Numerical Methods for Engineers

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Subject:

Science and Technology

Institution Name:

The Saylor Foundation

Collection:

Saylor Foundation

Grade Level:

Post-secondary

Abstract:

This course examines how numerical methods are used by engineers to translate the language of mathematics and physics into information that may be used to make engineering decisions. Often, this translation is implemented so that calculations may be done by machines (computers). Upon successful completion of this course, the student will be able to: Quantify absolute and relative errors; Distinguish between round-off and truncation errors; Interconvert binary and base-10 number representations; Define and use floating-point representations; Quantify how errors propagate through arithmetic operations; Derive difference equations for first and second order derivatives; Evaluate first and second order derivatives from numerical evaluations of continuous functions or table lookup of discrete data; Describe situations in which numerical solutions to nonlinear equations are needed; Implement the bisection method for solving equations; List advantages and disadvantages of the bisection method; Implement both Newton-Raphson and secant methods; Describe the difference between Newton-Raphson and secant methods; Demonstrate the relative performance of bisection, Newton-Raphson, and secant methods; Define and identify special types of matrices; Perform basic matrix operations; Define and perform Gaussian elimination to solve a linear system; Identify pitfalls of Gaussian elimination; Define and perform Gauss-Seidel method for solving a linear system; Use LU decomposition to find the inverse of a matrix; Define and perform singular value decomposition; explain the significance of singular value decomposition; Define interpolation; Define and use direct interpolation to approximate data and find derivatives; Define and use NewtonŐs divided difference method of interpolation; Define and use Lagrange and spline interpolation; Define regression; Perform linear least-squares regression and nonlinear regression; Derive and apply the trapezoidal rule and Simpson's rule of integration; Distinguish Simpson's method from the trapezoidal rule; Estimate errors in trapezoidal and Simpson integration; Derive and apply Romberg and Gaussian quadrature for integration; Define and distinguish between ordinary and partial differential equations; Implement Euler's methods for solving ordinary differential equations; Investigate how step size affects accuracy in Euler's method; Implement and use the Runge-Kutta 2nd order method for solving ordinary differential equations; Apply the shooting method to solve boundary-value problems; Define Fourier series and the Fourier transform; Find Fourier coefficients for a given data set or function and domain; Describe the finite element method for one-dimensional problems. (Mechanical Engineering 205)

Languages:

English

Material Type:

Assessments, Full Course, Homework and Assignments, Readings, Syllabi, Textbooks, Video Lectures

Media Format:

Graphics/Photos, Text/HTML, Downloadable docs, Video

Conditions of Use:

Creative Commons Attribution-Noncommercial 3.0
You are welcome to share, remix, and adapt this course under the terms of the Creative Commons Attribution 3.0 Unported License; however, many linked materials within this course are copyright of their respective authors/owners and may not be openly-licensed. Please respect the copyright and terms of use associated with each resource.

Copyright Holder:

The Saylor Foundation