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B. Riviere


CAAM 553 NUMERICAL ANALYSIS

Fall 2013

    Meeting time and place:MWF 9am-9:50am, DCH 1075
    Office Hours:by appointment (send email to: riviere at rice dot edu; Duncan Hall 3022)
    Course Objectives
    This course covers fundamental algorithms for obtaining numerical approximations of solutions to continuous problems.
    Course Outcomes
    Upon completion of the course, students will know how to construct and analyze numerical methods for interpolation and approximation of functions, quadrature, and the solution of ordinary differential equations. They will have a good understanding of sensitivity analysis, floating point errors, the solution of linear systems by matrix factorizations, least squares problems, the singular value decomposition and eigenvalue problems.
    Grades
    Homeworks (60%), Midterm I (20%) and Midterm II (20%)
    Midterms
    Midterms are pledged (see Rice honor code) and individual. Problems cannot be discussed with classmates. Midterm I is due in class October 9.
    Textbooks and Class Notes
    Class notes by Dr. Embree are available on owl-space and at the bookstore.
    E. Suli and D. Mayers. "An Introduction to Numerical Analysis", Cambridge 2003.
    L.N. Trefethen and D. Bau, III. "Numerical Linear Algebra", SIAM 1997.
    Homeworks
    You may discuss homework problems with classmates, but you have to write your solution individually.
    Homework1: due on September 4.
    Homework2: due on September 18.
    Homework3: due on September 25.
    Lectures
    Summary of lectures can be found on the class page on owlspace.
    *Lectures 1,2: floating point numbers. Reading Trefethen and Bau pages 97-113.
    *Lectures 3,4: stability, condition number. Reading Trefethen and Bau pages 1-17 and pages 89-96.
    *Lectures 5-10: interpolation. Reading Suli and Mayers pages 179-199, pages 292-309.
    *Lectures 11-15: numerical quadrature. Reading Suli and Mayers pages 200-223, pages 277-291.
    *Lectures 16-17: approximation. Reading Suli and Mayers pages 224-276.
    *Lectures 18-26: numerical solution of ODEs. Reading Suli and Mayers pages 310-360.
    Additional reading
    The definition of numerical analysis by L.N. Trefethen, 1992.
    Analysis: W. Rudin "Principles of Mathematical Analysis", 3rd ed. McGraw-Hill, New York, 1976.
    Linear algebra: P. Lax "Linear Algebra", Wiley, New York 1997.
    Linear algebra: C. Meyer "Applied Matrix Analysis and Linear Algebra", SIAM Philadelphia 2000
    Numerical analysis: W. Cheney and D. Kincaid "Numerical Mathematics and Computing", 5th ed. Thomson, 2004.
    Class web site and owlspace
    Students are responsible for viewing the class web site regularly as material will be added to the site throughout the semester. Additional material is posted on the class page on owlspace.
    Late policy
    Homeworks are to be given during class on the due date. If the homework is turned in after the class is over, it is considered late. Late homeworks will incur penalties in increments of 10%.
    Disability
    Any student with a documented disability requiring accomodations in this course is encouraged to contact me after class or during office hours. Additionally, students also need to contact Disability Support Services in the Ley Student Center.