Course Overview
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Course Synopsis
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Emphasis will be laid in this course, on learning the Numerical methods to solve the Linear, Non-linear Equations, Interpolation and Different Numerical Methods to solve the problems of Integration, Differentiation and Differential Equations that cannot be solved exactly by the Integration and Differentiation Techniques. So, the use of Numerical Techniques for these sorts of problems will be very handy.
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Course Learning Outcomes
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At the end of the course, you should be able to:
- Describe difficulties that can arise because computers usually use finite precision.
- Grasp the numerical techniques and should be able to use a variety of methods in solving real-life, practical, technical, and theoretical problems which cannot be solved by other methods.
- Apply the Bisection, Regula Falsi, Newton and Iteration methods to solve a non-linear equation
- Apply the different method to solve linear Equations
- Construct Lagrange and Newton forward difference interpolation polynomials for a given set of data.
- Apply Trapezoidal and Simpson’s rules to find the approximate value of an integral.
- Describe the basic concepts behind the R-K method and apply specific R-K methods in given problems.
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Course Calendar
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2
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Errors in Computations.
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3
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Solution of Non Linear Equations (Bisection Method)
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4
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Solution of Non Linear Equations (Regula-Falsi Method)
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5
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Solution of Non Linear Equations (Method of Iteration)
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6
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Solution of Non Linear Equations (Newton Raphson Method)
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7
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Solution of Non Linear Equations (Secant Method)
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Assignment 1
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9
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Solution of Linear System of Equations (Gaussian Elimination Method)
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10
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Solution of Linear System of Equations(Gauss–Jordon Elimination Method)
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11
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Solution of Linear System of Equations(Jacobi Method)
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12
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Solution of Linear System of Equations(Gauss–Seidel Iteration Method)
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13
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Gauss–Seidel Iteration Method
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Quiz 1
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14
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Relaxation Method and Matrix inversion
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15
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Eigen Value Problems (Power Method)
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16
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Eigen Value Problems (Jacobis Method)
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17
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Eigen Value Problems (continued)
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18
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Interpolation(Introduction and Difference Operators)
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19
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Interpolation(Difference Operators Cont.)
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Quiz 2
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20
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Interpolation(Difference Operators, important formulas)
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21
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Interpolation(Newtons Forward Difference Formula)
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22
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Interpolation(Newtons Backward Difference formula)
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Mid-semester Exam
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23
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Interpolation (Newton’s Forward and backward Difference Interpolation Formula)
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24
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Interpolatiom (LAGRANGE’S INTERPOLATION FORMULA)
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25
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Interpolation (NEWTON’S DIVIDED DIFFERENCE INTERPOLATION FORMULA)
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26
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Interpolation (Newton’s Divided Difference Formula with Error Term)
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27
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DIFFERENTIATION USING DIFFERENCE OPERATORS
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28
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Numerical Differentiation and Integration (Differentiation using Difference operator)
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29
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Numerical Differentiation and Integration (Differentiation using Difference operator II)
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30
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Numerical Differentiation and Integration (Differentiation using Interpolation I)
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31
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Numerical Differentiation and Integration(Newton-Cotes Integration Formulae)
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32
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Numerical Differentiation and Integration(Trapezoidal and Simpsons Rules)
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33
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Numerical Differentiation and Integration(Trapezoidal and Simpsons Rules)Cont.
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34
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Numerical Differentiation and Integration(Rombergs Integration and Double integration)
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35
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Ordinary Differential Equations
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36
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Ordinary Differential Equations
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37
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Ordinary Differential Equations
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38
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Ordinary Differential Equations
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39
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Ordinary Differential Equations
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40
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Ordinary Differential Equations
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42
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Numerical Differenciation ,Numerical Integration,Five points formula
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43
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Introduction to Maple,Symbolic computations
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44
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Solution o f non linear equation using MAPLE
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45
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Revision of previos topics
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End-semester Exam
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