Transform Calculus and its applications in Differential Equations
Indian Institute of Technology, Kharagpur and NPTEL via Swayam
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43
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Overview
INTENDED AUDIENCE : MATHEMATICS(Any student with a course in Mathematics in their curriculum)PREREQUISITES : NONEINDUSTRY SUPPORT : NONE
Syllabus
COURSE LAYOUT
Week 1: Introduction to Laplace transform: Definition and propertiesWeek 2: Laplace Transform of derivatives and integrals
Week 3: Laplace Transform of some special functions
Week 4: Inverse Laplace Transform
Week 5: Application of Laplace Transform to Ordinary Differential Equationsand Integral Equations
Week 6: Fourier Series
Week 7: Introduction to Fourier Transforms: Definition and properties
Week 8: Fourier Sine and Cosine transforms of different functions
Week 9: Parseval’s Identity for Fourier Sine and Cosine Transforms
Week 10: Application of Fourier Transform to Ordinary Differential Equations and Integral Equations
Week 11: Application of Fourier Transform to Partial Differential Equations
Week 12: Finite Fourier transform and its application to Boundary ValuedProblems.
Taught by
Prof. Adrijit Goswami
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