Course Contents
This course is intended to give you a significant experience in solving relatively complicated problems in applied mathematics and some introduction to the approximate solution of mathematical problems using numerical methods. The course will involve a significant component in modelling. The modelling will be used to translate real problems or idealized versions of real problems into mathematical terms. A large number of numerical methods will be introduced throughout the semester. Students will be expected to implement algorithms and analyse the output of your computer code relative to the original problem.
Course Synopsis
Upon successful completion of this course, one should be able to:
1. Describe di_culties that can arise because computers usually use finite precision, often non-decimal arithmetic.
2. List sources of error in computation, particularly to be able to identify when catastrophic cancellation may occur in a given computation.
Course Learning Outcomes
Upon successful completion of this course, the student will be able to
• Analyze a practical problem, understand the mathematical basis of the problem,
• Then proceed to develop and implement an algorithm to find a numerical solution of the problem.
• Study the solution and develop a practical interpretation of the numerical results.
• Effectively communicate the solution and its interpretation to others
Newton-Cotes Formulae for Integration
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Numerical Integration Composite Trapezoidal and Simpson's rules
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Numerical Integration Composite Trapezoidal and Simpson's rules
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Numerical Integration Composite Trapezoidal and Simpson's rules
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Euler's Method
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Euler's Method - Example 1
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Runge-Kutta method
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Runge-Kutta method
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Multistep methods
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Approximating eigen value and eigen vectors by Power method
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Book Title : Applied Numerical Analysis
Author : Gerald/Weatley
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Book Title : Applied Numerical Analysis
Author : Addison Wesley
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Book Title : Numerical Analysis
Author : Saeed Akhtar Bhatti
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Book Title : Numerical Methods in Scientific Computing
Author : Germund Dahlquist and Åke Björck
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Book Title : Numerical Methods for Scientific Computing
Author : J.H. Heinbockel
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Book Title : Numerical Analysis
Author : I.A. Khubaza
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Book Title : Numerical Analysis and Programming
Author : Shan S Kuo
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Book Title : Numerical Analysis
Author : Berden Fairs
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Book Title : Numerical Analysis
Author : Gerald
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