# InfoCoBuild

## 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.