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MECH501 NUMERICAL METHODS IN ME I

Course Objectives

At the end of this course, the student will learn: 

• representation of machine numbers and estimates of roundoff errors.
• numerical methods for approximation and interpolation of functions.
• numerical differentiation and integration techniques.
• numerical methods for solving systems of linear algebraic equations.
• numerical methods for solving eigenvalue problems.
• numerical methods for solving systems of nonlinear algebraic equations.
• provide illustrative examples of application of the numerical methods in mechanical engineering problems.

Course Content

Sources of error in numerical analysis. Interpolating polynomials. Difference tables. Lagrange and Chebyshev polynomials. Approximations by rational functions. Cubic splines. Least squares. Numerical differentiation and integration. Roots of equations. Systems of linear and non-linear equations. Eigenvalues and eigenvectors. Power and Jacobi methods. Quadratic forms. (R)

Course Learning Outcomes

Student, who passed this course, will:

• Operate with machine numbers and calculate absolute and relative roundoff erros.
• Interpolate functions using Lagrange, Chebyshev and Hermite polynomials.
• Learn basics of spline interpolation.
• Be introduced to approximaton and interpolation by rational functions.
• Perform numerical differentiation and integration and estimate their errors.
• Solve systems of linear and nonlinear algebraic equations using iterative methods.
• Solve numerically matrix eigenvalue problems.
• Be introduced to analysis of convergence and stability of different numerical schemes.
• Be introduced to the method of succesfull approximatons and its convergence analysis.
• Construct function approximations using least-squares theory.
• Apply the matrix singular value decomposition theorem to quadratic forms.