AKTU Computer Based Numerical Techniques (BOE065) Syllabus PDF – B.Tech Open Elective (3rd Year)
Computer Based Numerical Techniques BOE065
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- Semester 6
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Syllabus — Computer Based Numerical Techniques
Download PDFBOE065 · 3 credits · L-T-P 3-0-0
Course Objectives
The objective of this course is to familiarize the graduate engineers with techniques in errors, approximations, approximates roots, Interpolation, finite differences, numerical differentiation and integration programming, numerical solution of differential equations and boundary value problems. It aims to equip the students with standard concepts and tools from previously gained knowledge to an advanced level that will enable them to tackle more advanced level of Optimization techniques and applications that they would find useful in their disciplines.
The students will learn: To apply the knowledge of errors, roots and application in the field of engineering. To deal deals with finite differences and interpolation to solve engineering problems involving complicated real life situations etc. To deal with numerical integration and differentiation that is required in different branches of Engineering to graduate engineers for applying more difficult problems in case of complex structures. To deals with numerical solution of differential Equations for engineering problems involving real life situations etc. To deal with boundary value problems of real life systems and Engineers.
| BOE 065 COMPUTER BASED NUMERICAL TECHNIQUES | ||
| Unit | Topic | Lectures |
| 1 | Error and roots of Algrabraic and Transcendental Equations: Introduction of Numbers and their accuracy, Computer Arithmetic, Mathematical preliminaries, Errors and their Computation, General error formula, Error in a series approximation. Solution of Algebraic and Transcendental Equation: Bisection Method, Iteration method, Method of false position, Newton-Raphson method, Methods of finding real and complex roots, Muller’s method, Rate of convergence of Iterative methods, Polynomial Equations. | 8 |
| 2 | Interpolation: Introduction Finite Differences, Difference tables Polynomial Interpolation: Newton’s forward and backward formula Central Difference Formulae: Gauss forward and backward formula, Stirling’s, Bessel’s, Everett’s formula. Interpolation with unequal intervals: Lagrange’s Interpolation, Newton Divided difference formula, Hermite’s Interpolation. | 8 |
| 3 | Numerical Integration and Differentiation: Introduction: Numerical differentiation of Newton’s forward and backward formula, Stirling’s, Bessel’s, Everett’s formula, Lagrange’s Interpolation and Newton Divided difference formula. Numerical Integration: Newton cotes formula, Trapezoidal rule, Simpson’s 1/3 and 3/8 rules, Boole’s rule, Waddle’s rule. | 8 |
| 4 | Solution of differential Equations: Introduction, Picard’s Method, Euler’s Method, Taylor’s Method, Runge-Kutta Methods, Predictor Corrector Methods, Automatic Error Monitoring and Stability of solution. | 8 |
| 5 | Boundary Value problems: Introduction, Finite difference method, solving Eigen value problems, polynomial method and power methods. Numerical solution of Partial Differential equations. Elliptic, Parabolic and hyperbolic PDEs. Distillation in a Plate Column, Unsteady-state Operation, Starting a Stirred-tank Reactor, Rate at which a Plate Absorber Approaches Steady State. | 8 |
Note: PS: Practice session: Students should practice the Flow Charts and algorithm of some important programs Open Elective I AICTE Model Curriculum B series (VI Semester) Syllabus 2024-25
Text Books
- Jain, Iyengar and Jain, “Numerical Methods for Scientific and Engineering Computations”, New Age International.
- Grewal B S, “Numerical methods in Engineering and Science”, Khanna Publishers, Delhi.
Reference Books
- Rajaraman V, Computer Oriented Numerical Methods, Pearson Education
- T Veerarajan, T Ramachandran, “Theory and Problems in Numerical Methods, McGraw Hill
- Pradip Niyogi, Numerical Analysis and Algorithms, McGraw Hill.
- Francis Scheld, Numerical Analysis, McGraw Hill.
- Sastry S. S, Introductory Methods of Numerical Analysis, Pearson Education.
- Kiusalaas, J.: Numerical methods in engineering with MATLAB, Cambridge University Press
- Woodford, C and Phillips, C: Numerical methods with worked examples: MATLAB Edition, Springer
Course Outcomes
| Course Outcome (CO) | Bloom’s Knowledge Level (KL) | |
| CO 1 | Understand the concept of errors to evaluate approximate roots of several types of equations | K & K 2 5 |
| CO 2 | Analyze the problem and evaluate data by different interpolation methods and creating interpolating graphs | K , K &K 4 5 6 |
| CO 3 | Understand the concept of interpolation to analyze and evaluate the numerical differentiation and integration | K & K 2 5 |
| CO 4 | Remember the concept of formula based the solution of ordinary differential equations to evaluate differential equations withy initial conditions | K &K 1 5 |
| CO 5 | Apply the concept of partial differential equation to evaluate the partial differential equations | K & K 3 5 |
K – Remember, K – Understand, K – Apply, K – Analyze, K – Evaluate, K – Create 1 2 3 4 5 6 Open Elective I AICTE Model Curriculum B series (VI Semester) Syllabus 2024-25
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