Course Syllabus
Course: ENGR 2450
Division: Natural Science and Math
Department: Computer Science & Engineering
Title: Numerical Methods
Semester Approved: Fall 2022
Five-Year Review Semester: Summer 2027
End Semester: Summer 2028
Catalog Description: ENGR 2450 is an introduction to numerical methods of problem solving, including root finding, solutions of linear and nonlinear equations, eigen value problems, curve fitting and regression analysis, numerical differentiation and integration, numerical solution of ordinary differential equations, optimization, and numerical solution of partial-differential equations. Computer implementation of these methods using spreadsheets, various programming languages such as C++ or Python will be used.
Semesters Offered: Spring
Credit/Time Requirement: Credit: 3; Lecture: 3; Lab: 0
Prerequisites: Calculus II (MATH 1220) and either CS 1400 or ENGR 1400
Justification: This course is designed as a component of the standard pre-professional curriculum in engineering, which enables the student to transfer with junior level status into a four-year engineering program. ENGR 2450 is to be taken during the sophomore year of the pre-engineering curriculum and will prepare the student for subsequent course work. Similar courses are offered in university engineering schools. This course is most similar to CH EN 2450 and ME EN 2450 at the University of Utah and MAE 2450 at Utah State University.
Student Learning Outcomes:
Students will be able to solve a variety of engineering problems using numerical methods. Students will demonstrate this through homework assignments, quizzes, projects, and/or exams.
Students will understand the power and the limitations of the various alternative numerical methods, and be able to select the most appropriate method for a given problem. Students will demonstrate this through homework assignments, quizzes, projects, and/or exams.
Students will demonstrate the ability to formulate computer algorithms using appropriate coding techniques which implement the numerical solution method required. Students will demonstrate this through homework assignments, quizzes, projects, and/or exams.
Content:
This course will include:
• principles from linear algebra, including Gaussian elimination, LU decomposition, and iterative methods
• finding roots of nonlinear equations using various methods
• using eigenvalues and eigenvectors to find solutions to systems of linear equations
• curve fitting, including numerical interpolation and extrapolation
• numerical differentiation and integration
• numerical solutions of differential equations using Euler's method and Runga-Kutta methods
• optimization by finding minima and maxima of a function
• numerical solutions of partial-differential equations, both Laplace's equation and Poisson's equation.
• the C++ or Python language with computational software will be used to implement the above numerical methods.
In addition to teaching numerical methods principles and solution methods, ENGR 2450 highlights the wide variety of application paths that can leverage these skills in concert with diverse personal interests, careers, and aptitudes.
Key Performance Indicators:
Students will be assessed according to the methods outlined below:
Daily homework assignments 20 to 35%
Quizzes 0 to 10%
Midterm exams 20 to 50%
Projects 0 to 20%
Final Exam 15 to 30%
Representative Text and/or Supplies:
Chapra, Clough, Applied Numerical Methods with Python for Engineers and Scientists, current edition, McGraw-Hill.
Chapra, Canale, Numerical Methods for Engineers, current edition, McGraw-Hill.
Pedagogy Statement:
Class time employs a variety of inclusive learning techniques, including small group collaboration, class discussion, interactive demonstrations, and hands-on exercises that receive personal instructor or TA feedback.
Instructional Mediums:
Lecture
Maximum Class Size: 24
Optimum Class Size: 20
