SHAW UNIVERSITY

MAT 417: NUMERICAL ANALYSIS

COURSE OUTLINE

Instructor:Dr. Simon Ugwuoke            Office Phone: 546-8543

Office Hours:                         e-mail: sugwuoke@shawu.edu

MWF 12N - 1PM, 2PM - 3PM                  Office Location: Graphics Rm 4

T,Th 10:50AM - 11:50AM, 1:20PM - 2:20PM

General Description

After completing this course successfully, students should be able to do the following:

· Approximate and compute functions using Taylor Series.

· Use computer and graphics calculator to solve complex problems in

· Use one of the programming languages listed above to solve problems in

· Write a simple computer program for generating a table of iterations of roots, such

· Demonstrate an understanding of the basic sources of error in computations

  and how these errors are minimized.

· Demonstrate an understanding of computer representation of numbers and

  change of bases between binary, octal, decimal, and hexadecimal.

· Locate roots of equations using the bisection method, secant method,

  and Newton’s method.

· Interpolate functions by polynomials.

· Demonstrate an understanding of the numerical differentiation of a function.

· Demonstrate an understanding of the numerical integration of a function.

· Apply trapezoidal and Simpson’s rules in numerical integration of functions.

· Solve a system of n linear equations in n unknowns using Gaussian

  elimination, and using computer and graphing calculators.

1.2 Review of Taylor Series

    Taylor and Maclaurin series

    Taylor and Maclaurin's polynomials

    Power and Binomial Series

2   Number Representation and Errors

    Machine number: mantissa and characteristic

    Computer representation of numbers

    Roundoff errors, Errors due to underflow and overflow, Other errors

    Absolute error and Relative error, Significant digits

    Base B Numbers; Conversion of Integer Parts

    Conversion of Fractional Parts

    Base Conversion: 10 <----> 8 <----> 2 <---->16

Chapter 3 Locating Roots of Equations

3.2 The Newton's Method     3.3 Secant Method

    Advantages and Disadvantages of each method

    Comparison of the three methods;  Convergence Analyses

    in these methods; Comparison of the methods

    Computer Algorithms related to each method

    Zeros of Polynomials; Synthetic division; Horner's method

4.1 Polynomial Interpolation:

    Newton's interpolatory divided difference formula

    Newton's forward-difference formula

    Newton's backward-difference formula

    Centered-difference formulas

4.2 Errors in Polynomial Interpolation

4.3 Estimating Derivatives and Richardson Extrapolation(NCDPI 3.4)

5.2 Trapezoidal Rule

Chapter 6 More on Numerical Integration

6.1 Simpson's Rule;    6.2 Gaussian Quadrature Formulas

    Errors of Numerical Integration

    Linear Systems of Equations (NCDPI 1.1, 1.2)

    Linear Algebra and Matrix Inversion (NCDPI 1.1, 1.2)

    The Determinant of a Matrix

    Taylor Series Methods; Euler's Method

    12.1 Method of Least Squares: Linear Least-Squares

To enhance the learning atmosphere of the classroom, students are expected to dress and behave in a fashion conducive to learning in the classroom. More specifically, students will refrain from disruptive classroom behavior, e.g., talking to classmates, disrespectful responses to teacher instructions; swearing; wearing clothes that impede academic learning such as but not limited to, wearing body-revealing clothing and excessively baggy pants; hats/caps, and/or headdress. Students will turn off telephones prior to entering the classroom.

Students who exhibit the behaviors described above, or similar behaviors will be immediately dismissed from class at the third documented offense. The student will be readmitted to class only following a decision by the department chair. The student may appeal the decision of the department chair to the Dean of the College offering the course, and, subsequently, to the Office of the Vice President for Academic Affairs, and then to the President of Shaw University. The decision of the President will be final. Failure to follow the procedures herein outlined will result in termination of the appeal, and revert to the decision of the department chair.

Each behavior construed by the teacher/professor as non-contributive to learning will be recorded, properly documented, and appropriately reported to the student and to the chair of the academic department offering the course. The report will be in written form with a copy provided to both the student and the department chair. The faculty member should retain a copy for his/her own records.

Additional student behavior codes may be found in Student Affairs.