Lecture#12 Numerical Analysis || Secant Method || Chord Method || Solution of Non-Linear Equations.

Описание: Topic: In this lecture I shall discuss Method of Secant also called Chord Method and related problem.
COURSE: NUMERICAL ANALYSIS- I||PUNJAB UNIVERSITY|| 7TH SEMESTER|| CODE MATH-403
LEVEL: B.S MATHEMATICS
CHAPTER # 1 Solution of Non-Linear Equations
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This course is specially designed for students of B.S MATHEMATICS 7th semester and students doing M.SC MATHEMATICS annually from Punjab University Lahore Pakistan.
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Number Systems and Errors
 Round off errors and computer arithmetic
 Error estimation
 Floating point arithmetic
Solution of Non-Linear Equations
 Iterative methods and convergence: Bisection method, fixed point iterative method, Regula
Falsi, Secant and Newton’s method
Systems of Linear Equations
 Direct methods: Gaussian elimination method, Gauss-Jordan method, matrix inversion
method, factorization (Doolittle, Crout and Cholesky) method and its various forms
 Iterative methods and convergence: Gauss-Jacobi method and Gauss-Seidel method
 Ill-condition system and condition number
 Eigen values and eigenvectors
 Power and Rayleigh quotient method
Interpolation and Polynomial Approximation
 Difference operators
 Interpolation with unequal intervals: Lagrange’s interpolation formula, Newton’s divided
difference formula, error in polynomial interpolation
 Interpolation with equal intervals: Gregory Newton forward/backward interpolation
formula, error in polynomial interpolation
 Central difference interpolation formulae: Gauss’s forward/backward interpolation
formula, Stirling’s formula, Laplace Everett’s formula, Bessel’s formula
Recommended Books
1. Curtis F. Gerald and Patrick O. Wheatley, Applied Numerical Analysis, 6th edition,
(Addison-Wesley Pearson Education, 2003)
2. Richard L. Burden and J. Douglas Faires, Numerical Analysis, 6th edition, (Brooks/Cole
Publishing Company,1997)
3. John H. Mathews, Numerical Methods for Mathematics, 3rd edition (Prentice Hall
International, 2003)
4. V. N. Vedamurthy and N. Ch. S. N. Iyenger, Numerical Methods, (Vikas Publishing House
Pvt. Ltd, 2002)
5. Steven C. Chapra and Raymond P. Canale, Numerical Methods for Engineers, 3rd edition,
(McGraw Hill International Edition, 1998)
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