Todorova, Tamara
(2013):
*An Easy Way to Teach First-order Linear Differential and Difference Equations with a Constant Term and a Constant Coefficient.*

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## Abstract

We present a simple method of solving first-order linear differential and difference equations with a constant term and a constant coefficient. When solving such equations standard books in mathematical economics resort to a particular integral and a complementary function without further explaining those to beginning undergraduate students. We use the derivative and the difference, respectively, which give rise to a number of parental functions whose time path is studied by economic dynamics. A derived function is “shared” by multiple parental functions, but a number of parental functions give rise to one derived function. The method is smooth and easy to understand. Instead of spending time on complicated theoretical math techniques, the professor teaching quantitative methods could emphasize substantive economic models applying such simple equations.

Item Type: | MPRA Paper |
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Original Title: | An Easy Way to Teach First-order Linear Differential and Difference Equations with a Constant Term and a Constant Coefficient |

English Title: | An Easy Way to Teach First-order Linear Differential and Difference Equations with a Constant Term and a Constant Coefficient |

Language: | English |

Keywords: | simple differential equations, simple difference equations, particular integral, complementary function, phase lines, Solow growth model |

Subjects: | A - General Economics and Teaching > A2 - Economic Education and Teaching of Economics > A22 - Undergraduate C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling |

Item ID: | 48187 |

Depositing User: | Dr. Tamara Todorova |

Date Deposited: | 10 Jul 2013 07:42 |

Last Modified: | 26 Sep 2019 20:39 |

References: | 1. Chiang, Alpha C., “Fundamental Methods of Mathematical Economics,” McGraw-Hill Inc., 3rd edition, 1984 2. de la Fuente, Angel, “Mathematical Methods and Models for Economists,” Cambridge University Press, 2000 3. Dowling, Edward T., "Introduction to Mathematical Economics," in Schaum's Outline Series, 2nd edition, McGraw Hill, 1992 4. Intriligator, Michael D., “Mathematical Optimization and Economic Theory,” Society for Industrial and Applied Mathematics, Philadelphia, 2002, republication from Prentice-Hall, Englewood Cliffs, New Jersey, 1971 5. Pemberton, Malcolm and Nicholas Rau, "Mathematics for Economists," Manchester University Press, 2001 6. Rainville, Earl David, Phillip E. Bedient and Richard E. Bedient, “Elementary Differential Equations,” Prentice Hall, Upper Saddle River, NJ 07458, 8th edition, 1996 7. Silberberg, Eugene and Wing Suen, “The Structure of Economics: A Mathematical Analysis,” McGraw-Hill/Irwin, 2000 8. Simon, Carl and Lawrence Blume, “Mathematics for Economists,” W. W. Norton and Company, 1994 9. Todorova, Tamara, “Problems Book to Accompany Mathematics for Economists,” Wiley-Blackwell, Hoboken, New Jersey, 2010 |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/48187 |