Inverse of a Matrix. 2.3.7 System of Linear Equations. 2.3.8 Determinant. 2.3.9 Eigenvalues and Eigenvectors. 2.3.10 Partitioned Matrix. 2.3.11 Kronecker
Product. 2.3.12 Definiteness of Matrices. 2.3.13 Decomposition. 2.4 Applications in Economics. 2.4.1 BudgetSet . 2.4.2 Applying Cramer’s Rule to the IS-LM Model . 2.4.3 Leontief Input-Output Model. 2.4.4 Network Analysis. 2.4.5 Linear Model and the Dummy Variable Trap. 2.5 Exercises. 2.5.1 Exercise 1 . 2.5.2 Exercise 2. 2.5.3 Exercise3. 2.5.4 Exercise 4. 2.5.5 Exercise 5. 2.5.6 Exercise 6. 2.5.7 Exercise 7. 62 71 72 73 76 76 78 82 84 90 91 94 95 96 100 125 160 177 183 187 196 213 213 218
220 226 231 236 236 237 237 238 239 239 240 Functions of One Variable. 3.1 What is a Function?. 3.1.1 Domain and Range. 3.1.2 Monotonicity, Boundednessand Extrema. 3.1.3 Convex and Concave Functions. 3.1.4 Function Operations. 3.2 Linear Function. 3.2.1 Slope of Linear Function. 3.2.2 Applications in Economics. 243 243 246 248 249 249 250 251 258
xvii Contents Quadratic Function. 3.3.1 Roots and Vertex. 3.3.2 The Graph of the Quadratic Function. 3.3.3 Discriminant. 3.3.4 Applications in Economics. Cubic Function. 3.4.1 How to Solve Cubic Equations . 3.4.2 Applications in Economics. Polynomials of Degree Greater Than Three. Logarithmic and Exponential Functions. 3.6.1 What is a Logarithm?. 3.6.2 Logarithms and Exponents. 3.6.3 The Natural Logarithm. 3.6.4 The Natural Logarithmic Function . 3.6.5 Applications in Economics. 3.6.6 Exponential Function. 3.6.7 Applications in Economics. Radical Function. 3.7.1 How to Solve Radical
Equation. 3.7.2 Find the Domain of a Radical Function. 3.7.3 Radicals and Rational Exponents. 3.7.4 Applications in Economics. Rational Function . 3.8.1 Intercepts and Asymptotes. 3.8.2 Applications in Economics. Exercises. 3.9.1 Exercise 1. 3.9.2 Exercise 2. 3.9.3 Exercise 3. 3.9.4 Exercise 4. 3.9.5 Exercise 5. 266 269 271 278 284 287 289 295 297 300 300 301 304 304 309 317 323 331 335 337 338 339 341 342 344 348 348 348 349 349 349 Differential Calculus. 4.1 What is the Meaning of Derivatives?. 4.2 The Limit of a Function. 4.3 Limits, Derivatives and
Slope. 4.3.1 Newton-Raphson Method. 4.4 Notation of Derivatives . 4.5 Differentials . 4.6 Rules of Differentiation. 4.6.1 Power Rule. 4.6.2 Product Rule. 4.6.3 Quotient Rule. 4.6.4 Chain Rule. 4.6.5 Radicals Differentiation. 351 351 352 358 361 368 370 371 371 373 373 374 376 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4
xviii Conienis 4.6.6 Logarithmic Differentiation. 4.6.7 Exponential Differentiation. 4.6.8 Derivatives of Elementary Functions. Derivatives andInverse Functions. Tangent Line to the Function. Points of Minimum, Maximum and Inflection. Taylor Expansion. 4.10.1 Nth-Derivative Test. 4.10.2 Newton-Raphson Method. L’Hôpital Theorem. Derivatives with R. Taylor Expansion with R. Applications in Economics. 4.14.1 Marginal Cost. 4.14.2 Marginal Cost and Average Cost . 4.14.3 Profit Maximization. 4.14.4 Elasticity. Exercise.
4.15.1 Exercise 1. 4.15.2 Exercise 2. 4.15.3 Exercise3. 376 378 380 381 382 391 399 407 408 408 409 411 412 412 418 419 429 437 437 437 439 5Integral Calculus. 5.1 Indefinite Integrals . 5.1.1 Anti-derivative Process. 5.2 Definite Integrals. 5.2.1 Area Under a Curve. 5.2.2 Area Between Two Lines. 5.3 Fundamental Theorem of Calculus. 5.4 Improper Integrals and Convergence. 5.4.1 Case 1 : Convergence. 5.4.2 Case 2: Divergence. 5.5 Integration with R. 5.6 Applications in Economics . 5.6.1 Marginal Cost and Cost Function. 5.6.2 Example: A
Problem. 5.6.3 The Surplus of Consumerand Producer. 5.7 Exercise. 441 441 442 461 461 466 471 472 472 476 477 479 479 480 481 484 6 485 485 491 501 501 505 508 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 Multivariable Calculus. 6.1 Functions of Several Variables. 6.1.1 Applications in Economics. 6.2 Partial and Total Derivatives. 6.2.1 Partial Derivatives. 6.2.2 Total Derivatives. 6.2.3 Derivatives with R.
Contents 6.2.4 Applications in Economies. Unconstrained Optimization. 6.3.1 First Order Condition. 6.3.2 Second Order Condition. 6.3.3 Optimization with R. 6.3.4 Applications in Economics. Integration with Multiple Variables . Exercises. 6.5.1 Exercise 1 . 6.5.2 Exercise 2. 510 512 513 515 519 521 527 529 529 530 Constrained Optimization. 7.1 Equality Constraints. 7.1.1 First-Order Condition . 7.1.2 Multiple Equality Constraints. 7.1.3 Lagrange Multiplier. 7.1.4 Second-Order Conditions. 7.2 Inequality Constraints. 7.2.1 Kuhn-Tucker
Conditions. 7.3 Constrained Optimization with R . 7.4 Applications in Economics. 7.4.1 Utility Maximization Problem. 7.4.2 Firm's Cost Minimization Problem. 7.4.3 Transportation Problem. 7.4.4 CGE Model with R. 7.5 Exercise. 531 532 532 534 537 542 547 548 554 562 562 567 570 575 581 6.3 6.4 6.5 7 xix Part II Introduction to Mathematics for Dynamic Economics 8 Trigonometry. 8.1 Right Triangles and Angles. 8.2 Trigonometric Functions. 8.3 Sum and Differences of Angles. 8.4 Derivatives of Trigonometric Functions. 585 585 588 596 596 9 Complex Numbers. 9.1 Set of Complex Numbers. 9.2 Complex Numbers: Real Part and Imaginary Part. 9.3
Arithmetic Operations. 9.4 Geometric Interpretation and Polar Form. 9.5 Exponential Form . 599 599 599 601 602 604 Difference Equations. 10.1 First-Order Linear Difference Equations. 10.1.1 Solution by Iteration. 10.1.2 Solution by General Method. 10.1.3 Time Path and Equilibrium. 609 610 611 614 623 10
Contents XX 10.2 10.3 10.4 10.5 10.6 11 Second-Order Linear Difference Equations. 10.2.1 Solution to Second-Order Linear Homogeneous Difference Equation. 10.2.2 Solution to Second-Order Linear Nonhomogeneous Difference Equation . 10.2.3 Time Path and Equilibrium. System of Linear Difference Equations. 10.3.1 Equilibrium. 10.3.2 Solution with the Powers of a Matrix. 10.3.3 Eigenvalues Method. 10.3.4 Graphing Trajectory of a Discrete System . Transforming High-Order DifferenceEquations . Applications in Economics. 10.5.1 A Problem with Interest Rate. 10.5.2 The Cobweb Model. 10.5.3 The Harrod-Domar Growth Model. 10.5.4 Law of Motion for Public Debt. 10.5.5 Linear Difference Equations and Autoregressive Process Exercises. 10.6.1 Exercise 1. 10.6.2 Exercise
2. 10.6.3 Exercise 3. Differential Equations. 11.1 On the Solution of Differential Equations . 11.1.1 Existence and Uniqueness. 11.1.2 Implicit and Explicit S olutions. 11.1.3 Complementary and Particular Solutions. 11.1.4 Verification of the Solution. 11.1.5 Initial Value Problem. 11.1.6 Analytical Solution and Numerical Solution. 11.1.7 Geometric Interpretation. 11.2 Methods to Solve First-Order Differential Equations . 11.2.1 Separation of Variables. 11.2.2 Substitution Method for Homogeneous-Type Equations . 11.2.3 Integrating Factor. 11.2.4 Exact Equations. 11.2.5 Reduction to Linearity: Bernoulli Equation. 11.3 Time Path and Equilibrium. 11.4 Second-Order Linear Differential Equations. 11.4.1
Solution to Second-Order Linear Homogeneous Differential Equation. 11.4.2 Solution to Second-Order Linear Nonhomogeneous Differential Equation. 11.4.3 The Dynamic Stability of the Equilibrium. 626 627 635 637 638 639 640 642 658 664 668 668 671 676 678 683 688 688 688 689 691 692 692 693 693 694 695 696 706 709 709 711 714 717 720 723 729 730 737 741
Contents xxi 11.4.4 Method of Undetermined Coefficients . System of Linear Differential Equations. 11.5.1 Eigenvalues Method. 11.5.2 Equilibrium. Transforming High-Order Differential Equations. Differential Equations with R. Applications in Economics. 11.8.1 A Problem with Interest Rate. 11.8.2 Advertising Model. 11.8.3 The Harrod-Domar Growth Model. 11.8.4 The Solow Growth Model. Exercises. 741 744 745 752 767 771 781 781 784 788 790 798 A Packages Used in Chapters. 801 В Appendix to Chap. 2. 803 C Appendix to Chap. 3. 807 D Appendix to Chap. 4. 811 E Appendix to Chap.
5. 817 F Appendix to Chap. 7. 823 G Appendix to Chap. 8. 827 H Appendix to Chap. 9. 833 I Appendix to Chap. 10. 835 J AppendixtoChap.il . 839 Bibliography. 843 11.5 11.6 11.7 11.8 11.9 Index. 847 |
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| author | Porto, Massimiliano |
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| discipline_str_mv | Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV048532090 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:52:33Z |
| indexdate | 2024-07-10T09:40:44Z |
| institution | BVB |
| isbn | 9783031052019 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033908788 |
| oclc_num | 1351547353 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-N2 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-N2 |
| physical | xxix, 853 Seiten Diagramme |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Springer |
| record_format | marc |
| spelling | Porto, Massimiliano Verfasser (DE-588)1209134926 aut Introduction to mathematics for economics with R Massimiliano Porto Cham Springer [2022] xxix, 853 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Quantitative Economics Econometrics Statistics in Business, Management, Economics, Finance, Insurance Statistics Erscheint auch als Online-Ausgabe 978-3-031-05202-6 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033908788&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Porto, Massimiliano Introduction to mathematics for economics with R Quantitative Economics Econometrics Statistics in Business, Management, Economics, Finance, Insurance Statistics |
| title | Introduction to mathematics for economics with R |
| title_auth | Introduction to mathematics for economics with R |
| title_exact_search | Introduction to mathematics for economics with R |
| title_exact_search_txtP | Introduction to mathematics for economics with R |
| title_full | Introduction to mathematics for economics with R Massimiliano Porto |
| title_fullStr | Introduction to mathematics for economics with R Massimiliano Porto |
| title_full_unstemmed | Introduction to mathematics for economics with R Massimiliano Porto |
| title_short | Introduction to mathematics for economics with R |
| title_sort | introduction to mathematics for economics with r |
| topic | Quantitative Economics Econometrics Statistics in Business, Management, Economics, Finance, Insurance Statistics |
| topic_facet | Quantitative Economics Econometrics Statistics in Business, Management, Economics, Finance, Insurance Statistics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033908788&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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