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It includes operators and interpolation formula
Typology: Lecture notes
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Numerical analysis provides the theoretical foundation for the numerical algorithms we rely on to solve a multitude of computational problems in science. This course covers a wide range of such problems ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations. Throughout the course, particular attention is paid to the essential qualities of a numerical algorithm stability, accuracy, reliability and efficiency. The present course go further than simply providing recipes for solving computational problems. This course carefully analyse the reasons why methods might fail to give accurate answers, or why one method might return an answer in seconds while another would take billions of years. This course is ideal as a text for students in the present semester of a university mathematics course. It combines practicality regarding applications with consistently high standards of rigour.
Contact information: Email: [email protected] / [email protected] Phone #: +923348266836 + Emergency phone #: +923348266836 + Contact restrictions: No calls between 9:00 pm and 9:00 am Expected response time for emails, as- signment submissions and grading: With in 48 hours
Interpolation and extrapolations: Linear and higher order interpolating polynomials, Newton’s Gregory forward and backward difference interpolation formulas and their utilizations as extrapolation, Lagrange’s interpolations, numerical differentiation. Numerical integration: Trapezoidal and Simpson’s approximations, Romberg integration. Rout finding: Bracketing methods and iteration methods and their applications as multiple root methods. Numerical linear algebra: Solution of the system of linear equations (direct method) Gause elimination, direct and indirect factorizations, symmetric factorization tridiagonal factorization, iterative methods like Jocobi and Guss-Seidel methods, LU-decomposition, Runge-Kutta methods. Error Analysis: Absolute, relative, round-off, truncation, overflow and underflow errors. Finite Differences: Forward, backward and central difference formulas. Teaching Methodology: Lectures, Written Assignments, Semester Project, Presentations Course Assessment: Sessional Exam, Home Assignments, Quizzes, Project, Presentations, Final Exam Reference Materials: (1). Curtis F.Gerald Patrick O.Wheatley: Applied Numerical Analysis, Addison-Wesley. (2). Numerical Analysis (8th ed) By Burden and Faires. (3). Numerical Methods Using Matlab (4th Edition) By John H. Mathews and Kurtis D. Fink , Pearson Education. (4). E. Kreyszing. Advanced Engineering Mathematics 9th ed.
Course Schedule: Lecture: 3 hrs/week, Meets twice weekly Contact hours: 48 Practical: 0 Office Hours: 3 hrs/week, by instructor
Course Assessment: Exam: 1 OHT, 1 Final Exam Home work: Quizzes: Quizzes: 10 percent Grading(Tentative) 2 quizzes / tests: Each quizz / test will be con- ducted after 16 lectures. Assignments: 10 percent Grading(Tentative) 2 Assignments: Each assignment will be con- ducted after 16 lectures. 1 One Hour Tests (OHT): 20 percent Grading(Tentative) Final Exam: 60 percent Grading(Tentative)
Course Objectives: To learn techniques of numerical analysis.
At the end of the course the students will be able to: Domain BT. Level PLOs
terpolating and extrapolating the data.
ear algebra.
C=Cognitive domain, P=Psychomotor domain, A= Affective domain, BT= Bloom’s Taxonomy
Belongs to CLOs Topics covered in the Course and Level of Coverage: Topics/Teaching plan/Course division lecture wise. Estimated Contact Hours Clo.1 Mathematical Preliminaries, round off error and computer arithmetic, algorithms and convergence.
Clo.1 Introduction of interpolation and extrapolations. 1. Clo.1 Lagrange interpolation. 1. Clo.1 Newton’s divided difference interpolation. 3 Clo.2 Forward Difference and Backward Difference Interpolation. 3 Clo.2 utilizations of interpolation as extrapolation. 1. Clo.1 Numerical differentiation. 3 Clo.1 Introduction to numerical integration. 1. Clo.2 Elements of numerical 1ntegration. 1. Clo.1 Trapezoidal and Simpson’s approximations. 3
Belongs to CLOs Topics covered in the Course and Level of Coverage: Topics/Teaching plan/Course division lecture wise. Estimated Contact Hours Clo.2 Romberg integration. 1. Clo.1 Bracketing methods and iteration methods. 1. Clo.2 Solution of the system of linear equations. 1. Clo.2 Gause elimination method. 1. Clo.2 Iterative methods, Jocobi’s method. 1. Clo.2 Guss-Seidel method. 1. Clo.2 LU-decomposition method, Runge-Kutta method. 1. Clo.3 Absolute, relative, overflow and underflow errors. 1. Clo.1 Forward, backward and central difference formulas. 3 Clo.3 Introduction to non-linear equations (Bisection Method). 3 Clo.3 Newton Raphson Method. 3 Clo.3 Secant Method. 3
