ME502

ME502 [Applied Numerical Methods]  -  1st Semester 2023-24

Course Outline [PDF File]

Course content: Introduction and motivation, Types of solutions, algorithms and programming languages, error analysis, types of errors, Roots of equations, bracketing methods, graphical method, bisection method, false-position method, open methods, Newton-Raphson method, Secant method, convergence & divergence, Interpolation and polynomial approximation, Finite difference approximations, Newton’s forward and backward differences, Lagrange’s interpolation, divided differences, Cubic spline method, Numerical integration and differentiation, Differentiation using finite difference operators, Richardson’s method, differentiation using interpolation, trapezoidal rule, Simpson’s rule, Solutions of systems of linear algebraic equations, Matrix inversion and Eigen value problems, Gaussian elimination method, Gauss-Jordan elimination method, Solutions of ordinary and partial differential equations, Taylor series method, Euler method, Runge-Kutta method, finite difference methods, explicit, implicit, Crank-Nicholson method, alternate direction implicit method, finite volume method. 

Useful books:

• Steven C. Chapra, and Raymond P. Canale, Numerical Methods for Engineers, 8th ed., McGraw Hill Education India Pvt Ltd, India, 2021.

• M.K. Jain, S.R.K. Iyenger, R.K. Jain, Numerical Methods for Scientific and Engineering Computation, 7th Ed., New Age International, New Delhi, 2019.

Assignments:

• Assignment#1, Sample solution of Assign#1 (File) {Approximations, Errors, Taylor Series}

• Assignment#2, Sample solution of Assign#2 (File) {Roots of equations}

• Assignment#3, Sample solution of Assign#3 (File) {Curve Fitting}

• Assignment#4 {Numerical Differentiation & Integration, Ordinary Differential Equations}

Tests & Exams:

• Sample solution of Mid-Sem Exam (File)

• Sample solution of End-Sem Exam (File)

Some useful files:

• EXCEL Files: 

  • • Plotting polynomials (XLS file)

    • Taylor Series Approximation - Solved Example (XLS file)

    • Bisection method - Solved Example (XLS file)

    • Linear systems of equations (XLS File)

    • Linear regression (XLS File)

    • Numerical Differentiation - Example of Error in Data (XLS File)

    • ODE - Euler's method (XLS File)

• SCILAB Files:

  • • Basics of SCILAB (File), Creating Graphs/Plots in Scilab (File), Control flows, loops, conditions, in Scilab (File)

    • Bisection method (File)

    • Linear systems of equations, using matrix operations (File)

    • Some applications of numerical methods in Heat Transfer (Conduction)

      • 1-D Heat Conduction (Steady State), 1-D Heat Conduction (Transient State)

      • Handwritten notes on 1-D Steady State Heat Conduction (PDF file), 1-D Transient State Heat Conduction (PDF file)

      • 2-D Heat Conduction - (Steady State*), 2-D Heat Conduction (Transient State*)   *Credit:  These files were created by Abhishek S. Kashyap (PhD Scholar)

• MATLAB Files:

  • • 1-D Heat Conduction (Steady State), 1-D Heat Conduction (Transient State)

    • Handwritten notes on 1-D Steady State Heat Conduction (PDF file), 1-D Transient State Heat Conduction (PDF file)

• Python Files:

  • • ODE: Solution of Lotka-Volterra equations, Predator-prey model, (Link to read-only *.ipynb file) using RK1 Euler's technique

    • ODE: Solution of Lorenz equations (Link to read-only *.ipynb file) using RK1 Euler's technique

    • 1-D Heat Conduction Steady State (Link to read-only *.ipynb file)

Notes/slides:

• File , File

Useful links:

• SCILAB {Scilab is a free and open source software for engineers & scientists}

  • Link for downloading SCILAB version 6.0.2 (Link1) (Link2)

  • Useful Youtube videos (How to install Scilab Link) (Introduction to Scilab Link)

• PYTHON {Python is a free and open source programming language}

  • Link for downloading PYTHON (https://www.python.org)

• FOSSEE (Free/Libre and Open Source Software for Education) The FOSSEE project is part of the National Mission on Education through Information and Communication Technology (ICT), Ministry of Education (MoE), Government of India, and is located at IIT Bombay campus. (Link: https://fossee.in/)

• MIT OpenCourseWare

  • Linear Algebra (Basics of matrix theory and linear algebra): It includes 34 video lectures; available on YouTube  (Link)

• Differential Equations

  • List of linear ordinary differential equations (Link on Wikipedia)

  • List of non-linear ordinary differential equations (Link on Wikipedia)

  • Partial differential equations (Link on Wikipedia)

  • List of non-linear partial differential equations (Link on Wikipedia)

.

.

.

.

.

.

.

.

.

.

Some useful files from previous years

1st Sem 2022-23

Course Outline [PDF File]

Practice Problem Sets: There problems are for practice purpose (they need not be submitted).

• Practice Problem Set#1 {Approximations, Errors, Taylor Series}

• Practice Problem Set#2 {Roots of Equations}

• Practice Problem Set#3 {Linear Algebraic Equations}

• Practice Problem Set#4 {Curve Fitting}

• Practice Problem Set#5 {Numerical Differentiation & Integration}

• Practice Problem Set#6 {ODE & PDE}

Assignments:

• Assignment#1, Sample solution of Assign#1 (File) {Approximations, Errors, Taylor Series}

• Assignment#2, Sample solution of Assign#2 (File) {Roots of Equations}

• Assignment#3, Sample solution of Assign#3 (File)  {Curve Fitting}

• Assignment#4 {Numerical Differentiation & Integration, Ordinary Differential Equations}

Tests & Exams:

• Sample solution of Mid-Sem Exam (File)

• Sample solution of End-Sem Exam (File)