Course Description
Numerical solution of mathematical models frequently encountered by mechanical engineers. Roots of nonlinear equations; solutions of system of linear equations; curve fitting using polynomial least squares regression, interpolation, and Fourier approximations; frequency domain analysis using Laplace and/or Fourier transforms; and numerical solutions of ordinary differential equations.
Athena Title
Numerical Methods in MCHE
Prerequisite
MATH 2500 and MATH 2700 and (ENGR 1140 or ENGR 1140H or MCHE 1140)
Semester Course Offered
Offered every year.
Grading System
A - F (Traditional)
Course Objectives
Upon successful completion of this course, students will be able to: • Determine roots of nonlinear equations, solve a system of linear equations, obtain the best fit (regression) and exact fit (interpolation) of curves for a set of discrete data, analyze systems in the frequency domain with Laplace and/or Fourier transforms, apply numerical equivalents of differentiation and integration, and solve ordinary differential equations numerically • Identify capabilities and limitations of various numerical techniques • Select appropriate numerical techniques to solve a given mathematical model • Develop computer programs to implement numerical algorithms using user-defined and built-in functions • Interpret the results obtained from numerical techniques while considering sources and extent of numerical error
Topical Outline
1. Basics of numerical analysis – mathematical models, accuracy, and error analysis 2. Roots of nonlinear equations 3. System of linear equations 4. Curve fitting (polynomial least squares regression, interpolation, and Fourier approximations) 5. Laplace and Fourier transforms 6. Numerical differentiation and integration 7. Numerical solutions to ordinary differential equations 8. Computer programs (user defined and built-in) to implement basic numerical algorithms
Syllabus