Course Overview
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Course Synopsis
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In this course, emphasis will be laid upon learning the basic and advanced Numerical methods to solve the Linear and Non-linear Equations. It also includes Interpolation and Different Numerical Methods to solve the problems of Integration, Differentiation and Differential Equations that cannot be solved exactly by the exact Integration and Differentiation Techniques. So, the use of Numerical Techniques for these sorts of problems will be very handy. In addition to that, MAPLE software will be taught to find the solution of nonlinear equations and to check the efficiency index and order of convergence.
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Course Learning Outcomes
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At the end of the course, you should be able to
- 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,fixed point, Newton and Iteration methods to solve a non-linear equation.
- Apply different methods 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.
- Apply the methods of Romberg’s Integration and Double Integration.
- To use MAPLE software to solve non-linear equations and to check efficiency index and order of convergence.
- Apply Aitkens Method to accelerate the rate of convergence of sequences.
- Apply Stephenson Method to find the roots of an equation.
- To learn the application of Halley’s and Householder Formulae.
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Course Calendar
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1
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Introduction to Numerical Methods
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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 (Fixed Point Method)
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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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9
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Interpolation (Introduction and Difference Operators)
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10
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Interpolation (Difference Operators, Continued)
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11
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Interpolation (Difference Operators, Continued).
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12
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Interpolation (Newtons Forward Difference Formula)
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13
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Interpolation (Newtons Backward Difference Formula)
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14
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Interpolation (Newton’s Forward and Backward Difference Interpolation Formulae)
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15
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Interpolation (Lagrange’s Interpolation Formula)
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16
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Interpolation (Newton’s Divided Difference Interpolation Formula)
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17
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Interpolation (Newton’s Divided Difference Interpolation Formula with Error Term)
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18
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Newton-Cotes Integration Formulae
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19
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Trapezoidal and Simpsons Rules
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20
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Trapezoidal and Simpsons Rules (Continued)
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21
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Romberg’s Integration and Double Integration
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22
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Introduction to MAPLE, Symbolic Computations
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23
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Solution of nonlinear equations using MAPLE
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25
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Applications of Fixed Point Method
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26
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Linear and Higher-Order Convergences
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27
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Aitken and Stephenson Methods
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28
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Applications of Aitken’s Method (Revisit of Jacobi and Gauss Seidel Methods)
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29
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Halley’s Formula and Applications
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30
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Order of Convergence through MAPLE
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