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Lecture 19: Introduction to Fourier Series
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Transform Calculus and Its Applications in Differential Equations
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- 1 Transform Calculus and its applications in Differential Equations
- 2 Lecture 01: Introduction to Integral Transform and Laplace Transform
- 3 Lecture 02: Existence of Laplace Transform
- 4 Lecture 03: Shifting properties of Laplace Transform
- 5 Lecture 04: Laplace Transform of Derivative and Integration of a Function - I
- 6 Lecture 05: Laplace Transform of Derivative and Integration of a Function - II
- 7 Lecture 06: Explanation of properties of Laplace Transform using Examples
- 8 Lecture 07: Laplace Transform of Periodic Function
- 9 Lecture 08: Laplace Transform of some special Functions
- 10 Lecture 09: Error Function, Dirac Delta Function and their Laplace Transform
- 11 Lecture 10: Bessel Function and its Laplace Transform
- 12 Lecture 11: Introduction to Inverse Laplace Transform
- 13 Lecture 12: Properties of Inverse Laplace Transform
- 14 Lecture 13: Convolution and its Applications
- 15 Lecture 14: Evaluation of Integrals using Laplace Transform
- 16 Lecture 15
- 17 Lecture 16
- 18 Lecture 17: Solution of Simultaneous Ordinary Differential Equations using Laplace Transform
- 19 Lecture 18: Introduction to Integral Equation and its Solution Process
- 20 Lecture 19: Introduction to Fourier Series
- 21 Lecture 20: Fourier Series for Even and Odd Functions
- 22 Lecture 21: Fourier Series of Functions having arbitrary period - I
- 23 Lecture 22: Fourier Series of Functions having arbitrary period - II
- 24 Lecture 23: Half Range Fourier Series
- 25 Lecture 24: Parseval's Theorem and its Applications
- 26 Lecture 25: Complex form of Fourier Series
- 27 Lecture 26: Fourier Integral Representation
- 28 Lecture 27: Introduction to Fourier Transform
- 29 Lecture 28: Derivation of Fourier Cosine Transform and Fourier Sine Transform of Functions
- 30 Lecture 29: Evaluation of Fourier Transform of various functions
- 31 Lecture 30: Linearity Property and Shifting Properties of Fourier Transform
- 32 Lecture 31: Change of Scale and Modulation Properties of Fourier Transform
- 33 Lecture 32: Fourier Transform of Derivative and Integral of a Function
- 34 Lecture 33: Applications of Properties of Fourier Transform - I
- 35 Lecture 34: Applications of Properties of Fourier Transform - II
- 36 Lecture 35: Fourier Transform of Convolution of two functions
- 37 Lecture 36: Parseval's Identity and its Application
- 38 Lecture 37: Evaluation of Definite Integrals using Properties of Fourier Transform
- 39 Lecture 38: Fourier Transform of Dirac Delta Function
- 40 Lecture 39: Representation of a function as Fourier Integral
- 41 Lecture 40: Applications of Fourier Transform to Ordinary Differential Equations - I
- 42 Lecture 41: Applications of Fourier Transform to Ordinary Differential Equations - II
- 43 Lecture 42: Solution of Integral Equations using Fourier Transform
- 44 Lecture 43: Introduction to Partial Differential Equations
- 45 Lecture 44: Solution of Partial Differential Equations using Laplace Transform
- 46 Lecture 45: Solution of Heat Equation and Wave Equation using Laplace Transform
- 47 Lecture 46:
- 48 Lecture 47:
- 49 Lecture 48: Solution of Partial Differential Equations using Fourier Transform - I
- 50 Lecture 49: Solution of Partial Differential Equations using Fourier Transform - II
- 51 Lecture 50: Solving problems on Partial Differential Equations using Transform Techniques
- 52 Lecture 51: Introduction to Finite Fourier Transform
- 53 Lecture 52: Solution of Boundary Value Problems using Finite Fourier Transform - I
- 54 Lecture 53: Solution of Boundary Value Problems using Finite Fourier Transform - II
- 55 Lecture 54: Introduction to Mellin Transform
- 56 Lecture 55: Properties of Mellin Transform
- 57 Lecture 56: Examples of Mellin Transform - I
- 58 Lecture 57: Examples of Mellin Transform - II
- 59 Lecture 58: Introduction to Z-Transform
- 60 Lecture 59: Properties of Z-Transform
- 61 Lecture 60: Evaluation of Z-Transform of some functions
