Numerical Analysis 1

News.

• 12/17:  Histograms for Final Exam (follow link Exams) and for Course Total (see below) are posted.

Instructor

Bengt Fornberg    ECOT 214    fornberg@colorado.edu    Office hours:  MW 1:00 -1:50 pm, F 10:00 -10:50 am.

Grading assistants:  Mike Ostroski and Nate Monnig.

Lectures

MWF  11:00-11:50 am,  ECCR 151

Important Information.

• Course syllabus
• Homework Assignments (Typically posted each Wednesday, and due the following Wednesday)

Textbook.

Required textbook:   Atkinson, An Introduction to Numerical Analysis 

Select Lecture Notes.

• Runge phenomenon
• Linear difference operators
• Linear recursion relations
• Spline illustrations
• Radial Basis Functions  (A recent survey-style article on their use for large-scale geoscience calculations)
• Fourier series ans transforms (This and the next note set are extracted from a manuscript in progress: 'Modeling in Applied Mathematics' by B. Fornberg and B.M. Herbst ).
• The FFT algorithm 
• Key FFT step Key step in arriving at the factorization
• Bisection Basic algorithm for rootfinding in 1-D
• Fixed point iterations Example given in Bradie "A Friendly Introduction to Numerical Analysis"
• Fractals Example of how fractals can arise from Newton iterations
• Aitken's algorithm An application of the algorithm to a slowly converging alternating sum
• Three Approximations of exp(x) Comparison when limited to 5 coefficients (interval [-1,1])
• Orthogonal polynomials A collection of formulas relating to orthogonal polynomials
• Padé Approximation Conversion of a Taylor expansion to rational form
• Gregory's method for numerical quadrature  
• Introduction to Finite Difference (FD) methods
• Lagrange's multipliers  (Example of fundamental subspaces of a matrix)

Course Total; Scores.

The final Course Total score was calculated as Homeworks 30%, each Midterm 15% and Final Exam 40%. For the homeworks, the two lowest scores were disregarded. This led to a distribution of Course Total scores as shown on the following histogram.

The translation from these scores into actual grades has not yet been made.

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