# Applied Numerical Methods

- Institution: IIT Kanpur
- Department: Mechanical Engineering
- Teacher: Prof. Malay K. Das
- Level: Graduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/112104318)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/112104318)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Lecture 01 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/d177a5367e83) (YouTube)
2. [Lecture 02 - Course Policy](https://invisiblenetwork.ai/learn/nptel/112104318/970742de0b1c) (YouTube)
3. [Lecture 03 - Example](https://invisiblenetwork.ai/learn/nptel/112104318/877d384e6632) (YouTube)
4. [Lecture 04 - Introduction](https://invisiblenetwork.ai/learn/nptel/112104318/0c22e4337874) (YouTube)
5. [Lecture 05 - Modeling](https://invisiblenetwork.ai/learn/nptel/112104318/dc3549e2ff9e) (YouTube)
6. [Lecture 06 - Validation](https://invisiblenetwork.ai/learn/nptel/112104318/ab8ab04043fb) (YouTube)
7. [Lecture 07 - Bisection method](https://invisiblenetwork.ai/learn/nptel/112104318/6053106bc5fa) (YouTube)
8. [Lecture 08 - Newton Raphson method](https://invisiblenetwork.ai/learn/nptel/112104318/63b22ba19d09) (YouTube)
9. [Lecture 09 - Week 1 closure](https://invisiblenetwork.ai/learn/nptel/112104318/5f37658fd1ed) (YouTube)
10. [Lecture 10 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/9544b74246c6) (YouTube)
11. [Lecture 11 - Python Fundamentals](https://invisiblenetwork.ai/learn/nptel/112104318/b1368246e462) (YouTube)
12. [Lecture 12 - Python Fundamentals](https://invisiblenetwork.ai/learn/nptel/112104318/75546d650475) (YouTube)
13. [Lecture 13 - Pseudocode](https://invisiblenetwork.ai/learn/nptel/112104318/f7ecd89b33d8) (YouTube)
14. [Lecture 14 - Python Program for gcd](https://invisiblenetwork.ai/learn/nptel/112104318/5f34cf8f1ddd) (YouTube)
15. [Lecture 15 - Numpy Fundamentals](https://invisiblenetwork.ai/learn/nptel/112104318/540c684636a9) (YouTube)
16. [Lecture 16 - Numpy vectorized operations](https://invisiblenetwork.ai/learn/nptel/112104318/5d8286b8db1b) (YouTube)
17. [Lecture 17 - Numpy Exercise](https://invisiblenetwork.ai/learn/nptel/112104318/a6ae4fa12241) (YouTube)
18. [Lecture 18 - Python Programming: Closure](https://invisiblenetwork.ai/learn/nptel/112104318/61b131bb5ff5) (YouTube)
19. [Lecture 19 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/1f83077accbe) (YouTube)
20. [Lecture 20 - Linear Algebra: Outline](https://invisiblenetwork.ai/learn/nptel/112104318/1f056aad5de2) (YouTube)
21. [Lecture 21: Vectors](https://invisiblenetwork.ai/learn/nptel/112104318/a8f882ba745d) (YouTube)
22. [Lecture 22: Linear Equations](https://invisiblenetwork.ai/learn/nptel/112104318/d5b9607bfa49) (YouTube)
23. [Lecture 23: Matrix Algebra](https://invisiblenetwork.ai/learn/nptel/112104318/c3cc1535e585) (YouTube)
24. [Lecture 24: Special Matrices](https://invisiblenetwork.ai/learn/nptel/112104318/31048d483c1b) (YouTube)
25. [Lecture 25: Gaussian Elimination](https://invisiblenetwork.ai/learn/nptel/112104318/c550405785bb) (YouTube)
26. [Lecture 26: Gaussian Elimination: Generalization](https://invisiblenetwork.ai/learn/nptel/112104318/fe416a224fa1) (YouTube)
27. [Lecture 27: Gaussian Elimination: Elementary Operations](https://invisiblenetwork.ai/learn/nptel/112104318/da4450e89ad2) (YouTube)
28. [Lecture 28: Partial Pivoting](https://invisiblenetwork.ai/learn/nptel/112104318/2df63c53cc98) (YouTube)
29. [Lecture 29: Scaling](https://invisiblenetwork.ai/learn/nptel/112104318/6651783e1db5) (YouTube)
30. [Lecture 30 - LU Decomposition](https://invisiblenetwork.ai/learn/nptel/112104318/f4f27fae5378) (YouTube)
31. [Lecture 31 - LU Decomposition CROUT/DOOLITTLE Methods](https://invisiblenetwork.ai/learn/nptel/112104318/9199767a30b2) (YouTube)
32. [Lecture 32 - System of Simultaneous Non-Linear Equations](https://invisiblenetwork.ai/learn/nptel/112104318/07c86b195551) (YouTube)
33. [Lecture 33 - Direct vs Iterative Linear Solvers](https://invisiblenetwork.ai/learn/nptel/112104318/3d73d356961e) (YouTube)
34. [Lecture 34 - Jacobi Iteration](https://invisiblenetwork.ai/learn/nptel/112104318/ae9277acd25a) (YouTube)
35. [Lecture 35 - Gauss Seidel Method, Successive Overrelaxation](https://invisiblenetwork.ai/learn/nptel/112104318/35da73bb7834) (YouTube)
36. [Lecture 36 - Iterative Linear Solvers: Theory](https://invisiblenetwork.ai/learn/nptel/112104318/4f3323b91a7d) (YouTube)
37. [Lecture 37 - Iterative Linear Solvers: Convergence](https://invisiblenetwork.ai/learn/nptel/112104318/e874d427e624) (YouTube)
38. [Lecture 38 - Eigenvalues and Eigenvectors: Power Method](https://invisiblenetwork.ai/learn/nptel/112104318/27c115116fec) (YouTube)
39. [Lecture 39 - Inverse Power Method](https://invisiblenetwork.ai/learn/nptel/112104318/aa196199ec60) (YouTube)
40. [Lecture 40 - Power Method: Theory](https://invisiblenetwork.ai/learn/nptel/112104318/48d3d0f0a52d) (YouTube)
41. [Lecture 41 - Closure](https://invisiblenetwork.ai/learn/nptel/112104318/2b3f2df2b36f) (YouTube)
42. [Lecture 42 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/b5383090f3a0) (YouTube)
43. [Lecture 43 - Calculus: Outline](https://invisiblenetwork.ai/learn/nptel/112104318/4c1d6424304e) (YouTube)
44. [Lecture 44 - Polynomial Interpolation](https://invisiblenetwork.ai/learn/nptel/112104318/10b741be3514) (YouTube)
45. [Lecture 45 - Newton's Interpolating Polynomials](https://invisiblenetwork.ai/learn/nptel/112104318/53f01e05c410) (YouTube)
46. [Lecture 46 - Lagrange Interpolating Polynomials](https://invisiblenetwork.ai/learn/nptel/112104318/3af573ba9a2b) (YouTube)
47. [Lecture 47 - Lagrange Polynomials: Example](https://invisiblenetwork.ai/learn/nptel/112104318/473e9635bd4f) (YouTube)
48. [Lecture 48 - Errors in polynomial interpolations](https://invisiblenetwork.ai/learn/nptel/112104318/c76e2eb33a12) (YouTube)
49. [Lecture 49 - Numerical differentiation: finite difference method](https://invisiblenetwork.ai/learn/nptel/112104318/7ac440060077) (YouTube)
50. [Lecture 50 - Numerical Differentiation: Truncation Error](https://invisiblenetwork.ai/learn/nptel/112104318/46ad58efe603) (YouTube)
51. [Lecture 51 - Numerical Differentiation: Double Derivative](https://invisiblenetwork.ai/learn/nptel/112104318/cebc6ef88dc1) (YouTube)
52. [Lecture 52 - Higher Order Numerical Differentiation: Finite DIfference Method](https://invisiblenetwork.ai/learn/nptel/112104318/19f05076b23a) (YouTube)
53. [Lecture 53 - Numerical Differentiation: General Procedure](https://invisiblenetwork.ai/learn/nptel/112104318/7017fc1bdcfe) (YouTube)
54. [Lecture 54 - Numerical Differentiation: Nonuniform Grids](https://invisiblenetwork.ai/learn/nptel/112104318/45d8768b5249) (YouTube)
55. [Lecture 55 - Numerical Differentiation: Polynomial Interpolation](https://invisiblenetwork.ai/learn/nptel/112104318/83679a900114) (YouTube)
56. [Lecture 56 - Partial Derivatives: Numerical Procedure](https://invisiblenetwork.ai/learn/nptel/112104318/0ab09aefe405) (YouTube)
57. [Lecture 57 - Numerical Differentiation: Example](https://invisiblenetwork.ai/learn/nptel/112104318/9ea24c0fb972) (YouTube)
58. [Lecture 58: Closure](https://invisiblenetwork.ai/learn/nptel/112104318/b5d83e661aad) (YouTube)
59. [Lecture 59: Outline](https://invisiblenetwork.ai/learn/nptel/112104318/aba5a7786c67) (YouTube)
60. [Lecture 60 - Numerical Integration: Trapezoidal Rule](https://invisiblenetwork.ai/learn/nptel/112104318/a24850f765ec) (YouTube)
61. [Lecture 61 - Simpson's One-Third Rule](https://invisiblenetwork.ai/learn/nptel/112104318/6c0ed9bff5b4) (YouTube)
62. [Lecture 62 - Simpson's 3/8 rule](https://invisiblenetwork.ai/learn/nptel/112104318/48d141c31355) (YouTube)
63. [Lecture 63 - Numerical Integration: Example](https://invisiblenetwork.ai/learn/nptel/112104318/adeb43ce22c4) (YouTube)
64. [Lecture 64 - Gaussian Quadrature](https://invisiblenetwork.ai/learn/nptel/112104318/d7112137123b) (YouTube)
65. [Lecture 65 - Double Integral](https://invisiblenetwork.ai/learn/nptel/112104318/dddb2654feb6) (YouTube)
66. [Lecture 66 - Closure](https://invisiblenetwork.ai/learn/nptel/112104318/267de2167f45) (YouTube)
67. [Lecture 67 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/6029d3aa36d0) (YouTube)
68. [Lecture 68 - Ordinary Differential Equations (ODE)](https://invisiblenetwork.ai/learn/nptel/112104318/09d89b770395) (YouTube)
69. [Lecture 69 - First Order ODE](https://invisiblenetwork.ai/learn/nptel/112104318/5cf0bacfe482) (YouTube)
70. [Lecture 70 - Ordinary Differential Equations: Euler Method](https://invisiblenetwork.ai/learn/nptel/112104318/ba693d4fced7) (YouTube)
71. [Lecture 71 - Runge-Kutta Method](https://invisiblenetwork.ai/learn/nptel/112104318/99bad9823680) (YouTube)
72. [Lecture 72 - Higher-Order IVP](https://invisiblenetwork.ai/learn/nptel/112104318/40a20690a6be) (YouTube)
73. [Lecture 73 - Application: Poplulation Growth Models](https://invisiblenetwork.ai/learn/nptel/112104318/75a6f0fcedf1) (YouTube)
74. [Lecture 74 - Boundary Value Problem: Shooting Method](https://invisiblenetwork.ai/learn/nptel/112104318/be02c5fd71bc) (YouTube)
75. [Lecture 75 - BVP: Finite Difference Method ((FDM)](https://invisiblenetwork.ai/learn/nptel/112104318/d0d2f421a455) (YouTube)
76. [Lecture 76 - FDM: Differential to Difference Equations](https://invisiblenetwork.ai/learn/nptel/112104318/4c3ea7a0bfa8) (YouTube)
77. [Lecture 77 - Solution of Tridiagonal Systems: Thomas Algorithm](https://invisiblenetwork.ai/learn/nptel/112104318/fe659379ac00) (YouTube)
78. [Lecture 78 - Closure](https://invisiblenetwork.ai/learn/nptel/112104318/a16aa5ca629c) (YouTube)
79. [Lecture 79 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/caa6e42c21e6) (YouTube)
80. [Lecture 80 - Partial Differential Equations (PDE): Introduction](https://invisiblenetwork.ai/learn/nptel/112104318/5f06741408aa) (YouTube)
81. [Lecture 81 - Heat Conduction (Diffusion) Equation](https://invisiblenetwork.ai/learn/nptel/112104318/fc25e0c2d18d) (YouTube)
82. [Lecture 82 - 1D Transient Diffusion: nondimensionalization](https://invisiblenetwork.ai/learn/nptel/112104318/f22f3d535f22) (YouTube)
83. [Lecture 83 - 1D Transient Diffusion: Analytical Solution](https://invisiblenetwork.ai/learn/nptel/112104318/eee0ceff0e1d) (YouTube)
84. [Lecture 84 - 1D Transient Diffusion: Explicit Scheme](https://invisiblenetwork.ai/learn/nptel/112104318/86565bef3b4f) (YouTube)
85. [Lecture 85 - Numerical Experiments with Explicit Scheme](https://invisiblenetwork.ai/learn/nptel/112104318/b2709ef68314) (YouTube)
86. [Lecture 86 - Stability of Explicit Scheme](https://invisiblenetwork.ai/learn/nptel/112104318/a40d01bb30f6) (YouTube)
87. [Lecture 87 - 1D Transient Diffusion: Implicit, Crank-Nicolson (CN) Scheme](https://invisiblenetwork.ai/learn/nptel/112104318/4a4064611a25) (YouTube)
88. [Lecture 88 - Stability of Implicit, CN Schemes](https://invisiblenetwork.ai/learn/nptel/112104318/6bdc3d23344c) (YouTube)
89. [Lecture 89 - Closure](https://invisiblenetwork.ai/learn/nptel/112104318/e31f1b05148d) (YouTube)
90. [Lecture 90 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/605c1ab4726d) (YouTube)
91. [Lecture 91 - Heat transfer in a nuclear fuel rod](https://invisiblenetwork.ai/learn/nptel/112104318/f3d108b271c7) (YouTube)
92. [Lecture 92 - Discretization of Poisson's equation](https://invisiblenetwork.ai/learn/nptel/112104318/9c29ac0f3d6a) (YouTube)
93. [Lecture 93 - Review of Gauss-Seidal Method](https://invisiblenetwork.ai/learn/nptel/112104318/d9f4fe6e8922) (YouTube)
94. [Lecture 94 - Solution of Poisson's equation](https://invisiblenetwork.ai/learn/nptel/112104318/ce9552e0058b) (YouTube)
95. [Lecture 95 - Solution of Poisson's equation](https://invisiblenetwork.ai/learn/nptel/112104318/1c93f0994924) (YouTube)
96. [Lecture 96 - Validating our solution](https://invisiblenetwork.ai/learn/nptel/112104318/cffa1c15f094) (YouTube)
97. [Lecture 97 - Suggested project: cooling of electronic chip](https://invisiblenetwork.ai/learn/nptel/112104318/c4a9c2cb8df3) (YouTube)
98. [Lecture 98 - Discretization: 2D unsteady conduction](https://invisiblenetwork.ai/learn/nptel/112104318/4afdc6b8cdc4) (YouTube)
99. [Lecture 99 - Alternating direction implicit (ADI) method](https://invisiblenetwork.ai/learn/nptel/112104318/dfc51ec14856) (YouTube)
100. [Lecture 100 - Stability](https://invisiblenetwork.ai/learn/nptel/112104318/46cded792ea7) (YouTube)
101. [Lecture 101 - Closure](https://invisiblenetwork.ai/learn/nptel/112104318/cac62b9ac8c4) (YouTube)
102. [Lecture 102 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/217a44318a2d) (YouTube)
103. [Lecture 103 - Regression: Learning from data](https://invisiblenetwork.ai/learn/nptel/112104318/320ce80c7302) (YouTube)
104. [Lecture 104 - Simple Linear Regression: Theory](https://invisiblenetwork.ai/learn/nptel/112104318/49909a3b8c10) (YouTube)
105. [Lecture 105 - Regression Quality](https://invisiblenetwork.ai/learn/nptel/112104318/a28d42a2b9df) (YouTube)
106. [Lecture 106 - Simple Linear Regression: Example](https://invisiblenetwork.ai/learn/nptel/112104318/a4926d31883a) (YouTube)
107. [Lecture 107 - Multiple Linear Regression](https://invisiblenetwork.ai/learn/nptel/112104318/87680fa50a44) (YouTube)
108. [Lecture 108 - Linear Regression: vector-matrix notation](https://invisiblenetwork.ai/learn/nptel/112104318/2770851a029a) (YouTube)
109. [Lecture 109 - Nonlinear Regression: Linearization](https://invisiblenetwork.ai/learn/nptel/112104318/3fda4479a1bc) (YouTube)
110. [Lecture 110 - Regression: Closure](https://invisiblenetwork.ai/learn/nptel/112104318/669f4142eaac) (YouTube)
111. [Lecture 111 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/f6864e187390) (YouTube)
112. [Lecture 112 - Optimization: example, definition](https://invisiblenetwork.ai/learn/nptel/112104318/aab665e25811) (YouTube)
113. [Lecture 113 - 1D unconstrained optimization: Random search](https://invisiblenetwork.ai/learn/nptel/112104318/d94d9c0e5a89) (YouTube)
114. [Lecture 114 - Golden Section Search](https://invisiblenetwork.ai/learn/nptel/112104318/0f0f09296526) (YouTube)
115. [Lecture 115 - Newton-Raphson Method](https://invisiblenetwork.ai/learn/nptel/112104318/afc96f0d3a49) (YouTube)
116. [Lecture 116 - Multidimensional unconstrained optimization](https://invisiblenetwork.ai/learn/nptel/112104318/61f6a3e56075) (YouTube)
117. [Lecture 117 - Gradients and its significance](https://invisiblenetwork.ai/learn/nptel/112104318/b90312870fa2) (YouTube)
118. [Lecture 118 - Steepest Descent Method](https://invisiblenetwork.ai/learn/nptel/112104318/e0e92abeeff2) (YouTube)
119. [Lecture 119 - Steepest Descent: Exercise](https://invisiblenetwork.ai/learn/nptel/112104318/7bb52f8c81d9) (YouTube)
120. [Lecture 120 - Newton's Method](https://invisiblenetwork.ai/learn/nptel/112104318/858ecf953b93) (YouTube)
121. [Lecture 121 - Optimization: Closure](https://invisiblenetwork.ai/learn/nptel/112104318/20889bac1112) (YouTube)
122. [Lecture 122 - Outline](https://invisiblenetwork.ai/learn/nptel/112104318/525048a485d4) (YouTube)
123. [Lecture 123 - Machine Learning](https://invisiblenetwork.ai/learn/nptel/112104318/44d580b1a9dd) (YouTube)
124. [Lecture 124 - Artificial Neuron](https://invisiblenetwork.ai/learn/nptel/112104318/565b5e704202) (YouTube)
125. [Lecture 125 - Artificial Neuron: Perception](https://invisiblenetwork.ai/learn/nptel/112104318/73e89bfd3009) (YouTube)
126. [Lecture 126 - Artificial Neural Network](https://invisiblenetwork.ai/learn/nptel/112104318/67034012af25) (YouTube)
127. [Lecture 127 - Artificial Neural Network: Closure](https://invisiblenetwork.ai/learn/nptel/112104318/3fd44514c04e) (YouTube)