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## Last updated:

September 23, 2023

## Duration:

Unlimited Duration

**FREE**

## This course includes:

Unlimited Duration

## Badge on Completion

## Certificate of completion

Unlimited Duration

### Description

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**)

### Course Curriculum

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

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