# ENGRMAE 140 Introduction to Engineering Analysis (2013-2014)

#### ENGRMAE 140 Introduction to Engineering Analysis

**ENGRMAE 140 Introduction to Engineering Analysis (Credit Units: 4)** Analytical methods of engineering. Nonhomogeneous linear ordinary differential equations. Variable coefficient linear ordinary differential equations. Eigenfunction expansions. Laplace transforms. Introduction to Fourier transforms. Linear partial differential equations. Prerequisite: Mathematics 2E or equivalent; Mathematics 3D. Aerospace Engineering, Civil Engineering, and Mechanical Engineering majors have first consideration for enrollment. (Design units: 0)

1. Ability to formulate differential equations for engineering problems based on physical principles. AE-1, ME-4 (EAC e)

2. Ability to solve ordinary differential equations by separation of variables, integrating factors, and integral methods, as well as solve systems of differential equations. ME-2 (EAC a)

3. Ability to utilize series methods and Sturm-Liouville analysis to solve ordinary differential equations. ME-2 (EAC a)

4. Ability to solve partial differential equations of the wave type, diffusion type, and Laplace type. ME-2 (EAC a)

5. Ability to analyze probability distributions and use statistical quantities. ME-3 (EAC a)

Applied Vector Calculus and Differential Equations

- Week 1: Review of prerequisite topics: First order ordinary differential equations with separation of variables, exact equations, integrating factors
- Week 2: Review of prerequisite topics: Constant coefficient ordinary differential equations, Laplace transforms, Green’s & influence functions
- Week 3: Review of prerequisite topics: Systems of first order ordinary differential equations, eigenvalues, eigenvectors, linearized systems
- Week 4: Variable coefficient linear ordinary differential equations, series solutions, Frobenius method, singular points, applications
- Week 5: Sturm-Liouville theory for boundary value problems, eigenfunction expansions, singular differential equations, applications
- Week 6: First order partial differential equations, method of characteristics, applications
- Week 7: Second order hyperbolic partial differential equations, wave equations, characteristics, Green’s & influence functions, applications
- Week 8: Second order parabolic partial differential equations, diffusion equations, separation of variables, Fourier series, Fourier transforms, Green’s & influence functions, applications
- Week 9: Second order elliptic partial differential equations, Laplace/Poisson/Helmholtz equations, separation of variables, Green’s & influence functions, method of images, applications
- Week 10: Instructor’s choice of special topics, e.g. probability, statistics, & sampling; numerical methods; phase space analysis

Meets for 3 hours of lecture and 1 hour of discussion each week for 10 weeks.

Computer usage is required for some integration and plotting.

Contributes toward the Mechanical Engineering Topics courses. Contributes toward the Aerospace Engineering Topics courses.

- Homework: 15%
- Midterm Exam: 40%
- Final Exam: 45%
- Total: 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 4.0 credit units

Engineering Science: 4.0 credit units

Engineering Design: 0.0 credit units