1. Final Examination – Fall 2018
San Jose State University
Department of Mechanical and Aerospace Engineering
ME 130 Applied Engineering Analysis
Instructor: Tai-Ran Hsu, Ph.D.
Review for
Final Examination – Fall 2018
Time: 7:15 – 9:30 AM for regular class
7: :00 AM for AEC qualified students
Date: Thursday, December 13, 2018
Place: Room 341, Engineering Building
(Review for final exam F18)

2. Approximate Scope on the Final Examination:
Materials coverage:
Printed lecture notes (Printed Notes F2018)
Slides presented at the classroom
Class lectures and presentations on the white board
Graded home works
Approximate Scope on the Final Examination:
0-20% on Chapter 1 to Chapter 3
80-100% on Chapters 4, 5, 6, 7, 8, 10

3. Chapter 1 Overview of Engineering Analysis
● Why engineering analysis?
(Figure 1.3 provides an answer)
● What engineers can use engineering analysis in their professional practices?
- in creating, problem solving and decision making
● The four stages in general engineering analysis
● Why Stage 2 and 4 are important to engineers?

4. Chapter 2 Mathematical Modeling
● What is mathematical modeling?
● What are involved in mathematical modeling of engineering problems?
● Physical meanings of: functions, variables, derivatives
● What roles do differential equations play in engineering analysis?
● How differential equations are derived for engineering analysis?
● What is curve fitting and why it is an important part of engineering analysis?
● What integrations can do in engineering analysis?
- compute plane areas
- determine average of physical quantities with nonlinear variation over
the range of a variable
- locate the centroid of plane areas
- determine revolution volume of solids with axisymmetric geometry

5. Application of First Order Differential Equations
Chapter 3
Application of First Order Differential Equations
● Typical forms of homogeneous and non-homogeneous equations
Homogeneous equation:
Non-homogeneous equation:
● Solution methods for both these equations
● Applications in fluid mechanics, e.g., time required to drain reservoirs
and funnels
● Application in heating and cooling of small solids
● Heat treatments in hot furnaces
● Refrigeration of small size of solids
● Design thermal conditions for thermal cycling
● Application in rise and fall of solids under influence of gravitation

6. Second Order Ordinary Differential Equations and Applications
Chapter 4
Second Order Ordinary Differential Equations and Applications
● Typical form of 2nd order homogeneous and non-homogeneous
differential equations:
Homogeneous equation:
Non-homogeneous equation:
● Solution method with u(x) = emx, leading to 3 cases:
a2 – 4b > 0, a2 – 4b < 0 and a2 – 4b = 0 for homogeneous equations
● Solution method with u(x) = uh(x) + up(x) for non-homogeneous equation, know how to
derive uh(x) and up(x)
● Application of homogeneous equations for free-vibration analysis with and
without damping – physical interpretation of analytical results?
● Consequences of mechanical vibrations to machines and devices
● Application of non-homogeneous equations for forced vibration analysis:
● Resonant vibration – engineering consequences
● Near-resonant vibration – engineering consequences
● Modal analysis – why it is important and what are involved in the analysis?

7. Introduction to Laplace Transform
Chapter 5
Introduction to Laplace Transform
● What is Laplace transform and why it is included in this course?
● Under what conditions can a function be transformed from a “variable domain” to
a “parametric domain?”
● Laplace transform of functions and derivatives
● What is inverse Laplace transform, and why?
● Inverse Laplace transform by “partial fraction” method
● Inverse Laplace transform by “convolution theorem”
● Using Laplace transform solving differential equations:
● Necessary conditions for using this technique
● General solution procedure
● The advantages of using Laplace transform in solving differential equations

8. Overview of Fourier Series
Chapter 6
Overview of Fourier Series
● What is Fourier series and why?
● What are necessary conditions to have a Fouries series?
● Mathematical expressions of Fourier series
● Applications of Fourier series in engineering analyses
● What is “convergence” of Fourier series?
● How Fourier series converge for:
● continuous functions, and
● piece-wise continuous functions?

9. Introduction to Partial Differential Equations
Chapter 7
Introduction to Partial Differential Equations
What are partial differential equations?
Under what situations one needs to use partial differential equations in
ME analysis?
Why partial differential equations are harder to solve than ODEs?
What is the principle of “Separation of Variables?”
Why transverse vibration of “strings” is an important subject of ME analysis?
Simple math models of transverse vibrations of strings
The partial differential equation and solution for transverse vibration of long
cables, and with good understanding of the physics of cable vibration
Modal analysis of vibrating strings and cables
Why modal analysis?
Natural frequencies of various modes of a string

10. Matrices and Solution to Simultaneous Equations
Chapter 8
Matrices and Solution to Simultaneous Equations
● Why matrices- a component of linear algebra is a critical tool for modern
engineering analysis?
● Matrices and determinants
● Different forms of matrices
● Arithmetic operations of matrices: +, -, and x
● Inverse of matrices
● Transposition of matrix of different forms
● Solution of large number of simultaneous equations using
● Inverse matrix method, and
● Gaussian elimination method
● Why large number of simultaneous equations?

11. Introduction to Finite Difference Method (FDM)
Chapter 9 (skip)
Introduction to Finite Difference Method (FDM)
● Why FDM is an important technique in engineering analysis?
● The difference between “finite differentials” and “finite differences?”
● The three-finite difference schemes:
● the forward difference
● the backward, and
● the central difference
● Derivation of finite difference schemes of higher order derivatives
● The general procedure and necessary conditions in using
the FDM solving differential equations
● Errors in using FDM solving differential equations
● General technique in mitigating error in using FDM for solving
differential equations

12. Chapter 10 Introduction to Statistics
● What is statistics, and what is the scope of statistics?
● The histogram – what does it tell and how to establish it?
● The “mode,” the “mean,” “median,” “variance,” and “standard deviation”
of statistical datasets, and their physical significances
● Method of determining: “mean,” “median” and “standard deviation”
● The “normal distribution curves” – what do they represent?
● The “normal distribution function” – what is it?
● Why “normal distribution function” is fundamentally significant in statistical analysis?
● Why “statistical process control” (SPC) is a realistic and effective way of
quality control of products in mass production?
● What tools do SPC provide?
● What are “control charts?” What are the control charts presented in this course and
how are they derived?
● How would engineers use these control charts in quality control in their production?

13. Tips on Doing Well in Quizzes and Final Examination
In preparation:
● Make sure that you understand what has been said in the printed notes.
● Pay attention to what the Instructor said in his lectures; For examples: He urged students not be in hurry to
determine the constants after having obtained the complementary solution of a non-homogeneous DE;
Not to jump on to the value of FS at discontinuities; Get the solution of homogeneous 2nd DEs on a piece
of paper. It will save you time in the derivation of solutions for these equations. There many other similar
remarks he made at the classes, or wrote on the white board.
● Be sure to do the assigned or unassigned HWs by your own effort (Honesty pays its dividend).
● Be sure you know what you did not do right in quizzes. Appreciate the way the Instructor solved
these problems as he demonstrated in the class upon returning the grade papers.
B. At the quiz or exam:
● Be sure to carefully read the problems and questions in the exam paper, and understand what you are
expected to do in solving these problems.
● Do not hesitate to ask the examiner on any question you may have on any problem in
the paper.
● Be sure to know the different weights assigned to all problems. Set the priority of solving first the
problems that have high assigned marks, which you know how to solve.
● Budget and manage your time in answering the problems, if you do not have enough time to reach the
required solutions, be sure to state in your paper on what the approach you have taken or will take in
solving the problem. (No “hand-waving” statements please)
● Quote the source, instead of deriving, the formula or equations that you use for solution of the problems
whenever you can. This will avoid wasting your time in deriving.
● Write you paper as neatly as you can. It’s human nature that grader may get tired of guessing what you
wrote on the paper.