ENGR& 240 - Engineering Computation

Credits: 5
Variable Credit Course: No

Lecture Hours: 55
Lab Hours: 0
Worksite/Clinical Hours: 0
Other Hours (LIA/Internships): 0

Course Description: An introduction to engineering and scientific computing using a high-level, interpreted programming language (e.g., MATLAB; Python). Topics include modeling physical quantities using vectors and matrices; program architecture (e.g., logic; loops; functions); data pre- and postprocessing; and visualization. Specific applications include solutions of linear and nonlinear systems; regression and interpolation; numerical differentiation and integration; and solution of ordinary differential equations. Emphasis given to practical applications and how the subject applies in industry.

Prerequisite: MATH& 153 with a grade of C or higher (or concurrent enrollment with concurrent enrollment in ENGR 119).
Distribution Requirements:

Natural Sciences Distribution Requirement

Meets FQE Requirement: No
Integrative Experience Requirement: No

Student Learning Outcomes

Write programs that model, manipulate, and visualize physical quantities represented by vectors and matrices using common programming architecture (e.g., logic; loops; functions; libraries; etc.).
Demonstrate proper programming documentation by implementing common best-practices.
Describe how binary numbers, numerical error, and finite precision are related to computing results.
Solve linear and nonlinear systems using either direct or iterative methods.
Apply interpolation and regression techniques as continuous estimates to discrete datasets.
Implement numerical differentiation and integration techniques to solve initial and boundary value problems.
Explain the context in which each numerical method (e.g., solution of linear/nonlinear systems; interpolation and regression; and numerical differentiation and integration) is applied.

Course Contents

Providing context: What is applied numerical methods? How are they used? And in what context relative to popular methods such as finite element analysis (FEA), computational fluid dynamics (CFD), and data analysis.
Introduction to vectors and matrices and how they can be used to represent physical quantities.
High-level, interpreted programming languages and common programming environments.
Vector and matrix operations, loops and conditionals, functions, and visualization.
Solution of non-linear equations: Bracketing, Newton-Raphson, and Secant Methods.
Introduction to binary numbers, Taylor series, and sources of numerical error.
Solution of linear systems: Direct (e.g., upper-triangular systems and back substitution; Gaussian elimination; LU decomposition; etc.) and iterative (e.g., Jacobi; Gauss-Seidel; Gradient Descent).
Solution of nonlinear systems: Newton-Raphson and its relationship with open-source finite element solvers.
Data analysis: Interpolation and regression techniques.
Solution of ordinary differential equations: Numerical differentiation; numerical integration; truncation error; single- (e.g., Euler; Heun; Taylor; Runge-Kutta); multi- (e.g., Predictor-Corrector); and adaptive stepping methods for numerical stiffness; finite difference method.

Instructional Units: 5