Lebelo, RSFedotov, IShatalov, M2009-03-242009-03-242008-09Lebelo, RS, Fedotov, I and Shatalov, M. 2008. Solution of heat equation with variable coefficient using derive. Technology and its Integration into Mathematics Education Conference (TIME). Buffelspoort, South Africa, 22 - 26 September 2008, pp 129 -1379780620434546http://hdl.handle.net/10204/3244Buffelspoort TIME2008 Peer-reviewed Conference Proceedings, 22 – 26 SeptemberIn this paper, the method of approximating solutions of partial differential equations with variable coefficients is studied. This is done by considering heat flow through a one-dimensional model with variable cross-sections. Two cases are considered. The first one involves quadratic approximation of the variable coefficient by direct integration. This case is studied using a conic domain. The second case approximates the variable coefficient quadratically and by step functions. The solution of the problem in each case is expressed using Green's function, and the results are compared. By the suitable use of a computer algebra system (CAS) all of these ideas can easily enough be introduced at the advanced undergraduate levelenPartial differential equationsCoefficientsGreen's functionHeat flowComputer algebra systemCASTechnology and its Integration into Mathematics Education ConferenceTIMEBuffelspoort TIME2008 Peer-reviewed Conference ProceedingsConference PresentationLebelo, R., Fedotov, I., & Shatalov, M. (2008). Solution of heat equation with variable coefficient using derive. Buffelspoort TIME2008 Peer-reviewed Conference Proceedings. http://hdl.handle.net/10204/3244Lebelo, RS, I Fedotov, and M Shatalov. "Solution of heat equation with variable coefficient using derive." (2008): http://hdl.handle.net/10204/3244Lebelo R, Fedotov I, Shatalov M, Solution of heat equation with variable coefficient using derive; Buffelspoort TIME2008 Peer-reviewed Conference Proceedings; 2008. http://hdl.handle.net/10204/3244 .TY - Conference Presentation AU - Lebelo, RS AU - Fedotov, I AU - Shatalov, M AB - In this paper, the method of approximating solutions of partial differential equations with variable coefficients is studied. This is done by considering heat flow through a one-dimensional model with variable cross-sections. Two cases are considered. The first one involves quadratic approximation of the variable coefficient by direct integration. This case is studied using a conic domain. The second case approximates the variable coefficient quadratically and by step functions. The solution of the problem in each case is expressed using Green's function, and the results are compared. By the suitable use of a computer algebra system (CAS) all of these ideas can easily enough be introduced at the advanced undergraduate level DA - 2008-09 DB - ResearchSpace DP - CSIR KW - Partial differential equations KW - Coefficients KW - Green's function KW - Heat flow KW - Computer algebra system KW - CAS KW - Technology and its Integration into Mathematics Education Conference KW - TIME KW - Buffelspoort TIME2008 Peer-reviewed Conference Proceedings LK - https://researchspace.csir.co.za PY - 2008 SM - 9780620434546 T1 - Solution of heat equation with variable coefficient using derive TI - Solution of heat equation with variable coefficient using derive UR - http://hdl.handle.net/10204/3244 ER -