IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/48187.html
   My bibliography  Save this paper

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

Author

Listed:
  • Todorova, Tamara

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.

Suggested Citation

  • Todorova, Tamara, 2013. "An Easy Way to Teach First-order Linear Differential and Difference Equations with a Constant Term and a Constant Coefficient," MPRA Paper 48187, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:48187
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/48187/1/MPRA_paper_48187.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293, October.
    2. Todorova, Tamara, 2010. "Problems Book to Accompany Mathematics for Economists," MPRA Paper 117866, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Todorova, Tamara, 2013. "Solving optimal timing problems elegantly," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 4(6), pages 95-105.
    2. Millock, Katrin & Xabadia, Angels & Zilberman, David, 2012. "Policy for the adoption of new environmental monitoring technologies to manage stock externalities," Journal of Environmental Economics and Management, Elsevier, vol. 64(1), pages 102-116.
    3. Terstiege, Stefan, 2013. "Precontractual Investigation and Sequential Screening," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 429, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    4. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Uniqueness of Nash Equilibrium in Continuous Weighted Potential Games," CSEF Working Papers 471, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 18 Jun 2017.
    5. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    6. Jagjit S. Chadha, 2009. "Monetary Policy Analysis: An Undergraduate Toolkit," Palgrave Macmillan Books, in: Giuseppe Fontana & Mark Setterfield (ed.), Macroeconomic Theory and Macroeconomic Pedagogy, chapter 3, pages 55-75, Palgrave Macmillan.
    7. Carina-Elena Stegăroiu & Valentin Stegăroiu, 2010. "Algorithms For The Processes Of Establishing Prices And Balanced Bank Interests," Annals of the University of Petrosani, Economics, University of Petrosani, Romania, vol. 10(4), pages 327-336.
    8. Herweg, Fabian, 2020. "Overlapping efforts in the EU Emissions Trading System," Economics Letters, Elsevier, vol. 193(C).
    9. Balart, Pau, 2021. "Semiorder preferences and price-oriented buyers in a Hotelling model," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 394-407.
    10. Miguel Viegas & Ana Ribeiro, 2015. "Welfare and inequality effects of debt consolidation processes: the case of Spain, 1996–2007," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 6(4), pages 479-496, November.
    11. Andreas Roider, 2006. "Delegation of Authority as an Optimal (In)Complete Contract," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 162(3), pages 391-411, September.
    12. Wolfram Merzyn & Gabor Virag & Stephan Lauermann, 2010. "Aggregate uncertainty and learning in a search model," 2010 Meeting Papers 1235, Society for Economic Dynamics.
    13. Sulka, Tomasz, 2022. "Planning and saving for retirement," DICE Discussion Papers 384, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    14. Yang, Hai & Leung, Cowina W.Y. & Wong, S.C. & Bell, Michael G.H., 2010. "Equilibria of bilateral taxi-customer searching and meeting on networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1067-1083, September.
    15. Jan Eeckhout & Philipp Kircher, 2010. "Sorting and Decentralized Price Competition," Econometrica, Econometric Society, vol. 78(2), pages 539-574, March.
    16. Basak Bayramoglu, 2010. "How does the design of international environmental agreements affect investment in environmentally-friendly technology?," Post-Print hal-01172961, HAL.
    17. Vasilev, Aleksandar, 2021. "How quantitatively important are shocks to consumption and income tax rates for business cycle fluctuations? Lessons from Bulgaria (1999-2020)," EconStor Preprints 243316, ZBW - Leibniz Information Centre for Economics.
    18. Cristián Troncoso-Valverde, 2018. "Releasing information in private-value second-price auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(3), pages 781-817, May.
    19. Muhammad Imran Chaudhry & Mario J. Miranda, 2024. "Endogenous price fluctuations: Evidence from the chicken supply chain in Pakistan," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(2), pages 637-658, March.
    20. Beker, Pablo F. & Cuevas, Conrado, 2018. "The social value of information in economies with mandatory savings," The Warwick Economics Research Paper Series (TWERPS) 1152, University of Warwick, Department of Economics.

    More about this item

    Keywords

    simple differential equations; simple difference equations; particular integral; complementary function; phase lines; Solow growth model;
    All these keywords.

    JEL classification:

    • A22 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Undergraduate
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:48187. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.