ESM 2074: Computational Methods

Fall 2009
Index: 92866

Section: T R 3:30 pm - 4:45 pm
Instructor: Canfield

Course objectives:
Upon successful completion of the course, students shall be able to:

• Estimate error magnitudes, distinguish between round off and truncation errors, and calculate absolute and relative, true and approximate errors in numerical computations
• Do function minimization; find roots of equations using bracketing and open methods; explain the differences between the two methods and point out the advantage of each method
• Solve linear algebraic equations using Gauss elimination, LU decomposition, and the Gauss-Seidel method; as well as perform pivoting to reduce error; explain the differences between the two methods and understand the advantages of the methods
• Fit curves to data using linear least squares regression, data linearization, and polynomial regression; explain the advantage and disadvantage of using higher order polynomials
• Interpolate polynomials and derive splines for interpolation; explain the benefits of using splines
• Integrate functions using the trapezoidal rule, Simpson’s rules, Romberg integration, and Gauss-Quadrature; explain the differences between the methods and understand the advantages of the methods
• Numerically solve initial value ODEs using finite-difference methods including Euler, and Runge-Kutta
• Find eigenvalues of matrices
• Perform each of the above using structured professional-standard code

Prerequisites:
ENGE 1114

Corequisites:
MATH 2214