MAT201 ComplexVariablesandPartialDifferentialEquations LTPC3104

VersionNo. 1.1 CoursePrerequisites

MAT105Differential And Difference Equations Objectives The aim of this course is to develop the skills of the students in the areas of complex variables, evaluation of definite integral by using contour integration, boundary value problems and trans form techniques. This will be necessary for their effective studies in Engineering subjects like heat conduction, fluid flow and electric current flow etc.

ExpectedOutcome At the end of this course, the students are expected to develop the necessary mathematical skills, physical understanding of problems and intuition to independently analyze the mathematical equations which model the problems in their respective fields of study. Unit1 FunctionsofaComplexVariable 9+3 hours Limits and continuity- Cauchy Riemann equations- analytic and harmonic functions complex potential applications to flow around a corner and around a cylinder, bilinear transformations-cross-ratio- conformal mapping and mapping properties of

zewzw == ,2 . Unit2 ComplexIntegration 9+3 hours Integration of a complex plane along a contour Statement of Cauchy-Goursat theorem,Cauchys integral formula Evaluation of contour integral- Taylor and Laurent series- zeros- singularities poles- residues- Statement of Cauchys residue theorem evaluation of integrals by the method of residues- Integration over a unit circle-semi-circular contour. Unit3 FourierTransforms 9+3 hours Complex form of Fourier series Fourier integral theorem- Fourier transform pairs Fourier sine and cosine transform pairs simple problems-properties of Fourier transforms Convolution theorem for Fourier transforms Parsevals identity for Fourier transforms . Unit4 PartialDifferentialEquations 9+3 Hours Formation of PDEs solutions of PDEs- solution of standard four types of first order PDE - Lagranges linear equations linear PDE of higher order with constant coefficients homogeneous and non homogeneous equations solution of PDEs by the method of separation of variables. Unit5 ApplicationsofPartialDifferentialEquations 9+3 Hours One dimensional wave equations one dimensional heat equations - Fourier series solutions. Heat flow in an infinite bar - Wave propagation on a semi infinite string Two dimensional heat equations in steady state- using Fourier transforms.

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Proceedings of the 26th Academic Council held on 18.5.2012

HPCross-Out

HPReplacement TextVersion : 1.20

TextBooks 1. B.S. Grewal, HigherEngineeringMathematics, 40th Edition. Khanna Publications (2010). (TopicsintheChapters:17,18,19,20,22)

ReferenceBooks

1. Erwin Kreysizing, Advanced EngineeringMathematics, 9th Edition, John Wiley & Sons, (Wiley student Edison)(2011)

2. MichaelD. Greenberg, Advanced Engineering Mathematics, 2nd Edition, Pearson Education (2002).

3. Peter V. O Neil, AdvancedEngineeringMathematics, 5th Edition, Thomson, Book/Cole (2003).

ModeofEvaluation: RecommendedbytheBoardofStudieson:12052012

DateofapprovalbytheAcademicCouncil:

817

Proceedings of the 26th Academic Council held on 18.5.2012

Minutes of 25th Academic Council (06-04-2012).pdfMinutes of 25th Academic Council (06-04-2012)25AC Minutes - Signed page

26th AC Minutes.pdfMinutes of the 26th AC26AC Signed last page

SC_7.8.10_MAT511 Advanced Numerical Methods 3 1 0 4.pdfMinutes of the SC of AC (Aug 2010)Minutes of SC on 7Aug2010 - Signed page only1. Dir(Acad) items.pdfGraduandsListAug10 Final - For SC proceedingsSheet1

Dir(Acad) itemsGraduandsList(04-Aug-2010)Graduands Summary

Dir(Acad) itemsGraduandsList(04-Aug-2010)Graduands Summary

Dir(Acad) items

GraduandsListAug10 Final - For SC proceedings - Modified-27.8.10.pdfSheet1

Minutes of the Standing Committee held on 07.08.2010.pdfMinutes of the SC of AC (Aug 2010)Minutes of SC on 7Aug2010 - Signed page onlyMinutes of the Standing Committee held on 07.08.10_pg3.pdfMinutes of the SC of AC (Aug 2010)Minutes of SC on 7Aug2010 - Signed page only

26_cover page.pdfMinutes of 25th Academic Council (06-04-2012).pdfMinutes of 25th Academic Council (06-04-2012)25AC Minutes - Signed page

26th AC Minutes.pdfMinutes of the 26th AC26AC Signed last page

SC_7.8.10_MAT511 Advanced Numerical Methods 3 1 0 4.pdfMinutes of the SC of AC (Aug 2010)Minutes of SC on 7Aug2010 - Signed page only1. Dir(Acad) items.pdfGraduandsListAug10 Final - For SC proceedingsSheet1

Dir(Acad) itemsGraduandsList(04-Aug-2010)Graduands Summary

Dir(Acad) itemsGraduandsList(04-Aug-2010)Graduands Summary

Dir(Acad) items

GraduandsListAug10 Final - For SC proceedings - Modified-27.8.10.pdfSheet1

Minutes of the Standing Committee held on 07.08.2010.pdfMinutes of the SC of AC (Aug 2010)Minutes of SC on 7Aug2010 - Signed page onlyMinutes of the Standing Committee held on 07.08.10_pg3.pdfMinutes of the SC of AC (Aug 2010)Minutes of SC on 7Aug2010 - Signed page only

26_cover page.pdfMinutes of 25th Academic Council (06-04-2012).pdfMinutes of 25th Academic Council (06-04-2012)25AC Minutes - Signed page

26th AC Minutes.pdfMinutes of the 26th AC26AC Signed last page

SC_7.8.10_MAT511 Advanced Numerical Methods 3 1 0 4.pdfMinutes of the SC of AC (Aug 2010)Minutes of SC on 7Aug2010 - Signed page only1. Dir(Acad) items.pdfGraduandsListAug10 Final - For SC proceedingsSheet1

Dir(Acad) itemsGraduandsList(04-Aug-2010)Graduands Summary

Dir(Acad) itemsGraduandsList(04-Aug-2010)Graduands Summary

Dir(Acad) items

GraduandsListAug10 Final - For SC proceedings - Modified-27.8.10.pdfSheet1

Minutes of the Standing Committee held on 07.08.2010.pdfMinutes of the SC of AC (Aug 2010)Minutes of SC on 7Aug2010 - Signed page onlyMinutes of the Standing Committee held on 07.08.10_pg3.pdfMinutes of the SC of AC (Aug 2010)Minutes of SC on 7Aug2010 - Signed page only