NDLI: Lecture-13: ODE: Solution of Exact ODEs, First Order Linear Systems - Transcript [English]

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Aerospace Engineering

Acoustic Instabilities in Aerospace Propulsion

Advanced Control System Design for Aerospace Vehicles

Aero elasticity

Aerospace Propulsion

Aircraft Performance, Stability and control with experiments in Flight

Aircraft Structural Dynamics

Airplane design (Aerodynamic)

Composite Materials

Composite Materials and Structures

Experimental Gas/Aerodynamics

Flight Dynamics II (Stability)

Flight dynamics I - Airplane performance

Flight dynamics II - Airplane stability and control

Foundation of Scientific Computing

Fundamentals of Combustion

Guidance of Missiles

High Speed Aero Dynamics

Hypersonic Aerodynamics

Instability and Transition of Fluid Flows

Introduction to Aerodynamics

Introduction to Aerospace Propulsion

Introduction to CFD

Introduction to Helicopter Aerodynamics and Dynamics

Introduction to Propulsion

Introduction to Turbulent Flows and their prediction

Jet Aircraft Propulsion

Jet and Rocket Propulsion

NOC:Advance Aircraft Maintenance

NOC:Aerodynamic Design of Axial Flow Compressors & Fans

NOC:Aircraft Design

NOC:Aircraft Dynamic Stability & Design Stability Augmentation System

NOC:Aircraft Maintenance

NOC:Aircraft Stability and Control

NOC:Aircraft Structures - I

NOC:Combustion in air breathing aero engines

NOC:Computational Science in Engineering

Week-01: Linear Algebra: Introduction to Vectors, Vector spaces and subspaces, Solving Linear systems

Week-02: Linear Algebra: Orthogonality, Determinants, Eigenvalues & Eigen vectors, SVD

Week-03: Ordinary Differential Equations: ODE, Homogeneous and Non-homogeneous ODEs, Second Order Linear ODE, Higher Order ODEs

Week-04: Solution of Higher Order ODEs, Fourier Analysis, Fourier Integrals, Laplace Transforms

Week-05: Partial Differential Equations: Classification, 1D & 2D Equations, BC, 2nd Order PDEs

Week-06: Basis of Numerical Analysis, Errors, Stability, Interpolation and Extrapolation

Week-07: System of Linear Algebraic Equations and Eigenvalue Problems: Direct Methods, Iterative Methods, Convergence Analysis, Eigenvalues and Eigenvectors, Bounds on Eigenvalues, Methods for Symmetric Matrices and Arbitrary Matrices

Week-08: Solution of ODEs: Difference equation, Numerical methods, convergence, stability, Single step and multistep methods, Predictor-corrector methods, stability analysis of multistep methods, IVP (shooting methods), BVP (methods and solutions)

Lecture-01: Linear Algebra: Introduction - Transcript

Lecture-02: Linear Algebra: Introduction (contd.) - Transcript

Lecture-03: Linear Algebra: Permutation Matrix, Existence of Solution - Transcript

Lecture-04: Linear Algebra: Permutation Matrix, Existence of Solution (contd.) - Transcript

Lecture-05: Linear Algebra: Linear Independence, Basis Vector and Dimensions - Transcript

Lecture-06: Linear Algebra: Null Space, Column Space, Row Space, Introduction to Orthogonal System - Transcript

Lecture-07: Linear Algebra: Orthogonal System, Projection, Determinant - Transcript

Lecture-08: Linear Algebra: Orthogonal System, Projection, Determinant (contd.) - Transcript

Lecture-09: Linear Algebra: Properties of Determinant, Cramer's Rule, Introduction to Eigen Values - Transcript

Lecture-10: Linear Algebra: Eigen Values, Eigen Vectors, SVD - Transcript

Lecture-11: Linear Algebra: Eigen Values, Eigen Vectors, SVD (contd.) - Transcript

Lecture-12: ODE: Introduction to ODEs, Initial Value Problem, Separation of Variables - Transcript

Lecture-13: ODE: Solution of Exact ODEs, First Order Linear Systems - Transcript

Lecture-14: ODE: Solution of Second Order Linear ODEs - Transcript

Lecture-15: ODE: Existence and Uniqueness of Solution, Non-Homogeneous System - Transcript

Lecture-16: ODE: Higher Order Linear ODEs, Variation of Parameters, System of ODEs - Transcript

Lecture-17: ODE: Linear Systems, Superposition for Homogeneous Systems - Transcript

Lecture-18: Fourier Analysis, Orthogonality of Trigonometric Systems, Euler's Formula - Transcript

Lecture-19: Parseval's Theorem, Fourier Integrals, Laplace Transforms - Transcript

Lecture-20: PDE: Introduction to PDEs, Solution of PDEs using Characteristics Curve - Transcript

Lecture-21: PDE: First Order PDEs, Dilation Invariant Solution of Differential Equations - Transcript

Lecture-22: PDE: Solution of Linear PDEs - Transcript

Lecture-23: PDE: Separation of Variables, Eigenvalue Problem, Poisson Integral Representation - Transcript

Lecture-24: PDE: Boundary Conditions, Solution of 2D systems - Transcript

Lecture-25: Introduction to Numerical Methods, Mathematical Models, Errors - Transcript

Lecture-26: Errors, Numerical Differentiation, Stability - Transcript

Lecture-27: Roots of Equations: Graphical Method, Bi-Section Mehtod, False-Position Method - Transcript

Lecture-28: Secant Method, Brent's Method, Multipoint Iteration Method, Derative Free Method - Transcript

Lecture-29: Complex Roots, Birge-Vieta Method, Bairstow's method - Transcript

Lecture-30: Solution of Linear Algebric Equations, Gauss Elimination Method - Transcript

Lecture-31: Direct Methods: Gauss Elimination, Gauss-Jordan, Crout's Method, Cholesky Method, Iterative Methods: Jacobi Iteration Method, Gauss-Seidel - Transcript

Lecture-32: Extrapolation Method, Eigenvalue Problem, Jacobi Method, Householder's Method for Symmetric Matrices, Power Method, Inverse Power Method - Transcript

Lecture-33: Interpolation: Taylor's Series, Lagrange and Newton Interpolation, Iterated Interpolation, Hermite Interpolation, Finite Difference Operations - Transcript

Lecture-34: Piecewise and Spline Interpolation, Bivariate Interpolation, Least Square Approximation, Uniform Polynomial Approximation - Transcript

Lecture-35: Numerical Differentiation and Intergration, Methods Based on Finite Differences, Methods based on Undetermined Coefficients, Extrapolation Methods, Partial Differentiation - Transcript

Lecture-36: Numerical Integration: Newton-Cotes Method, Gaussian Integration Methods, Lobatto Integration Method, Radau Integration Method, Composite Integration Methods - Transcript

Lecture-37: Double Integration: Trapezoidal Rule, Simpson's Rule, Solution of ODEs: Difference Equation, Single Step Methods, Explicit Methods - Transcript

Lecture-38: Runge-Kutta Methods, Euler-Cauchy Method, Multi-step Methods, Predictor-Corrector Methods - Transcript

Lecture-39: System of Differential Equations, Stability Analysis, Solution of Boundary Value Problem: Shooting Method - Transcript

Lecture-40: Numerical Approach to Solution of PDEs: Heat Conduction Equation, Convergence and Stability - Transcript

NOC:Design of fixed wing Unmanned Aerial Vehicles

NOC:Engineering Thermodynamics

NOC:Fundamentals Of Combustion - I

NOC:Fundamentals of Combustion (Part 2)

NOC:Fundamentals of Theoretical and Experimental Aerodynamics

NOC:Gasdynamics: Fundamentals and Applications

NOC:Introduction to Aerospace Engineering

NOC:Introduction to Airbreathing Propulsion

NOC:Introduction to Aircraft Design

NOC:Introduction to Ancient Indian Technology

NOC:Introduction to CFD

NOC:Introduction to Experiments in Flight

NOC:Introduction to Finite Volume Methods I

NOC:Introduction to Finite Volume Methods II

NOC:Introduction to Launch Vehicle Analysis and Design

NOC:Introduction to Rocket Propulsion

NOC:Introduction to airplane performance

NOC:Lighter than Air Systems

NOC:Rocket Propulsion

NOC:Satellite Attitude Dynamics and Control

NOC:Space Flight Mechanics

NOC:UAV Design - Part II

NOC:Vibration and Structural Dynamics

Navigation, Guidance, And Control

Optimal Control, Guidance and Estimation

Principles of Fluid Dynamics

Space Flight Mechanics

Space Technology

Turbomachinery Aerodynamics

Atmospheric Science

Basic courses-Sem 1 and 2

Chemical Engineering

Chemistry and Biochemistry

Civil Engineering

Computer Science and Engineering

Electrical Engineering

Electronics & Communication Engineering

Engineering Design

Environmental Science

Humanities and Social Sciences

Mechanical Engineering

Metallurgy and Material Science

Mining Engineering

Multidisciplinary

Ocean Engineering

Textile Engineering

Lecture-13: ODE: Solution of Exact ODEs, First Order Linear Systems - Transcript [English]

Content Provider	NPTEL
Author	De, Ashoke
Organization	IIT Kanpur
Abstract	The Computational Science in Engineering is a rapidly evolving field that exploits the power of computation as an approach to major challenges on the frontiers of natural and social science and all engineering fields. The primary focus lies on developing problem-solving methodologies and robust tools for numerical simulation. The goal is to present the fundamentals of scientific computing, with short codes to implement the key concepts. This includes a framework for applied mathematics such as Linear Algebra, ODEs and PDEs. To understand phenomena and processes from science and engineering, these simulations require advanced skills in mathematical modelling, numerical analysis, efficient algorithms, computer architecture, software design and implementation, validation, and visualization of results.
Unique ID	101104086
Language	English
Access Restriction	Open
Subject Keyword	Post Graduate Course Under Graduate Course Higher Education Remote Studies Web Resources Web Course Undergraduate/Post Graduate Engineering Course Lectures Basic Science Course Lecture Undergraduate Engineering Course Engineering Video Course Engineering Course Content Course Assignments Transcripted Engineering Video Course NPTEL Course Content Post Graduate Engineering Course Self-learning Engineering Course Engineering Course e-content Online Engineering Course Content Open Online Engineering Course UG Engineering Course Engineering Course Lectures PG Engineering Course Lectures UG Engineering Course Lectures PG Engineering Course Learning Video Course Course-based Video Lecture Lecture Notes Video Lecture Courseware Aerospace Engineering
Content Type	Text
Educational Use	Self Learning Research
Resource Type	Course Material
Education Level	Under Graduate Post Graduate
Subject	Other branches of engineering

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