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Mathematical Methods and its Applications

Mathematical Methods and its Applications. Instructors: Dr. P. N. Agarwal and Dr. S. K. Gupta, Department of Mathematics, IIT Roorkee. This course is a basic course offered to students of Engineering/Science background. It contains ODE, PDE, Laplace transforms, z-transforms, Fourier series and Fourier transforms. It plays an important role for solving various engineering sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences. (from nptel.ac.in)

Introduction to Linear Differential Equations


Lecture 01 - Introduction to Linear Differential Equations
Lecture 02 - Linear Dependence, Independence and Wronskian of Functions
Lecture 03 - Solution of Second Order Homogenous Linear Differential Equations with Constant Coefficients I
Lecture 04 - Solution of Second Order Homogenous Linear Differential Equations with Constant Coefficients II
Lecture 05 - Method of Undetermined Coefficients
Lecture 06 - Methods for Finding Particular Integral for Second Order Linear Differential Equations with Constant Coefficients I
Lecture 07 - Methods for Finding Particular Integral for Second Order Linear Differential Equations with Constant Coefficients II
Lecture 08 - Methods for Finding Particular Integral for Second Order Linear Differential Equations with Constant Coefficients III
Lecture 09 - Cauchy-Euler Equation
Lecture 10 - Method of Reduction for Second Order Linear Differential Equations
Lecture 11 - Method of Variation of Parameters
Lecture 12 - Solution of Second Order Differential Equations by Changing Dependent Variable
Lecture 13 - Solution of Second Order Differential Equations by Changing Independent Variable
Lecture 14 - Solution of Higher Order Homogeneous Linear Differential Equations with Constant Coefficients
Lecture 15 - Methods for Finding Particular Integral for Higher Order Linear Differential Equations
Lecture 16 - Formulation of Partial Differential Equations
Lecture 17 - Solution of Lagrange Equation I
Lecture 18 - Solution of Lagrange Equation II
Lecture 19 - Solution of First Order Nonlinear Equations I
Lecture 20 - Solution of First Order Nonlinear Equations II
Lecture 21 - Solution of First Order Nonlinear Equations III
Lecture 22 - Solution of First Order Nonlinear Equations IV
Lecture 23 - Introduction to Laplace Transforms
Lecture 24 - Laplace Transforms of Some Standard Functions
Lecture 25 - Existence Theorem for Laplace Transforms
Lecture 26 - Properties of Laplace Transforms I
Lecture 27 - Properties of Laplace Transforms II
Lecture 28 - Properties of Laplace Transforms III
Lecture 29 - Properties of Laplace Transforms IV
Lecture 30 - Convolution Theorem for Laplace Transforms I
Lecture 31 - Convolution Theorem for Laplace Transforms II
Lecture 32 - Initial and Final Value Theorems for Laplace Transforms
Lecture 33 - Laplace Transforms of Periodic Functions
Lecture 34 - Laplace Transforms of Heaviside Unit Step Function
Lecture 35 - Laplace Transforms of Dirac Delta Functions
Lecture 36 - Applications of Laplace Transforms I
Lecture 37 - Applications of Laplace Transforms II
Lecture 38 - Applications of Laplace Transforms III
Lecture 39 - z-Transform and Inverse z-Transform of Elementary Functions
Lecture 40 - Properties of z-Transforms I
Lecture 41 - Properties of z-Transforms II
Lecture 42 - Initial and Final Value Theorem for z-Transforms
Lecture 43 - Convolution Theorem for z-Transforms
Lecture 44 - Convergence of z-Transform
Lecture 45 - Applications of z-Transforms I
Lecture 46 - Applications of z-Transforms II
Lecture 47 - Fourier Series and its Convergence I
Lecture 48 - Fourier Series and its Convergence II
Lecture 49 - Fourier Series of Even and Odd Functions
Lecture 50 - Fourier Half-range Series
Lecture 51 - Parseval's Identity
Lecture 52 - Complex Form of Fourier Series
Lecture 53 - Fourier Integrals
Lecture 54 - Fourier Sine and Cosine Integrals
Lecture 55 - Fourier Transforms
Lecture 56 - Fourier Sine and Cosine Transforms
Lecture 57 - Convolution Theorem for Fourier Transforms
Lecture 58 - Applications of Fourier Transforms to Boundary Value Problem I
Lecture 59 - Applications of Fourier Transforms to Boundary Value Problem II
Lecture 60 - Applications of Fourier Transforms to Boundary Value Problem III

References
Mathematical Methods and its Applications
Instructors: Dr. P. N. Agarwal and Dr. S. K. Gupta, Department of Mathematics, IIT Roorkee. This course contains ODE, PDE, Laplace transforms, z-transforms, Fourier series and Fourier transforms.