UNIQUE SERIES AKTU Syllabus
BOE065

Computer Based Numerical Techniques

L-T-P3-0-0 Credits3 Session2024-25 TypeTheory
Appears in 35 semesters · 35 branches

B.Tech Civil Engineering · Sem 6 (Open Elective-I) · B.Tech Mechanical Engineering · Sem 6 (Open Elective-I) · B.Tech Computer Science & Engineering · Sem 6 (Open Elective-I) · B.Tech Information Technology · Sem 6 (Open Elective-I) · B.Tech Artificial Intelligence & Machine Learning · Sem 6 (Open Elective-I) · B.Tech Artificial Intelligence & Data Science · Sem 6 (Open Elective-I) · B.Tech CSE (Artificial Intelligence) · Sem 6 (Open Elective-I) · B.Tech CSE (AI & ML) · Sem 6 (Open Elective-I) · B.Tech CSE (Data Science) · Sem 6 (Open Elective-I) · B.Tech CSE (Cyber Security) · Sem 6 (Open Elective-I) · B.Tech CSE (Internet of Things) · Sem 6 (Open Elective-I) · B.Tech Computer Science & Design · Sem 6 (Open Elective-I) · B.Tech Computer Science (Hindi) · Sem 6 (Open Elective-I) · B.Tech Electrical Engineering · Sem 6 (Open Elective-I) · B.Tech Electrical & Electronics Engineering · Sem 6 (Open Elective-I) · B.Tech Electrical & Computer Engineering · Sem 6 (Open Elective-I) · B.Tech Electronics & Communication Engineering · Sem 6 (Open Elective-I) · B.Tech Electronics & Instrumentation / Instrumentation & Control · Sem 6 (Open Elective-I) · B.Tech Electronics & Computer Engineering · Sem 6 (Open Elective-I) · B.Tech ECE (Advanced Communication Technology) · Sem 6 (Open Elective-I) · B.Tech Electronics Engineering (VLSI Design & Technology) · Sem 6 (Open Elective-I) · B.Tech Automobile Engineering · Sem 6 (Open Elective-I) · B.Tech Aeronautical Engineering · Sem 6 (Open Elective-I) · B.Tech Mechanical & Industrial Engineering · Sem 6 (Open Elective-I) · B.Tech Production & Industrial Production Engineering · Sem 6 (Open Elective-I) · B.Tech Manufacturing Technology · Sem 6 (Open Elective-I) · B.Tech Mining Engineering · Sem 6 (Open Elective-I) · B.Tech Chemical Engineering · Sem 6 (Open Elective-I) · B.Tech Plastic Engineering · Sem 6 (Open Elective-I) · B.Tech Food Technology · Sem 6 (Open Elective-I) · B.Tech Handloom & Textile Technology · Sem 6 (Open Elective-I) · B.Tech Carpet & Textile Technology · Sem 6 (Open Elective-I) · B.Tech Biotechnology · Sem 6 (Open Elective-I) · B.Tech Bioinformatics · Sem 6 (Open Elective-I) · B.Tech Agricultural Engineering · Sem 6 (Open Elective-I)

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Syllabus

5 units · 40 lecture hours
Unit1

Unit 1: Error and roots of Algrabraic and Transcendental Equations

8 hrs

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.

Unit2

Unit 2: Interpolation

8 hrs

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.

Unit3

Unit 3

8 hrs

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.

Unit4

Unit 4: Solution of differential Equations

8 hrs

Introduction, Picard’s Method, Euler’s Method, Taylor’s Method, Runge-Kutta Methods, Predictor Corrector Methods, Automatic Error Monitoring and Stability of solution.

Unit5

Unit 5: Boundary Value problems

8 hrs

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. Note: PS: Practice session: Students should practice the Flow Charts and algorithm of some important programs

Course Objectives1 points
  • 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.
Course Outcomes (COs)5 outcomes

After completion of the course student will be able to:

  1. CO1Understand the concept of errors to evaluate approximate roots of several types of equationsK2&K5
  2. CO2Analyze the problem and evaluate data by different interpolation methods and creating interpolating graphsK4, K5&K6
  3. CO3Understand the concept of interpolation to analyze and evaluate the numerical differentiation and integrationK2&K5
  4. CO4Remember the concept of formula based the solution of ordinary differential equations to evaluate differential equations withy initial conditionsK1&K5
  5. CO5Apply the concept of partial differential equation to evaluate the partial differential equations K1 – Remember, K2 – Understand, K3 – Apply, K4 – Analyze, K5 – Evaluate, K6 – CreateK3&K5

Text Books

  1. Jain, Iyengar and Jain, “Numerical Methods for Scientific and Engineering Computations”, New Age International.
  2. Grewal B S, “Numerical methods in Engineering and Science”, Khanna Publishers, Delhi.

Reference Books

  1. Rajaraman V, Computer Oriented Numerical Methods, Pearson Education
  2. T Veerarajan, T Ramachandran, “Theory and Problems in Numerical Methods, McGraw Hill
  3. Pradip Niyogi, Numerical Analysis and Algorithms, McGraw Hill.
  4. Francis Scheld, Numerical Analysis, McGraw Hill.
  5. Sastry S. S, Introductory Methods of Numerical Analysis, Pearson Education.
  6. Kiusalaas, J.: Numerical methods in engineering with MATLAB, Cambridge University Press
  7. Woodford, C and Phillips, C: Numerical methods with worked examples: MATLAB Edition, Springer

Official AKTU syllabus

This subject is on page 9, 10 of the original AKTU PDF.

Official AKTU syllabus PDF ↗