Learn · Mathematical Methods and its Applications
Lecture 12 of 60Week 3
Solution of second order differential equations by changing dependent variables
Prof. S. K. Gupta and Prof. P. N. Agrawal · IIT Roorkee
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- Mathematical Methods and its Applications, IIT Roorkee (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- Introduction to linear differential equations
- Linear dependence, independence and Wronskian of functions, Existence and Uniqueness theorem
- Solution of second order homogeneous linear differential equations with constant coefficient-
- Solution of second order homogeneous linear differential equations with constant coefficient-II
- Methods of Undetermined coefficients
- Methods for finding particular integrals for second order linear differential equations with constant coefficients I
- Methods for finding particular integrals for second order linear differential equations with constant coefficients II
- Methods for finding particular integrals for second order linear differential equations with constant coefficients III
- Cauchy-Euler equation
- Methods of reduction for second order-linear differential equations
- Methods of variation of parameters
- Solution of second order differential equations by changing dependent variables
- Solution of second order differential equations by changing independent variable
- Solution of higher-order homogeneous linear differential equations with constant coefficients
- Methods for finding particular integral for higher-order linear differential equations with constant coefficient s
- Formulation of partial differential equations
- Solution of Lagrange's equation I
- Solution of Lagranage's equations II
- Solution of first order non-linear equation I
- Solution of first order non-linear equation II
- Solution of first order non linear equation III
- Solution of first order non linear equation IV
- Introduction to Laplace transforms
- Laplace transforms of some standard functions
- Existence theorem for Laplace transforms
- Properties of Laplace transforms-I
- Properties of Laplace transforms-II
- Properties of Laplace transforms-III
- Properties of Laplace transforms-IV
- Convolution Theorem for Laplace Transforms-I
- Convolution Theorem for Laplace Transforms-II
- Initial and Final Value Theorems for Laplace Transforms
- Laplace Transforms of Periodic Functions
- Laplace Transforms of Unit Step Function
- Laplace Transforms of Dirac delta Functions
- Applications of Laplace Transforms-I
- Applications of Laplace Transforms-II
- Applications of Laplace Transforms-III
- Z- transform and inverse Z- transform of elemetary functions
- Properties of Z-transforms-I
- Properties of Z - transformatons - II
- Initial and final theorems for Z- transforms
- Convolution theorem for Z-transforms
- Convergence of Z- transform
- Application of Z-transforms-I
- Applications of Z- transform- II
- Fourier Series and its Convergence-I
- Fourier Series and its Convergence-II
- Fourier Series of Even and Odd functions
- Fourier half-range series
- Parseval’s Identity
- Complex form of Fourier series
- Fourier integrals
- Fourier sine and cosine integrals
- Fourier transforms
- Fourier sine and cosine transforms
- Convolution theorem for Fourier transforms
- Applications of Fourier transforms to BVP–I
- Applications of Fourier transforms to BVP–II
- Applications of Fourier transforms to BVP–III