Course11210403540 lectures
Mathematical Methods in Engineering and Science
Prof. Bhaskar Dasgupta · IIT Kanpur
Lectures
Module I. Solution of Linear Systems
- Introduction
- Basic Ideas of Applied Linear Algebra
- Systems of Linear Equations
- Square Non-Singular Systems
- Ill-Conditioned and Ill-Posed Systems
Module II. The Algebraic Eigenvalue Problem
- The Algebraic Eigenvalue Problem
- Canonical Forms, Symmetric Matrices
- Methods of Plane Rotations
- Householder Method, Tridiagonal Matrices
- QR Decomposition, General Matrices
Module III. Selected Topics in Linear Algebra and Calculus
- Singular Value Decomposition
- Vector Space: Concepts
- Multivariate Calculus
- Vector Calculus in Geometry
- Vector Calculus in Physics
Module IV. An Introductory Outline of Optimization Techniques
- Solution of Equations
- Introdcution to Optimization
- Multivariate Optimization
- Constrained Optimization: Optimality Criteria
- Constrained Optimization: Further Issues
Module V. Selected Topics in Numerical Analysis
- Interpolation
- Numerical Integration
- Numerical Solution of ODE's as IVP
- Boundary Value Problems, Question of Stability in IVP Solution
- Stiff Differential Equations, Existence and Uniqueness Theory
Module VI. Ordinary Differential Equations
- Theory of First Order ODE's
- Linear Second Order ODE's
- Methods of Linear ODE's
- ODE Systems
- Stability of Dynamic Systems
Module VII. Application of ODE\'s in Approximation Theory
- Series Solutions and Special Functions
- Sturm-Liouville Theory
- Approximation Theory and Fourier Series
- Fourier Integral to Fourier Transform, Minimax Approximation
Module VIII. Overviews: PDE\'s, Complex Analysis and Variational Calculus
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Kanpur
- Department
- Mechanical Engineering
- Teacher
- Prof. Bhaskar Dasgupta
- Level
- Undergraduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
More like this
NPTEL101104001
Course
Computational Fluid Dynamics using the Finite Element Method
45 lectures · Source's player
NPTEL101104061
Course
Introduction to Airplane Performance
48 lectures · Source's player
NPTEL101104062
Course
Aircraft Stability and Control
61 lectures · Source's player
NPTEL101104078
Course
Introduction to Rocket Propulsion
60 lectures · Source's player
NPTEL101104084
Course
Introduction to Airbreathing Propulsion
60 lectures · Source's player
NPTEL101104450
Course
Applied Computational Fluid Dynamics
62 lectures · Source's player
NPTEL101104796
Course
Space Environment and its Effects on Orbital Spacecrafts
62 lectures · Source's player
NPTEL101104013
Course
Foundation of Scientific Computing
39 lectures · Video
NPTEL101104015
Course
Instability and Transition of Fluid Flows
39 lectures · Video
NPTEL101104018
Course
Introduction to Propulsion
40 lectures · Video
NPTEL101104019
Course
Jet and Rocket Propulsion
40 lectures · Video
NPTEL101104063
Course
Engineering Thermodynamics
38 lectures · Video