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Course112104318127 lectures

Applied Numerical Methods

Prof. Malay K. Das · IIT Kanpur

Start with lecture 1 At NPTEL

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

  1. Lecture 01 - Outline YouTube
  2. Lecture 02 - Course Policy YouTube
  3. Lecture 03 - Example YouTube
  4. Lecture 04 - Introduction YouTube
  5. Lecture 05 - Modeling YouTube
  6. Lecture 06 - Validation YouTube
  7. Lecture 07 - Bisection method YouTube
  8. Lecture 08 - Newton Raphson method YouTube
  9. Lecture 09 - Week 1 closure YouTube

Week 2

  1. Lecture 10 - Outline YouTube
  2. Lecture 11 - Python Fundamentals YouTube
  3. Lecture 12 - Python Fundamentals YouTube
  4. Lecture 13 - Pseudocode YouTube
  5. Lecture 14 - Python Program for gcd YouTube
  6. Lecture 15 - Numpy Fundamentals YouTube
  7. Lecture 16 - Numpy vectorized operations YouTube
  8. Lecture 17 - Numpy Exercise YouTube
  9. Lecture 18 - Python Programming: Closure YouTube

Week 3

  1. Lecture 19 - Outline YouTube
  2. Lecture 20 - Linear Algebra: Outline YouTube
  3. Lecture 21: Vectors YouTube
  4. Lecture 22: Linear Equations YouTube
  5. Lecture 23: Matrix Algebra YouTube
  6. Lecture 24: Special Matrices YouTube
  7. Lecture 25: Gaussian Elimination YouTube
  8. Lecture 26: Gaussian Elimination: Generalization YouTube
  9. Lecture 27: Gaussian Elimination: Elementary Operations YouTube
  10. Lecture 28: Partial Pivoting YouTube
  11. Lecture 29: Scaling YouTube

Week 4

  1. Lecture 30 - LU Decomposition YouTube
  2. Lecture 31 - LU Decomposition CROUT/DOOLITTLE Methods YouTube
  3. Lecture 32 - System of Simultaneous Non-Linear Equations YouTube
  4. Lecture 33 - Direct vs Iterative Linear Solvers YouTube
  5. Lecture 34 - Jacobi Iteration YouTube
  6. Lecture 35 - Gauss Seidel Method, Successive Overrelaxation YouTube
  7. Lecture 36 - Iterative Linear Solvers: Theory YouTube
  8. Lecture 37 - Iterative Linear Solvers: Convergence YouTube
  9. Lecture 38 - Eigenvalues and Eigenvectors: Power Method YouTube
  10. Lecture 39 - Inverse Power Method YouTube
  11. Lecture 40 - Power Method: Theory YouTube
  12. Lecture 41 - Closure YouTube

Week 5

  1. Lecture 42 - Outline YouTube
  2. Lecture 43 - Calculus: Outline YouTube
  3. Lecture 44 - Polynomial Interpolation YouTube
  4. Lecture 45 - Newton's Interpolating Polynomials YouTube
  5. Lecture 46 - Lagrange Interpolating Polynomials YouTube
  6. Lecture 47 - Lagrange Polynomials: Example YouTube
  7. Lecture 48 - Errors in polynomial interpolations YouTube
  8. Lecture 49 - Numerical differentiation: finite difference method YouTube
  9. Lecture 50 - Numerical Differentiation: Truncation Error YouTube
  10. Lecture 51 - Numerical Differentiation: Double Derivative YouTube
  11. Lecture 52 - Higher Order Numerical Differentiation: Finite DIfference Method YouTube
  12. Lecture 53 - Numerical Differentiation: General Procedure YouTube
  13. Lecture 54 - Numerical Differentiation: Nonuniform Grids YouTube
  14. Lecture 55 - Numerical Differentiation: Polynomial Interpolation YouTube
  15. Lecture 56 - Partial Derivatives: Numerical Procedure YouTube
  16. Lecture 57 - Numerical Differentiation: Example YouTube
  17. Lecture 58: Closure YouTube

Week 6

  1. Lecture 59: Outline YouTube
  2. Lecture 60 - Numerical Integration: Trapezoidal Rule YouTube
  3. Lecture 61 - Simpson's One-Third Rule YouTube
  4. Lecture 62 - Simpson's 3/8 rule YouTube
  5. Lecture 63 - Numerical Integration: Example YouTube
  6. Lecture 64 - Gaussian Quadrature YouTube
  7. Lecture 65 - Double Integral YouTube
  8. Lecture 66 - Closure YouTube

Week 7

  1. Lecture 67 - Outline YouTube
  2. Lecture 68 - Ordinary Differential Equations (ODE) YouTube
  3. Lecture 69 - First Order ODE YouTube
  4. Lecture 70 - Ordinary Differential Equations: Euler Method YouTube
  5. Lecture 71 - Runge-Kutta Method YouTube
  6. Lecture 72 - Higher-Order IVP YouTube
  7. Lecture 73 - Application: Poplulation Growth Models YouTube
  8. Lecture 74 - Boundary Value Problem: Shooting Method YouTube
  9. Lecture 75 - BVP: Finite Difference Method ((FDM) YouTube
  10. Lecture 76 - FDM: Differential to Difference Equations YouTube
  11. Lecture 77 - Solution of Tridiagonal Systems: Thomas Algorithm YouTube
  12. Lecture 78 - Closure YouTube

Week 8

  1. Lecture 79 - Outline YouTube
  2. Lecture 80 - Partial Differential Equations (PDE): Introduction YouTube
  3. Lecture 81 - Heat Conduction (Diffusion) Equation YouTube
  4. Lecture 82 - 1D Transient Diffusion: nondimensionalization YouTube
  5. Lecture 83 - 1D Transient Diffusion: Analytical Solution YouTube
  6. Lecture 84 - 1D Transient Diffusion: Explicit Scheme YouTube
  7. Lecture 85 - Numerical Experiments with Explicit Scheme YouTube
  8. Lecture 86 - Stability of Explicit Scheme YouTube
  9. Lecture 87 - 1D Transient Diffusion: Implicit, Crank-Nicolson (CN) Scheme YouTube
  10. Lecture 88 - Stability of Implicit, CN Schemes YouTube
  11. Lecture 89 - Closure YouTube

Week 9

  1. Lecture 90 - Outline YouTube
  2. Lecture 91 - Heat transfer in a nuclear fuel rod YouTube
  3. Lecture 92 - Discretization of Poisson's equation YouTube
  4. Lecture 93 - Review of Gauss-Seidal Method YouTube
  5. Lecture 94 - Solution of Poisson's equation YouTube
  6. Lecture 95 - Solution of Poisson's equation YouTube
  7. Lecture 96 - Validating our solution YouTube
  8. Lecture 97 - Suggested project: cooling of electronic chip YouTube
  9. Lecture 98 - Discretization: 2D unsteady conduction YouTube
  10. Lecture 99 - Alternating direction implicit (ADI) method YouTube
  11. Lecture 100 - Stability YouTube
  12. Lecture 101 - Closure YouTube

Week 10

  1. Lecture 102 - Outline YouTube
  2. Lecture 103 - Regression: Learning from data YouTube
  3. Lecture 104 - Simple Linear Regression: Theory YouTube
  4. Lecture 105 - Regression Quality YouTube
  5. Lecture 106 - Simple Linear Regression: Example YouTube
  6. Lecture 107 - Multiple Linear Regression YouTube
  7. Lecture 108 - Linear Regression: vector-matrix notation YouTube
  8. Lecture 109 - Nonlinear Regression: Linearization YouTube
  9. Lecture 110 - Regression: Closure YouTube

Week 11

  1. Lecture 111 - Outline YouTube
  2. Lecture 112 - Optimization: example, definition YouTube
  3. Lecture 113 - 1D unconstrained optimization: Random search YouTube
  4. Lecture 114 - Golden Section Search YouTube
  5. Lecture 115 - Newton-Raphson Method YouTube
  6. Lecture 116 - Multidimensional unconstrained optimization YouTube
  7. Lecture 117 - Gradients and its significance YouTube
  8. Lecture 118 - Steepest Descent Method YouTube
  9. Lecture 119 - Steepest Descent: Exercise YouTube
  10. Lecture 120 - Newton's Method YouTube
  11. Lecture 121 - Optimization: Closure YouTube

Week 12

  1. Lecture 122 - Outline YouTube
  2. Lecture 123 - Machine Learning YouTube
  3. Lecture 124 - Artificial Neuron YouTube
  4. Lecture 125 - Artificial Neuron: Perception YouTube
  5. Lecture 126 - Artificial Neural Network YouTube
  6. Lecture 127 - Artificial Neural Network: Closure YouTube

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.
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