Course112104318127 lectures
Applied Numerical Methods
Prof. Malay K. Das · IIT Kanpur
About
Objective: - To approximately solve problems of algebra and calculus, using repetitive calculations, implemented in a computer
Learning Outcome: At the end of the course the students should be able to
- write the algorithms for numerical solution of basic problems of algebra and calculus, such as solution of algebraic and differential equations, optimization using gradient descent, prediction using regression,
- implement the above algorithms in a computer writing their own programs from scratch,
- write the limitations of the above algorithms, and
- solve complex problems combining multiple algorithms.
Intended audience: 3rd, 4th year UG students and PG students in any branch of engineering
Prerequisites: Undergraduate engineering mathematics Knowledge of a programming language (preferable)
Lectures
Week 1
- Lecture 01 - Outline
- Lecture 02 - Course Policy
- Lecture 03 - Example
- Lecture 04 - Introduction
- Lecture 05 - Modeling
- Lecture 06 - Validation
- Lecture 07 - Bisection method
- Lecture 08 - Newton Raphson method
- Lecture 09 - Week 1 closure
Week 2
- Lecture 10 - Outline
- Lecture 11 - Python Fundamentals
- Lecture 12 - Python Fundamentals
- Lecture 13 - Pseudocode
- Lecture 14 - Python Program for gcd
- Lecture 15 - Numpy Fundamentals
- Lecture 16 - Numpy vectorized operations
- Lecture 17 - Numpy Exercise
- Lecture 18 - Python Programming: Closure
Week 3
- Lecture 19 - Outline
- Lecture 20 - Linear Algebra: Outline
- Lecture 21: Vectors
- Lecture 22: Linear Equations
- Lecture 23: Matrix Algebra
- Lecture 24: Special Matrices
- Lecture 25: Gaussian Elimination
- Lecture 26: Gaussian Elimination: Generalization
- Lecture 27: Gaussian Elimination: Elementary Operations
- Lecture 28: Partial Pivoting
- Lecture 29: Scaling
Week 4
- Lecture 30 - LU Decomposition
- Lecture 31 - LU Decomposition CROUT/DOOLITTLE Methods
- Lecture 32 - System of Simultaneous Non-Linear Equations
- Lecture 33 - Direct vs Iterative Linear Solvers
- Lecture 34 - Jacobi Iteration
- Lecture 35 - Gauss Seidel Method, Successive Overrelaxation
- Lecture 36 - Iterative Linear Solvers: Theory
- Lecture 37 - Iterative Linear Solvers: Convergence
- Lecture 38 - Eigenvalues and Eigenvectors: Power Method
- Lecture 39 - Inverse Power Method
- Lecture 40 - Power Method: Theory
- Lecture 41 - Closure
Week 5
- Lecture 42 - Outline
- Lecture 43 - Calculus: Outline
- Lecture 44 - Polynomial Interpolation
- Lecture 45 - Newton's Interpolating Polynomials
- Lecture 46 - Lagrange Interpolating Polynomials
- Lecture 47 - Lagrange Polynomials: Example
- Lecture 48 - Errors in polynomial interpolations
- Lecture 49 - Numerical differentiation: finite difference method
- Lecture 50 - Numerical Differentiation: Truncation Error
- Lecture 51 - Numerical Differentiation: Double Derivative
- Lecture 52 - Higher Order Numerical Differentiation: Finite DIfference Method
- Lecture 53 - Numerical Differentiation: General Procedure
- Lecture 54 - Numerical Differentiation: Nonuniform Grids
- Lecture 55 - Numerical Differentiation: Polynomial Interpolation
- Lecture 56 - Partial Derivatives: Numerical Procedure
- Lecture 57 - Numerical Differentiation: Example
- Lecture 58: Closure
Week 6
- Lecture 59: Outline
- Lecture 60 - Numerical Integration: Trapezoidal Rule
- Lecture 61 - Simpson's One-Third Rule
- Lecture 62 - Simpson's 3/8 rule
- Lecture 63 - Numerical Integration: Example
- Lecture 64 - Gaussian Quadrature
- Lecture 65 - Double Integral
- Lecture 66 - Closure
Week 7
- Lecture 67 - Outline
- Lecture 68 - Ordinary Differential Equations (ODE)
- Lecture 69 - First Order ODE
- Lecture 70 - Ordinary Differential Equations: Euler Method
- Lecture 71 - Runge-Kutta Method
- Lecture 72 - Higher-Order IVP
- Lecture 73 - Application: Poplulation Growth Models
- Lecture 74 - Boundary Value Problem: Shooting Method
- Lecture 75 - BVP: Finite Difference Method ((FDM)
- Lecture 76 - FDM: Differential to Difference Equations
- Lecture 77 - Solution of Tridiagonal Systems: Thomas Algorithm
- Lecture 78 - Closure
Week 8
- Lecture 79 - Outline
- Lecture 80 - Partial Differential Equations (PDE): Introduction
- Lecture 81 - Heat Conduction (Diffusion) Equation
- Lecture 82 - 1D Transient Diffusion: nondimensionalization
- Lecture 83 - 1D Transient Diffusion: Analytical Solution
- Lecture 84 - 1D Transient Diffusion: Explicit Scheme
- Lecture 85 - Numerical Experiments with Explicit Scheme
- Lecture 86 - Stability of Explicit Scheme
- Lecture 87 - 1D Transient Diffusion: Implicit, Crank-Nicolson (CN) Scheme
- Lecture 88 - Stability of Implicit, CN Schemes
- Lecture 89 - Closure
Week 9
- Lecture 90 - Outline
- Lecture 91 - Heat transfer in a nuclear fuel rod
- Lecture 92 - Discretization of Poisson's equation
- Lecture 93 - Review of Gauss-Seidal Method
- Lecture 94 - Solution of Poisson's equation
- Lecture 95 - Solution of Poisson's equation
- Lecture 96 - Validating our solution
- Lecture 97 - Suggested project: cooling of electronic chip
- Lecture 98 - Discretization: 2D unsteady conduction
- Lecture 99 - Alternating direction implicit (ADI) method
- Lecture 100 - Stability
- Lecture 101 - Closure
Week 10
- Lecture 102 - Outline
- Lecture 103 - Regression: Learning from data
- Lecture 104 - Simple Linear Regression: Theory
- Lecture 105 - Regression Quality
- Lecture 106 - Simple Linear Regression: Example
- Lecture 107 - Multiple Linear Regression
- Lecture 108 - Linear Regression: vector-matrix notation
- Lecture 109 - Nonlinear Regression: Linearization
- Lecture 110 - Regression: Closure
Week 11
- Lecture 111 - Outline
- Lecture 112 - Optimization: example, definition
- Lecture 113 - 1D unconstrained optimization: Random search
- Lecture 114 - Golden Section Search
- Lecture 115 - Newton-Raphson Method
- Lecture 116 - Multidimensional unconstrained optimization
- Lecture 117 - Gradients and its significance
- Lecture 118 - Steepest Descent Method
- Lecture 119 - Steepest Descent: Exercise
- Lecture 120 - Newton's Method
- Lecture 121 - Optimization: Closure
Week 12
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Kanpur
- Department
- Mechanical Engineering
- Teacher
- Prof. Malay K. Das
- Level
- Graduate
- 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