Course11110512368 lectures
Transform Calculus and its applications in Differential Equations
Prof. Adrijit Goswami · IIT Kharagpur
Lectures
Week 1 :
- Lecture 1 : Introduction to Integral Transform and Laplace Transform
- Lecture 2 : Existence of Laplace Transform
- Lecture 3 : Shifting Properties of Laplace Transform
- Lecture 4 : Laplace Transform of Derivatives and Integration of a Function - I
- Lecture 5 : Laplace Transform of Derivatives and Integration of a Function - II
Week 2 :
- Lecture 06: Explanation of properties of Laplace Transform using Examples
- Lecture 07: Laplace Transform of Periodic Function
- Lecture 08: Laplace Transform of some special Functions
- Lecture 09: Error Function, Dirac Delta Function and their Laplace Transform
- Lecture 10: Bessel Function and its Laplace Transform
Week 3 :
- Lecture 11: Introduction to Inverse Laplace Transform
- Lecture 12: Properties of Inverse Laplace Transform
- Lecture 13: Convolution and its Applications
- Lecture 14: Evaluation of Integrals using Laplace Transform
- Lecture 15: Solution of Ordinary Differential Equations with constant coefficients using Laplace Transform
Week 4 :
- Lecture 16 : Solution of Ordinary Differential Equations with variable coefficients using Laplace Transform
- Lecture 17 : Solution of Simultaneous Ordinary Differential Equations using Laplace Transform
- Lecture 18 : Introduction to Integral Equation and its Solution Process
- Lecture 19 : Introduction to Fourier Series
- Lecture 20 : Fourier Series for Even and Odd Functions
Week 5 :
- Lecture 21: Fourier Series of Functions having arbitrary period - I
- Lecture 22: Fourier Series of Functions having arbitrary period - II
- Lecture 23: Half Range Fourier Series
- Lecture 24: Parseval's Theorem and its Applications
- Lecture 25: Complex form of Fourier Series
Week 6 :
- Lecture 26: Fourier Integral Representation
- Lecture 27: Introduction to Fourier Transform
- Lecture 28: Derivation of Fourier Cosine Transform and Fourier Sine Transform of Functions
- Lecture 29: Evaluation of Fourier Transform of various functions
- Lecture 30: Linearity Property and Shifting Properties of Fourier Transform
Week 7 :
- Lecture 31: Change of Scale and Modulation Properties of Fourier Transform
- Lecture 32: Fourier Transform of Derivative and Integral of a Function
- Lecture 33: Applications of Properties of Fourier Transform - I
- Lecture 34: Applications of Properties of Fourier Transform - II
- Lecture 35: Fourier Transform of Convolution of two functions
Week 8 :
- Lecture 36: Parseval's Identity and its Application
- Lecture 37: Evaluation of Definite Integrals using Properties of Fourier Transform
- Lecture 38: Fourier Transform of Dirac Delta Function
- Lecture 39: Representation of a function as Fourier Integral
- Lecture 40: Applications of Fourier Transform to Ordinary Differential Equations - I
Week 9 :
- Lecture 41 : Applications of Fourier Transform to Ordinary Differential Equations - II
- Lecture 42 : Solution of Integral Equations using Fourier Transform
- Lecture 43 : Introduction to Partial Differential Equations
- Lecture 44 : Solution of Partial Differential Equations using Laplace Transform
- Lecture 45 : Solution of Heat Equation and Wave Equation using Laplace Transform
Week 10 :
- Lecture 46 : Criteria for choosing Fourier Transform, Fourier Sine Transform, Fourier Cosine Transform in solving Partial Differential Equations
- Lecture 47 : Solution of Partial Differential Equations using Fourier Cosine Transform and Fourier Sine Transform
- Lecture 48 : Solution of Partial Differential Equations using Fourier Transform - I
- Lecture 49 : Solution of Partial Differential Equations using Fourier Transform - II
- Lecture 50 : Solving problems on Partial Differential Equations using Transform Techniques
Week 11 :
- Lecture 51: Introduction to Finite Fourier Transform
- Lecture 52: Solution of Boundary Value Problems using Finite Fourier Transform - I
- Lecture 53: Solution of Boundary Value Problems using Finite Fourier Transform - II
- Lecture 54: Introduction to Mellin Transform
- Lecture 55: Properties of Mellin Transform
Week 12 :
- Lecture 56: Examples of Mellin Transform - I
- Lecture 57: Examples of Mellin Transform - II
- Lecture 58: Introduction to Z-Transform
- Lecture 59: Properties of Z-Transform
- Lecture 60: Evaluation of Z-Transform of some functions
Live Session
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Kharagpur
- Department
- Mathematics
- Teacher
- Prof. Adrijit Goswami
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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