ENGRMAE 140 Introduction to Engineering Analysis (2015-2016)

ENGRMAE 140 Introduction to Engineering Analysis

(Required for CE.)
Catalog Data:

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)

Required Textbook:
. Edition, , 1969, ISBN-13 978-0470383346.

Recommended Textbook:
William A. Sirignano, Roger H. Rangel and
Relationship to Student Outcomes
No student outcomes specified.
Course Learning Outcomes. Students will:

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

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

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

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

5. Ability to analyze probability distributions and use statistical quantities. ME-3

Prerequisites by Topic

Applied Vector Calculus and Differential Equations

Lecture Topics:
  • 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
Class Schedule:

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

Computer Usage:

Computer usage is required for some integration and plotting.

Laboratory Projects:
Professional Component

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

Design Content Description
Laboratory Portion:
Grading Criteria:
  • Homework: 15%
  • Midterm Exam: 40%
  • Final Exam: 45%
  • Total: 100%
Estimated ABET Category Content:

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

August 6, 2014
Senate Approved:
April 29, 2013
Approved Effective:
2013 Fall Qtr