Lovely Professional University, PunjabCourse Code Course Title Course Planner Lectures Tutorials Practicals CreditsMEC318 NUMERICAL METHODS IN ENGINEERING 17093::Sachin Kansal 2.0 1.0 0.0 3.0Course Category Courses with numerical and conceptual focusTextBooks Sr No Title Author Edition Year Publisher NameT-1 APPLIED NUMERICAL METHODS WITH MATLAB FOR ENGINEERS AND SCIENTISTSSTEVEN C. CHAPRA 3rd 2012 TATA MCGRAW - HILL EDUCATIONReference BooksSr No Title Author Edition Year Publisher NameR-1 NUMERICAL METHODS FOR ENGINEERSCHAPRA AND CANALE 5th 2011 TATA MCGRAW HILL, INDIAR-2 ADVANCE NUMERICAL METHODSKREYSZIG 1st WILEYR-3 APPLIED NUMERICAL METHODS FOR ENGINEERING (USING MATLAB AND C)ROBERT J. SCHILLING, SANDRA L. HARRIS1st 2007 CENGAGE LEARNINGOther ReadingSr No Journals articles as Compulsary reading (specific articles, complete reference)OR-1 http://onlinelibrary.wiley.com/journal/10.1002/%28ISSN%291097-0207 , OR-2 http://www.elsevier.com/journals/subjects/engineering-and-technology/numerical-methods-in-engineering , Relevant WebsitesSr No (Web address) (only if relevant to the course) Salient FeaturesRW-1 http://www.avatto.com/engineering/mathematics/mcqs/numerical-methods/questions/97/1.htmlOnline practice objective questionsDetailed Plan For Lectures LTP week distribution: (LTP Weeks)Weeks before MTE 7Weeks After MTE 7Spill Over 2Week NumberLecture NumberBroad Topic(Sub Topic) Chapters/Sections of Text/reference booksOther Readings,Relevant Websites, Audio Visual Aids, software and Virtual LabsLecture Description Learning Outcomes Pedagogical ToolDemonstration/ Case Study / Images / animation / pptetc. PlannedLive ExamplesWeek 1 Lecture 1 Introduction to Numerical Methods(Simple mathematical model)T-1:1.1 OR-1 Definition of mathematical model, variables and conservation laws in engineering and sciencesKnowledge andunderstandingprerequisites for the effectiveimplementation of anyphysical laws in engineeringWhite boardIntroduction to Numerical Methods(Conservation Laws in Engineering)T-1:1.2 OR-2 Definition of mathematical model, variables and conservation laws in engineering and sciencesKnowledge andunderstandingprerequisites for the effectiveimplementation of anyphysical laws in engineeringWhite boardLecture 2 Introduction to Numerical Methods(Significant Figures)T-1:4.1 Description of significant figures, difference between accuracy and precision Students are able to learn difference between accuracy and precision White boardIntroduction to Numerical Methods(Accuracy and Precision)T-1: 4.1 Description of significant figures, difference between accuracy and precision Students are able to learn difference between accuracy and precision White board Example of target practice problem from bulletWeek 2 Lecture 3 Introduction to Numerical Methods(Error Definitions)T-1:4.1.24.2 Defination of error, Type of errors and description of round off errorsErrors associated withcalculations andmeasurementsWhite boardIntroduction to Numerical Methods(Round off Errors)T-1:4.1.24.2 Defination of error, Type of errors and description of round off errorsErrors associated withcalculations andmeasurementsWhite boardLecture 4 Introduction to Numerical Methods(Truncation Errors)T-1:4.3 Description of Taylor series and truncation errorErrors from approximation in place of an exactmathematical procedureWhite boardIntroduction to Numerical Methods(The Taylor Series)T-1:4.3 Description of Taylor series and truncation errorErrors from approximation in place of an exactmathematical procedureWhite boardWeek 3 Lecture 5 Introduction to Numerical Methods(Total numerical error)T-1:4.4 Total numerical error, Error analysis of numerical differentiationStudents are able to get knowledge about total numerical error and error propagationWhite boardLecture 6 Roots of Equations(Bracketing methods)T-1:5.15.25.3 Description of roots in engineering and science, graphical and bracketing methodExploit the fact that a function typically changes sign in the vicinity of a rootWhite boardRoots of Equations(Graphical methods)T-1:5.15.25.3 Description of roots in engineering and science, graphical and bracketing methodExploit the fact that a function typically changes sign in the vicinity of a rootWhite boardWeek 4 Lecture 7 Roots of Equations(Bisection method)T-1:5.4 Bisection method Students are able to find the root and error associated with bisection methodWhite boardLecture 8 Roots of Equations(False position method)T-1:5.5 False position method Students are able to find the root and error associated with false position methodWhite boardWeek 5 Lecture 10 Roots of Equations(Simple fixed point Iteration)T-1:6.1 Introduction to open method for root location and Simple fixed point IterationStudents are able to find roots with simple fixed point iteration methodWhite boardLecture 9 Test1Week 6 Lecture 11 Roots of Equations(Newton raphson method)T-1:6.26.3 Newton raphson method and secant method for root location Students are able to understand difference between newton raphson and secant method to find the root White boardRoots of Equations(Secant method)T-1:6.26.3 Newton raphson method and secant method for root location Students are able to understand difference between newton raphson and secant method to find the root White boardLecture 12 Curve Fitting(Least square regression)T-1:14.3 Linear least square regression, criteria for best fit, Quantification of error of linear regression, InterpolationTechniques of curve fitting by linearleastsquare regression, fit curve to such data to obtain intermediate estimatesWhite boardWeek 7 Lecture 13 Curve Fitting(Least square regression)T-1:14.3 Linear least square regression, criteria for best fit, Quantification of error of linear regression, InterpolationTechniques of curve fitting by linearleastsquare regression, fit curve to such data to obtain intermediate estimatesWhite boardWeek 7 Lecture 14 Curve Fitting(Interpolation) Spill over Spill overMID-TERMWeek 8 Lecture 15 Linear Algebraic Equations(Gauss Elimination)T-1:9.29.3 Introduction to linear algebra, Naive gauss elimination, Pivoting Students are able to solve linear algebraic equations by combining equations toeliminate unknownsWhite boardLecture 16 Linear Algebraic Equations(LU Decomposition and matrix Inversion)T-1:10.110.212.112.1.112.1.3LU Decomposition, Gauss seidel, Convergence and diagonal dominance, relaxation Students are able to solve linear algebraic equations by combining equations to eliminate unknownWhite boardWeek 9 Lecture 17 Linear Algebraic Equations(LU Decomposition and matrix Inversion)T-1:10.110.212.112.1.112.1.3LU Decomposition, Gauss seidel, Convergence and diagonal dominance, relaxation Students are able to solve linear algebraic equations by combining equations to eliminate unknownWhite boardLecture 18 Linear Algebraic Equations(LU Decomposition and matrix Inversion)T-1:10.110.212.112.1.112.1.3LU Decomposition, Gauss seidel, Convergence and diagonal dominance, relaxation Students are able to solve linear algebraic equations by combining equations to eliminate unknownWhite boardWeek 10 Lecture 19 Linear Algebraic Equations(Special matrices and Gauss seidel)Spill Over Spill OverLecture 20 Test2Week 11 Lecture 21 Numerical Differentiation and Integration(Newton cotes integration)T-1:19.119.2 Introduction to integration, Newton Cotes formulaStudents are able to integration an equation with Newton cotes method of integration White boardLecture 22 Numerical Differentiation and Integration(Trapezoidal rule)T-1:19.319.3.119.3.2Trapezoidal rule, Composite Trapezoidal ruleStudents are able to integration an equation with Newton cotes method of integration White boardWeek 12 Lecture 23 Numerical Differentiation and Integration(Simpson's rule)T-1:19.419.6 RW-1 Simpson's rule, Simpson's 1/3 and 1/8 rule, Composite Simpson's 1/3 and 1/8 rule, Integration with unequal segments Students are able to integration an equation with Newton cotes method of integrationWhite boardWeek 12 Lecture 24 Numerical Differentiation and Integration(Simpson's rule)T-1:19.419.6 RW-1 Simpson's rule, Simpson's 1/3 and 1/8 rule, Composite Simpson's 1/3 and 1/8 rule, Integration with unequal segments Students are able to integration an equation with Newton cotes method of integrationWhite boardWeek 13 Lecture 25 Test3Lecture 26 Numerical Differentiation and Integration(Gauss Quadrature)Spill Over Spill OverWeek 14 Lecture 27 Ordinary Differential Equations(Euler's Method)T-1:22.2 22.422.4.2Euler's Mehod,Runge- Kutta Method (Only fourth order)Solving OrdinaryDifferential EquationsWhite boardOrdinary Differential Equations(Runge kutta methods)T-1:22.2 22.422.4.2Euler's Mehod,Runge- Kutta Method (Only fourth order)Solving OrdinaryDifferential EquationsWhite boardLecture 28 Ordinary Differential Equations(Boundary value and Eigen value problems)T-1:Chapter 24 Boundary Value Problems (Introduction only)Solving OrdinaryDifferential EquationsWhite boardSPILL OVERWeek 15 Lecture 29 Spill OverLecture 30 Spill OverScheme for CA:Component Frequency Out Of Each Marks Total MarksTest 2 3 10 20Total :-10 20Details of Academic Task(s)AT No. Objective Topic of the Academic Task Nature of Academic Task(group/individuals/field workEvaluation Mode Allottment / submission WeekTest1 To evaluate the concepts of numerical methods and location of root in close interwalSimple mathematical model, Conservation Laws in Engineering, Significant Figures, Accuracy and Precision, Error Definitions, Bracketing methods, Graphical methods, Bisection method, False position method, Simple fixed point Iteration, Newton raphson method, Secant methodRound off Errors, Truncation Errors, The Taylor Series, Total numerical errorIndividual Student Performance4 / 5Test2 To evaluate the concepts of numerical methodsGauss Elimination, LU Decomposition and matrix Inversion, Special matrices and Gauss seidelIndividual Student Performance9 / 10Test3 To evaluate the concepts of numerical methodsNewton cotes integration, Trapezoidal rule, Simpson's rule, Gauss QuadratureIndividual Student Performance12 / 13Plan for Tutorial: (Please do not use these time slots for syllabus coverage)Tutorial No. Lecture Topic Type of pedagogical tool(s) planned(case analysis,problem solving test,role play,business game etc)Tutorial1 Prolems on Simple mathematical model, Conservation Laws in Engineering, Significant Figures, Accuracy and PrecisionCase Analysis,Problem SolvingTutorial2 Prolems on Error Definitions, Round off Errors, Truncation Errors, Taylor SeriesProblem SolvingTutorial3 Problems on Total numerical error, Bracketing methods, Graphical methodsProblem SolvingTutorial4 Problems on finding the roots with Bisection method, False position methodProblem SolvingTutorial5 Prolems on Simple fixed point Iteration Problem SolvingTutorial6Prolems on Newton raphson method, Secant method Problem SolvingTutorial7 Prolems on Curve fitting by least square regression, Interpolation Problem SolvingAfter Mid-TermTutorial8 Problems for solving the equations with Gauss Elimination, LU Decomposition and matrix InversionProblem SolvingTutorial9 Problems on Special matrices and Gauss seidel Problem SolvingTutorial10 Prolem related to Newton cotes integration Problem SolvingTutorial11 Prolems on Trapezoidal rule Problem SolvingTutorial12 Problems on Simpson's rule Problem SolvingTutorial13 Prolems on Gauss Quadrature Problem SolvingTutorial14 Prolems on Euler's Method, Runge kutta methods, Boundary value and Eigen value Problem SolvingType of pedagogical tool(s) planned(case analysis,problem solving test,role play,business game etc)Case Analysis,Problem SolvingProblem SolvingProblem SolvingProblem SolvingProblem SolvingProblem SolvingProblem SolvingAfter Mid-TermProblem SolvingProblem SolvingProblem SolvingProblem SolvingProblem SolvingProblem SolvingProblem Solving