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September 23, 2023

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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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