Transform Calculus and Its Applications In Differential Equations

For undergraduate students in the discipline of Mathematics, the course on Transform Calculus has become an integral part. This course is designed to train students with the basic Integral Transform techniques.Application of these transforms techniques in solving ordinary differential equations and partial differential equations will be discussed. We will also introduce some higher level concepts that will prepare them for future research and development projects. The course outline is given for each week. We will introduce each topic and give an overview of the topic and underlying theory. This will be followed by some solved numerical examples on each topic for their better understanding. Weekly assignments will be provided and gradedINTENDED AUDIENCE : MATHEMATICS(Any student with a course in Mathematics in their curriculum)PREREQUISITES : NONEINDUSTRY SUPPORT : NONE

Week 1: Introduction to Laplace transform: Definition and properties
Week 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.