PE207-Numerical-Methods-with-Programming.org

<<<PE207>>> NUMERICAL METHODS WITH PROGRAMMING

CO PO MAPPING

		PO1	PO2	PO3	PO4	PO5	PO6	PO7	PO8	PO9	PO10	PO11	PO12	PSO1	PSO2	PSO3
		K3	K4	K5	K5	K6	-	-	-	-	-	-	-	K5	K3	K6
CO1	K3	3	2	2	2	0	0	0	0	0	0	0	0	2	3	1
CO2	K2	2	2	1	1	0	0	0	0	0	0	0	0	1	2	1
CO3	K3	3	2	2	2	0	0	0	0	0	0	0	0	2	3	1
CO4	K3	3	2	2	2	0	0	0	0	0	0	0	0	2	3	1
CO5	K3	3	2	2	2	0	0	0	0	0	0	0	0	2	3	1
Score		14	10	9	9	0	0	0	0	0	0	0	0	9	14	5
Course Mapping		3	2	2	2	0	0	0	0	0	0	0	0	2	3	1

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L	T	P	C
3	0	0	3

COURSE OBJECTIVES

• To understand basic programming constructs
• To know about Interpolation methods
• To learn about Numerical Integration
• To learn about Numerical solutions of equations
• To study Numerical solutions for differential equations.

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UNIT I

APPROXIMATE NUMBERS

9

Sources of Errors in Numerical Calculations – Absolute and Relative Errors – Representation of Numbers – Significant Digits – Errors of Elementary Operations; Basic Programming Techniques( C/C++).

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UNIT II

INTERPOLATION

9

Finite differences – Newton’s Forward Interpolation formula – Newton’s Backward interpolation formula – Central Difference interpolation formula – Lagrange’s formula – Newton’s divided difference interpolation formula – Inverse Lagrange’s interpolation formula – Interpolating with a cubic spline – Curve Fitting: Method of least squares – Linear and polynomial regression.

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UNIT III

NUMERICAL INTEGRATION

9

Trapezoidal Rule – Simpson’s 1/3 Rule – Simpson’s 3/8 Rule – Gaussian Quadrature Formula – Double integration using Trapezoidal Rule – Simpson’s Rule.

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UNIT IV

NUMERICAL SOLUTION FOR ALGEBRAIC EQUATIONS

9

Direct methods – Gauss and Gauss–Jordan methods; Iterative methods – Gauss-Jacobi and Gausss-Seidel methods – Relaxation method – Newton’s method for nonlinear simultaneous equations – Power method for determination of eigen values – Convergence of Power method.

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UNIT V

NUMERICAL SOLUTION FOR DIFFERENTIAL EQUATIONS

9

Numerical solution of ordinary differential equations; Single step methods – Taylor series method – Picard’s Method – Euler and Modified Euler methods – Runge-Kutta methods of 2nd and 4th order.

\hfill Total Periods: 45

COURSE OUTCOMES

After the completion of this course, students will be able to:

• Develop simple applications in C using basic constructs (K3)
• Understand the numerical interpolation and integration (K2)
• Provide numerical solutions for differential equations (K3)
• Apply numerical methods to solve problems drawn from sciences (K3)
• Assess the reliabilty of numerical results (K3).

TEXT BOOKS

1. Titus Adrien Beu, “Introduction to Numerical Programming a Practical Guide for Scientists and Engineers Using Python and C/C++”, CRC Press, 2019.
2. Steven C Chapra, Raymond P Canale, “Numerical Methods for Engineering”, 6th Edition, McGraw-Hill Publications, 2010.

REFERENCES

1. Jaan Kiusalaas, “Numerical Methods in Engineering with Python 3”, Cambridge University Press, 2013.
2. T Veerarjan, T Ramachandran, “Numerical methods with programming in ‘C’”, 2nd Editiion, Tata McGraw-Hill Publishing.Co.Ltd, 2007.
3. R W Hamming, “Numerical Methods for Scientists and Engineerings”, 2nd Edition, Dover Publications Inc, New York, 1973.
4. C F Gerald, P O Wheatley, “Applied Numerical Analysis”, 6th Edition, Pearson Education Asia, New Delhi, 2006.
5. Brian, “A friendly introduction to Numerical analysis”, Pearson Education, Asia, New Delhi, 2007.