Math 105A, Fall 2009
Text: Numerical Analysis, by Burden and Faires (8th edition)
A calculator (any type) is required for this course.
Course Content: floating point arithmetic, roundoff, solving transcendental equations, linear
systems, matrix factorization, eigenvectors and eigenvalues.
Prerequisites: A passing grade in Math 2A, 2B and 2J plus computer programming experience
Homework: Each week a set of problems from the text will be assigned. These problems are to
be done by hand (without computer). Homework assignments will be due every Friday in lecture.
Computer Assignments: Each week a set of problems involving computer computations will be
assigned. These assignments are to be done by writing Matlab programs and will be handed in to
the course Drop Box each Friday by 6:00 pm.
Quizzes: There will be 5 quizzes in total. The quiz will take place during the last half hour of the
lecture. All quizzes are to be done independently and without books or notes.
Final Exam: Monday
The final exam is “closed book”- no books, notes, or phones. Picture I.D. is required and must be
presented upon request. Students are expected to be present for all quizzes and final exam. There
are no early exams. A late exam will be administered only at the discretion of the instructor in
the event of a verifiable emergency. In the event of a verifiable emergency, you must contact the
instructor as soon as possible, and in any case, prior to the next regularly scheduled class.
Grades: There are 500 points available for the student to earn- 100 points for homework, 100
points for weekly computer assignments, 100 points for quizzes, 50 points for the final computer
project and 150 points for the final exam. You are guaranteed a grade of
 A, if you earn 465 points (93%)
 A-, if you earn 450 points (90%)
 B+, if you earn 435 points (87%)
 B, if you earn 415 points (83%)
 B-, if you earn 400 points (80%)
 C+, if you earn 385 points (77%)
 C, if you earn 365 points (73%)
 C-, if you earn 350 points (70%)
 D+, if you earn 335 points (67%)
 D, if you earn 315 points (63%)
 D-, if you earn 300 points (60%)
The final grade for the course will be exactly determined by the points above and no rounding of
points to the next highest grade will be done.
Lab Grade: The grade for the laboratory will be the highest of either your grade in the lecture or
the grade on your final computer project.
Tentative Schedule:
Sections
Topics
1.1
Introduction to numerical analysis
1.2
Round-off errors, Algorithms
2.1
Bisection method
2.2
Fixed-point iteration
2.2 & 2.3
Fixed-point iteration, Newton’s method
2.3
Newton's method!
2.4
Rate of convergence
Review
Quiz 1
2.4
Multiplicity of zeros
6.3, 6.4
Review of linear algebra
6.1
Linear system of equations
6.1,6.2
Linear systems of equations, Pivoting
6.2
Pivoting strategies
6.4
Determinant of matrix
6.4 & 6.5
Determinant of matrix, Matrix factorization
6.5
Matrix factorization; Quiz 2
7.1
Norms of vectors and Matrices
7.2
Eigenvectors and eigenvalues
7.3
Iterative methods for solving linear systems
7.3
Iterative methods for solving linear systems
7.4
Error bounds and iterative refinement; Quiz 3
7.5
The conjugate gradient method
7.5
The conjugate gradient method
7.5
The conjugate gradient method
9.1
Linear algebra and Eigenvalues
9.2
The power method; Quiz 4
9.2
The power method
9.3
Householder's method
9.4
The QR method
9.4
The QR method, Review Quiz 5
Review for the final