# ENGRCEE 21 Computational Problem Solving (2015-2016)

#### ENGRCEE 21 Computational Problem Solving

**ENGRCEE 21 Computational Problem Solving (Credit Units: 4)** Engineering analysis and problem solving using MATLAB (or similar), including: matrix algebra, solving systems of linear and nonlinear equations, numerical integration of ordinary differential equations (ODEs) and coupled ODEs, and analysis of numerical errors. Corequisite: Mathematics 3D. Prerequisite: CEE20 and Mathematics3A. Civil Engineering and Environmental Engineering majors have first consideration for enrollment. (Design units: 1)

Study guide and lecture notes by Recktenwald also used extensively. Student Version of MATLAB or GNU Octave (recommended).

1. Perform matrix and vector operations involving matrix algebra (EAC a)

2. Solve systems of linear and non-linear equations (EAC a)

3. Numerically integrate functions and ordinary differential equations. (EAC e)

4. Solve single and coupled differential equations (EAC e)

5. Analyze and avoid numerical computing errors (EAC e)

6. Write programs to solve mathematical models of engineering systems and/or components (EAC c)

7. Carry out a design project in a small group that incorporates and applies numerical methods learned in the course and turn in a technical report.

- Introduction to computers and programming.
- Mathematics through linear algebra and differential equations.

- (Week 1-2: Chapters 2, 3, 4, & 6): Review of the MATLAB; Use of programs, functions, structures, while and for loops, scalars, matrices, vectors, and visualization; input and output, flow control, vectorization, global variables, inline function objects; good programming habits
- (Week 3: Chapter 7): Linear algebra review; matrix and vector operations; properties of vectors and matrices; special matrices; matrix eigenvalues and eigenvectors
- (Week 4 – 5: Chapter 8): Solving systems of linear equations
- (Week 6 – 7: Chapter 11): Numerical integration
- (Week 8 – 9: Chapter 12): Numerical integration of ordinary differential equations.
- (Week 10: Chapter 5): Numerical errors (discussed but not part of quiz / exams)

Meets for 3 hours of lecture and 2 hours of laboratory each week for 10 weeks.

- Course involves extensive use programming in MATLAB for data analysis, modeling, and graphical visualization.
- Required Lab Software: MATLAB (Mathworks, Natick, MA), and Numerical Methods with MATLAB (NMM) Toolbox, which is available on-line at: http://web.cecs.pdx.edu/~gerry/nmm/mfiles/

- Weekly laboratory/homework assignments involve working through a set of problems under the direction of the laboratory instructor. The assignment is begun in the laboratory session where each student works at a computer running MATLAB software, and it is completed at home or at a campus computer lab. The experience involves performing computations and writing MATLAB programs for engineering analysis and design purposes. A term project is also assigned to teams of 2-4 students. The term project involves developing a computer model of an engineering system or component of interest to each team. This assignment serves to provide an overview of the following problem solving method: 1. Problem identification, 2. Conceptual model, 3. Mathematical model, 4. MATLAB computer model, 5. Application.

- Contributes to the design experience and Engineering topics courses of engineering majors.

- Design is incorporated into this class in two distinct manners. On the one hand, the design process is presented to students in the context of a team project involving the development of engineering analysis software. In the context of this assignment, students identify and formulate a problem, develop software to solve it, and communicate both the nature of the problem and its solution method with a written report. On the other hand, design components such as problem formulation, determination of unknowns and constraints, etc., are developed throughout the course (e.g., solution of systems of equations). In weekly laboratory sessions, design components are emphasized while the team project allows students to work through the design process.

- Team Project: 10%
- Lab Participation: 15%
- Quizzes (3): 15% each
- Exams (3): 60% each
- Total: 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 4.0 credit units

Engineering Science: 3.0 credit units

Engineering Design: 1.0 credit units