Course Archives Theoretical Statistics and Mathematics Unit | ||||||||||||||||||||||||||||||
Course: Computer Science II Instructor: Siva Athreya Room: Computer Class Room Level: Undergraduate Time: Currently offered |
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Syllabus Past Exams Syllabus (Numerical Methods): Introduction to Matlab (or appropriate package) and Numerical Computing: Number representations, finite precision arithmetic, errors in computing. Convergence, iteration, Taylor series. Solution of a Single Non-linear Equation: Bisection method. Fixed point methods. Newton's method. Convergence to a root, rates of convergence. Review of Applied Linear algebra: Vectors and matrices. Basic operations, linear combinations, basis, range, rank, vector norms, matrix norms. Special matrices. Solving Systems of equations (Direct Methods): Linear systems. Solution of triangular systems. Gaussian elimination with pivoting. LU decomposition, multiple right-hand sides. Nonlinear systems. Newton's method. Least Squares Fitting of Data: Fitting a line to data. Generalized least squares. QR decomposition. Interpolation: Polynomial interpolation by Lagrange polynomials. Alternate bases: Monomials, Newton, divided differences. Piecewise polynomial interpolation. Cubic Hermite polynomials and splines. Numerical Quadrature: Newton - Cotes Methods: Trapezoid and Simpson quadrature. Gaussian quadrature. Adaptive quadrature. Ordinary Differential Equations: Euler's Method. Accuracy and Stability. Trapezoid method. Runge - Kutta method. Boundary value problems and finite differences. Reference Texts: 1. B. Kernighan and D. Ritchie: The C Programming Language 2. J. Nino and F. A. Hosch: An Introduction to Programming and Object Oriented Design using JAVA 3. G. Recketenwald: Numerical Methods with Matlab 4. Shilling and Harries: Applied Numerical methods for engineers using Matlab and C 5. S. D. Conte and C. De Boor: Elementary Numerical Analysis: An Algorithmic Approach 6. S. K. Bandopadhyay and K. N. Dey: Data Structures using C 7. J. Ullman and W. Jennifer: A first course in database systems Evaluation:
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Midterm
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[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute] |