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Lovely Professional University, Punjab

Course Code Course Title Course Planner Lectures Tutorials Practicals Credits

MTH204 NUMERICAL ANALYSIS 14850::Ramanjeet Kaur 3.0 0.0 0.0 3.0

Course Category Courses with Numerical focus

TextBooks

Sr No Title Author Edition Year Publisher Name

T-1 Numerical Methods in Engineering and Science

B.S. Grewal 9th 2010 Khanna Publishers

Reference Books

Sr No Title Author Edition Year Publisher Name

R-1 Elementary Numerical Analysis: An Algorithmic approach

Conte, S.D and Carl D. Boor

3rd 2005 Tata McGraw Hill

R-2 Numerical methods for Scientific and Engineering Computation

By M.K. Jain, S.R.KIyenger and R.K. Jain

6th 2012 New Age international Ltd.

R-3 INTRODUCTORY METHODS OF NUMERICAL ANALYSIS

SASTRY, S. S 4th Prentice Hall of India Private Limited, New Delhi

Other Reading

Sr No Journals articles as Compulsary reading (specific articles, complete reference)

OR-1 http://www.maths.manchester.ac.uk/~cp/frontpage157.htm , ,

OR-2 http://kr.cs.ait.ac.th/~radok/math/mat7/step13.htm#STEP13 , ,

OR-3 http://tinyurl.com/cnbyzdf , ,

Relevant Websites

Sr No (Web address) (only if relevant to the course) Salient Features

RW-1 http://www.damtp.cam.ac.uk/user/na/PartIB/ Lecture notes available

RW-2 http://nm.mathforcollege.com/ Contains detailed entries of all topics

RW-3 http://ocw.mit.edu/courses/mechanical-engineering/2-993j-introduction-to-numericalanalysis- for-engineering-13-002j-spring-2005/lecture-notes/

MIT Lecture Notes on Numerical Analysis

LTP week distribution: (LTP Weeks)

Weeks before MTE 7

Weeks After MTE 6

Week Number

Lecture Number

Broad Topic(Sub Topic) Chapters/Sections of Text/reference books

Other Readings,Relevant Websites, Audio Visual Aids, software and Virtual Labs

Lecture Description Learning Outcomes Pedagogical ToolDemonstration/ Case Study / Images / animation / ppt etc. Planned

Week 1 Lecture 1 Error Analysis(Introduction to errors)

T-1:T1;1.1-1.2R-3:R-3;1.3

OR-1 Introduction to errors Students will be able toknow about different errors

White board alongwith discussion

Lecture 2 Error Analysis(Types of errors) T-1:T1;1.3R-3:R-3;1.3

Error, Relative Error, Absolute error

Students will be able to know about different errors


Lecture 3 Solution of algebraic and Transcendental equations(Bisection method)

T-1:T-1;2.7 OR-1 Geometricalinterpretation, formulaand examples ofBisection method forfinding roots

Will be able to evaluatethe root of equation


Week 2 Lecture 4 Solution of algebraic and Transcendental equations(Method of false position)

T-1:T-1;2.8 Geometrical interpretation, formula and examples of Bisection method for finding roots

Student will be able to evaluate the root of equation


Lecture 5 Solution of algebraic and Transcendental equations(Iteration method)

T-1:T-1;2.10 Geometricalinterpretation, formulaand examples of Iterationmethod for finding roots

Student will be able to evaluate the root of equation


Lecture 6 Solution of algebraic and Transcendental equations(Newton-Raphson method)

T-1:T-1;2.11 Geometricalinterpretation, formulaand examples of NewtonRaphson's method forfinding roots

Will be able to evaluatethe root of equation


Week 3 Lecture 7 Solution of algebraic and Transcendental equations(Rate of convergence)

T-1:T-1;2.6 and 2.11 obs. 5

rate of convergence, rateof convergence ofNewton Raphson method

rate of convergence, rateof convergence ofNewton Raphson method


Lecture 8 Interpolation for equi-spaced data(Introduction)

T-1:T-1;7.1 introduction to interpolation

Students will master theconcept of Interpolation


Interpolation for equi-spaced data(Finite Difference Operator)

T-1:T-1;6.2 Definition of E, Forward,backward, averageoperators and relationbetween them,

Students will master theconcept of operatorsand can use any of theminterchangeblly


Detailed Plan For Lectures

Spill Over 3

Week 3 Lecture 9 Interpolation for equi-spaced data(Newton's Forward Interpolation Formula)

T-1:T-1;7.1-7.2 RW-3 Newton forwarddifference interpolationformula and examples

Student will be able tocompute the value ofdependent variable atany given value ofindependent variablelying near the start oftable


Week 4 Lecture 10 Interpolation for equi-spaced data(Newton's Backward Interpolation Formula)

T-1:T-1;7.3 Newton backwarddifference interpolationformula and examples

Student will be able to compute the value of dependent variable at any given value of independent variable lying near the end of table


Lecture 11 Test1

Lecture 12 Interpolation-I(Gauss forward interpolation formula)

T-1:T-1;7.5 Gauss forwardinterpolation formula andexamples

Student will be able tocompute the value ofdependent variable atany given value ofindependent variablelying near the mid oftable


Week 5 Lecture 13 Interpolation-I(Gauss backward interpolation formula.)

T-1:T-1;7.6 Gauss backwardinterpolation formula andexamples

Student will be able tocompute the value ofdependent variable atany given value ofindependent variablelying near the mid oftable


Lecture 14 Interpolation for equi-spaced data(Stirling's Formula)

T-1:T-1;7.7 Stirling interpolationformula and examples

Student will be able tocompute the value ofdependent variable atany given value ofindependent variablelying near the mid of table


Lecture 15 Interpolation for equi-spaced data(Bessel's Formula)

T-1:T-1;7.8;7.10 Bessel Interpolationformula and examples



Interpolation for equi-spaced data(Choice of an Interpolation Formula)

T-1:T-1;7.8;7.10 OR-3 Bessel Interpolationformula and examples



Week 6 Lecture 16 Interpolation With Unequal Intervals(Lagrange's Interpolation Formula)

T-1:T-1;7.11-7.12 RW-2 Lagrange Interpolationformula, partial fractionusing lagrange

student will learn tointerpolate the valuewhen independentvariable is unequallyspaced


Lecture 17 Test2

Lecture 18 Interpolation With Unequal Intervals(Newton Divided Difference Formula)

T-1:T-1;7.13-7.15R-2:R-2;4.9

Newton divideddifference interpolationformula and examples

student will learn tointerpolate the valuewhen independentvariable is unequallyspaced


Week 7 Lecture 19 Numerical differentiation(Derivatives Using Forward Difference Formula)

T-1:T-1;8.1-8.2R-3:R-3;6.1;6.2

Computation ofderivative usinginterpolation and error involved

Student will learn tocompute the derivativeat any given point whentabulated values aregiven instead offunction


Numerical differentiation(Derivatives Using Backward Difference Formula)

T-1:T-1;8.1-8.2 RW-1 Computation ofderivative usinginterpolation and error involved

Student will learn tocompute the derivativeat any given point whentabulated values aregiven instead offunction


Lecture 20 Method of Least Square for Curve fitting(Least square approximation)

T-1:T-1;5.4-5.5 Formula and examples offitting a straight lineusing least squareprinciple

Student will be able todemonstrate the bestline approximating thegiven set of tabulated values


Method of Least Square for Curve fitting(Fitting of straight line)

T-1:T-1;5.4-5.5 Formula and examples offitting a straight lineusing least squareprinciple

Student will be able todemonstrate the bestline approximating thegiven set of tabulated values


Lecture 21 Method of Least Square for Curve fitting(parabola)

T-1:T-1;5.5 and 5.7 Fitting of parabola and exponentialcurve using least squareprinciple

Student will be able todemonstrate the bestparabola and exponential curveapproximating thegiven set of tabulatedvalues


Method of Least Square for Curve fitting(exponential curves)

T-1:T-1;5.5 and 5.7 OR-2 Fitting of parabola and exponentialcurve using least squareprinciple

Student will be able todemonstrate the bestparabola and exponential curveapproximating thegiven set of tabulatedvalues


MID-TERM

Week 8 Lecture 22 Numerical Integration(Trapezoidal rule)

T-1:T-1;8.4-8.5 Trapezoidal rule formulaand based examples

Will learn how tocompute the integralwhen analyticalapproach is difficult


Numerical Integration(Newton Cotes Quadrature Formula)

T-1:T-1;8.5 Trapezoidal rule formulaand based examples



Lecture 23 Numerical Integration(Simpson 1/3 rule)

T-1:T-1;8.5 Simpson 1 over 3 ruleformula and basedexamples



Lecture 24 Numerical Integration(Simpson 3/8 rule)

T-1:T-1;8.5 Simpson 3 by 8 ruleformula and basedexamples



Week 9 Lecture 25 Numerical Integration(Guass-quadrature methods)

T-1:T-1;8.5R-2:R-2;5.8

Guass quadraturemethods formula andbased examples



Lecture 26 Numerical Solution of ODE(Solution of Differential Equation)

T-1:T-1;10.3R-3:R-3;8.2

Taylors Series Students will learn whatis meaning of solutionof a differentialequation and how to getan approximate solutionof ordinary differentialequation by Taylor series method


Numerical Solution of ODE(Taylor Series)

T-1:T-1;10.3 Taylors Series Students will learn whatis meaning of solutionof a differentialequation and how to getan approximate solutionof ordinary differentialequation by Taylor series method


Lecture 27 Numerical Solution of ODE(Picard Method)

T-1:T-1;10.2R-3:R-3;8.3

Picards Method Students will learn whatis meaning of solutionof a differentialequation and how to getan approximate solutionof ordinary differentialequation by Picards method


Week 10 Lecture 28 Numerical Solution of ODE(Euler's Method)

T-1:T-1;10.4 Euler's method Students will learn whatis meaning of solutionof a differentialequation and how to getan approximate solutionof ordinary differentialequation by Euler method


Lecture 29 Numerical Solution of ODE(Modified Euler method)

T-1:T-1;10.5R-3:R-3;8.4.2

Formula and examples ofModified Euler method

Students will be able totrace the solution ofIVP


Lecture 30 Numerical Solution of ODE(Modified Euler method)

T-1:T-1;10.5R-3:R-3;8.4.2

Formula and examples ofModified Euler method

Students will be able totrace the solution ofIVP


Week 11 Lecture 31 Numerical Solution of ODE(Runge-Kutta (fourth order) method)

T-1:T-1;10.7 Solution of ODE byusing Runge Kutta fourthorder method

Students will learn howto find accurate solutionof IVP


Lecture 32 Numerical Solution of ODE(Runge-Kutta (fourth order) method)

T-1:T-1;10.7 Solution of ODE byusing Runge Kutta fourthorder method

Students will learn howto find accurate solutionof IVP


Lecture 33 Test3

Week 12 Lecture 34 Multistep Methods and PDE(Adams Bash forth method)

T-1:T-1;10.1 Solution of ODE byusing Adams Bash forthmethod and milne's method

Students will learn howto find solution of IVPand then how toimprove it


Multistep Methods and PDE(Milne method)

T-1:T-1;10.8-10.9 Solution of ODE byusing Adams Bash forthmethod and milne's method



Lecture 35 Multistep Methods and PDE(Milne method)




Multistep Methods and PDE(Adams Bash forth method)




Lecture 36 Multistep Methods and PDE(Adams Bash forth method)




Multistep Methods and PDE(Milne method)




Week 13 Lecture 37 Multistep Methods and PDE(Jacobi Method for solving PDE)

T-1:T-1;11.1-11.5 Formula and examples ofJacobi Method

Students will learnnumerical approach offinding solution ofpartial differential equation


Multistep Methods and PDE(Gauss-Seidal method)

T-1:T-1;11.5 Formula and examples of Seidel Method



Lecture 38 Multistep Methods and PDE(Gauss-Seidal method)




Multistep Methods and PDE(Jacobi Method for solving PDE)




Lecture 39 Multistep Methods and PDE(Jacobi Method for solving PDE)




Multistep Methods and PDE(Gauss-Seidal method)




SPILL OVERWeek 14 Lecture 40 Spill Over

Lecture 41 Spill Over

Lecture 42 Spill Over

Scheme for CA:Component Frequency Out Of Each Marks Total Marks

Test 2 3 10 20

Total :- 10 20

Details of Academic Task(s)

AT No. Objective Topic of the Academic Task Nature of Academic Task(group/individuals/field

work

Evaluation Mode Allottment / submission Week

Test1 To test the root finding skills of students and analyze their error analyzing capabilities.

Test will be covering : Types of errors, Propagation of errors,Significant digits, Bisection method, Method of false position,Iteration method, Newton-Raphson method, Rate of convergence.It will consist of 30 marks and format will be as per the formatavailable in Academic manual for Spring term. It will beconducted in lecture and there will be two set of question papers .Test will be covering : Types of errors, Propagation of errors,Significant digits, Bisection method, Method of false position,Iteration method, Newton-Raphson method, Rate of convergence.It will consist of 30 marks and format will be as per the formatavailable in Academic manual for Spring term. It will beconducted in lecture and there will be two set of question papers .

Individual based upon performance stepwise evaluation will be done

3 / 4

Test2 To test the Interpolatioin concepts of student

Gauss-Seidel Iteration method, Finite difference operators,Gregory Newton forward and backward difference interpolation,Gauss forward and backward interpolation formula.

Individual Test will be of 30 marks and performance will be step wise evaluation of questions attempted

5 / 6

Test3 To test the learning outcome of differntiation, integration, Least square methods and single step methods for solving ODEconcepts

Various formulae for first and second derivative with errors,Trapezoidal rule, Simpson 1/3 and 3/8 rule, Least squareapproximation, Fitting of straight line, parabola and exponentialcurve, Fitting of straight line, Modified Euler method, Runge-Kutta (fourth order) method

Individual Test will be of 30 marks and performance will be step wise evaluation of questions attempted

10 / 11

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