Fall 2015


Course Number: EML 3041




Credit Hours: 3



MAP 2302: Differential Equations,

EML 3035: Programming Concepts for Mechanical Engineers,

EML3500 Mechanics of Solids,

EGN3343 Thermodynamics


Course Website: Go to CANVAS.  Click on Piazza.


Class Location & Time:

EDU 115

Tu Th 11:00AM-12:15PM


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Numerical methods are techniques to approximate mathematical procedures (example of a mathematical procedure is an integral).   Approximations are needed because we either cannot solve the procedure analytically (example is the standard normal cumulative  distribution function)


or because the analytical method is intractable (example is solving a set of a thousand simultaneous linear equations for a thousand unknowns for finding forces in a truss). 

In this course, you will

·         Learn the numerical methods for the following mathematical procedures and topics - Differentiation, Nonlinear Equations, Simultaneous Linear Equations, Interpolation, Regression, Integration, and Ordinary Differential Equations. 

·          Calculation of errors and their relationship to the accuracy of the numerical solutions is emphasized throughout the course.   

·         Programming via MATLAB will be used to reinforce the fundamentals of the course as well as to solve intractable/real-life problems.

By the end of the course, the students will be able to

  1. Develop mathematical models for solving complex engineering problems;
  2. Reinforce  programming skills using the MATLAB environment to solve intractable/real-life problems;
  3. Calculate, quantify, and minimize errors in solving complex engineering problems where neat analytical solutions may not exist;
  4. Solve the following types of problems numerically:
    • Computation of derivatives and integrals
    • Nonlinear equations
    • Systems of simultaneous equations
    • Curve fitting (interpolation and regression) of discrete data
    • Integration of continuous and discrete functions
    • Ordinary differential equations (initial value or boundary value problems)


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In the course EML 3041 – Computational Methods, the program objectives are met as follows (The letters in the brackets given at the end of each outcome corresponds to the outcomes of the Mechanical Engineering program at USF)


1.       Apply the concept and steps of problem solving - mathematical modeling, solution and implementation. (e)

2.      List the steps of concepts of error - identification, quantification and minimization of errors.  Understand error sources of round off and truncation error.  Introduce the concept of machine epsilon and significant digits, and its relation to relative errors.  Reinforce these concepts in all the numerical techniques. (a)

3.      Find how derivatives of functions can be calculated numerically (a,e).

4.      Find real roots of nonlinear equations of the form f(x)=0 using bisection method and Newton-Raphson method. (a, e)

5.      Develop methods to solve simultaneous linear equations.  Use Naive Gauss Elimination to obtain a solution.  Show how Gaussian elimination with partial pivoting reduces round off error.  Show how the LU Decomposition method works to find solution for multiple right hand arrays or inverse of a square matrix.  (a, e, n)

6.      Develop methods to fit a curve to given data points via interpolation and regression.  Develop direct and spline interpolation methods of interpolation.  Develop how to find linear and nonlinear regression models for give data. (a, b, e, n)

7.      Develop methods of integration such as Trapezoidal rule and Gauss-Quadrature to find integrals of continuous functions.  Develop methods of integration for discrete functions based on Trapezoidal rule, interpolation and regression models (a, e, m)

8.      Develop Euler’s method, Runge-Kutta and shooting methods to solve ordinary differential equations that are coupled and/or higher order, initial-value or boundary value problems. (a, e, m)



a)                 an ability to apply knowledge of mathematics, science and engineering;

b)                 an ability to design and conduct experiments, as well as to analyze and interpret data;

c)                  an ability to design a system, component, or process to meet desired needs;

d)                 an ability to function on multi-disciplinary teams;

e)                 an ability to identify, formulate, and solve engineering problems;

f)                   an understanding of professional and ethical responsibility;

g)                 an ability to communicate effectively;

h)                 the broad educational necessary to understand the impact of engineering solutions in a global and societal context;

i)                   a recognition of the need for and an ability to engage in life long learning;

j)                   a  knowledge of contemporary issues; 

k)                 an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice;

l)                   a knowledge of chemistry and physics with depth in at least one.

m)              an ability to apply advanced mathematics through multivariate calculus and differential equations.

n)                 a familiarity with statistics and linear algebra;

o)                 an ability to work professionally in both thermal and mechanical systems areas including the design and realization of such systems.


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Inverted. Students will complete self-study assignments (reading materials, videos, online quizzes, and feedback essay) before each class. In-class content includes: micro-lectures, hand calculation problems, outlining higher-order exercises, and clicker assessment.  After-class assignments include online quizzes, problems sets, computer projects and mini-projects.



Autar Kaw

Office Location: ENC 2215

Telephone: 813‑974-5626


Office Hours:

Tuesday 2:00pm-3:00pm

Thursday 2:00pm-3:00pm


call 813‑974-5626 for making an appointment for consultation outside office hours


Skype me at autarkaw during office hours.


Ask questions via Piazza.

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Name: Benjamin Rigsby

Location: ENG205

             Office Hours: 

Monday 11:45AM-1:45PM,

Wednesday 9:45AM-11:45AM



call 813-396-9350 for making an appointment for consultation outside office hours


Ask questions via Piazza.


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1.       Numerical Methods with Applications: Customized for Mechanical Engineering of University of South Florida (USF)
By Autar Kaw, Egwu Kalu

Go to for any discounts

Order now as it takes 5-7 days to get it by Fedex-Ground.  An online version of the part of the book that carries the first one week of lectures is available on the Blackboard site.  Most of the net proceeds from USF sales of the book are donated to the USF Foundation, USF Student Organizations, and several other charities.

2.      Your MATLAB book for EML 3035 (The one written by Kaw & Miller OR Chapman).  Either and any edition of book is good.

3.      Buying MATLAB software for home use is optional. 

a)     You can always use MATLAB free of charge in LIB 125C (first floor lab in the Library), and other open labs except EDU open lab. 

b)     The university has a program where you can access MATLAB online from anywhere (

c)      You may already have MATLAB when you took the EML3035 course. 


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Matlab overview and refresher:


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Only nonprogrammable calculators are allowed for class work, homework, and tests (except the concept test where no calculator or formula sheet is allowed).  The only acceptable calculators are TI-30Xa and TI-30Xa Solar (the solar and the new model have better display).  No other calculator is allowed.  No exceptions will be made.  Office Depot, Staples, and Wal-Mart stock these calculators.  Bring the calculator to every class.



This new model is better as it has a clearer display.




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We will use Clickers for in-class activities.  The instructor brings the clickers to class.  Pick a clicker if it is displayed in front of the class.  Put it back at the end of the class.



Techniques and computer programming tools to solve engineering problems using numerical methods.  Topics include roots of equations, matrix algebra, integration, differential equations and curve fitting.

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Total Weeks: 16

Day-by-day lecture schedule will be announced on Piazza.

Test 1: Tuesday September 29, 2015, 11AM-12:15PM

Test 2: Thursday October 29, 2015, 11AM-12:15PM

Test 3:  Tuesday December 1, 2015, 11AM-12:15PM

Concept test: Thursday December 3, 2015, 11AM-12:15PM.

Final Exam: Tuesday December 8, 2015: 10AM-12noon, EDU 115


Chapter 1 – 4 lectures

Chapter 2 – 1 lectures

Chapter 3 – 2 lectures

Chapter 4 – 4 lectures

Chapter 5 – 3 lectures

Chapter 6 – 4 lectures

Chapter 7 – 3 lectures

Chapter 8 – 4 lectures


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Test#1, 2, 3

14%, 14%, 14%

Special Assignments/Computer Projects


Online CANVAS Quizzes


Concept Inventory


Final Exam





Tests#1, 2, 3: Each test is graded out of 100.  Tests are closed book and closed notes.  A formula sheet made by the instructor is allowed.


Special Assignments/Computer Project Reports:  Computer project reports are due at the beginning of the class period they are due in.  If you are not coming to class, you can slip your report/special assignment under my door one hour before the class period begins on the day it is due.  If it is slipped after this time, it will not be graded.  Late reports are not accepted or graded.


Reports not submitted when they are due will be graded later only if you have a legitimate, verifiable, and documented excuse as given in the syllabus.   You need to submit your report/special assignment on the first day you are back in class.


The special assignments will be given throughout the semester.  These may include submitting assigned HW problems for a grade, mini-projects, essays, in-class assignments such as minute papers, reflective resubmission of graded quizzes, etc.


Online Quizzes: These are online quizzes that get automatically graded and are taken on CANVAS before and after each lecture.


Final Exam: The final exam includes combination of multiple-choice and free response questions.  The final exam is comprehensive examination of all the topics covered in the course.


Concept Test: This is a test of the conceptual knowledge of the course.  The test is a multiple choice questions test with anywhere from 16-30 questions asked in a 75-minute test.


 Grading Rubric: Each free-response question on test/final exam is graded on a scale of 0-4.

4: Demonstrates complete understanding of the problem. All requirements of the task are included in response.

3: Demonstrates considerable understanding of the problem. All requirements of the task are included.

2: Demonstrates partial understanding of the problem. Most requirements of the task are included.

1: Demonstrates little understanding of the problem. Many requirements of the task are missing. (There is something salvageable.)

0: Left blank or shows no demonstration of understanding of the problem. (Maybe simply repeated the data or copied formulas, or showing formulas that are not even relevant.)


Extra Credit: You can earn two (2) extra credit points applied directly to your overall grade by participating in a research project study funded by the National Science Foundation to enhance the educational experience received by students in the class. More information about this study will be made available on Piazza and Blackboard later during the semester. There is no penalty if you choose not to participate in this study. Alternatively, you can choose to write a 500-word essay on topics of numerical methods that are mutually agreed upon between you and the instructor for the same credit.


Attendance and Late Policy: YOU SHOULD NOT RUSH TO MY CLASS as nothing is that important in life. I myself may get to come late to a class for something that is beyond my control or even with the best of planning. In the last 28 years of teaching, I have been late to class five times.


Curving the Grade: The adjustments made to your course grade is as follows and is made to the tests#1, 2, 3, concept test, and the final examination. 


If the average for students registered for the course (all withdrawal students and students missing the exam are not included in the calculation) for any of the tests is less than 70%, the difference is added to every registered student's grade for that test (exception include students missing a test for verifiable excuse, where adjustments are at the discretion of the instructor).


Guaranteed Grading Scale:

Grade A+  is 98‑100 (4.00)  Grade A  is 90-97 (4.00)      Grade A- is  86-89 (3.67)

Grade B+ is 83-85 (3.33)      Grade B is 80-82 (3.00)        Grade B- is 76-79 (2.67)

Grade C+ is 73-75 (2.33)      Grade C is 70-72 (2.00)        Grade C– is 66-69 (1.67)

Grade D+ is 63-65 (1.33)      Grade D is 60-62 (1.00)        Grade D‑ is 56‑59 (0.67)

Grade F is 0‑55 (0.00).


Your final grade will be calculated as follows at the end of the course.  A number 0.999999 will be added to your overall percentage grade.  The integer part (INT function in Excel) of the grade will be recorded as your final grade.  Course grades will be evaluated on the above given percentages and a letter grade will be assigned to you as outlined in the University catalog for undergraduate students (2015-2016).


Course grades will be evaluated on percentage score and a letter grade will be assigned to you as outlined in the University catalog for undergraduate students (2015-2016). 


Do not wait until the last day before an examination or a test to ask questions. Graded assignments and quizzes not picked up when handed out in class can be picked up only during the above given office hours or at the end of the class.  Graded assignments and tests not picked up by January 14, 2016 will be discarded. Final exams or concept tests are not returned.


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Attendance is not compulsory and you are responsible for topics covered in class, announcements made in class, homework assigned in class, and submitting lab reports and special assignments on time.


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Re-grading of a test, lab report, essay or computer project should be requested within five working days of it being returned to you.  Re-grading after the final grade is assigned for the course will be allowed only in extreme circumstances.  Mistakes in the grade book entries should be rectified as soon as possible to avoid any change of grade issues.  You will need a copy of all your graded tests for verification.  KEEP ALL YOUR GRADED PAPERS TILL THE FINAL GRADE IS ASSIGNED.


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Grades will be updated on


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NO make‑up tests will be given.  However, in the event of a serious illness (physician's statement documenting severity of illness required), death in the family or other legitimate, documented, verifiable emergency resulting in the absence from a schedule test, each case will be evaluated separately.  The decision of the instructor is final.  An example of a make-up score is that if you miss a test, you may be given the same grade as the final exam score in the missed topics, and so on.  Curving of make-up grades is discretion of the instructor.


Notification of absence must be given before the commencement of the scheduled examination or test to me.  You need to type a professional memo (see sample) about your absence addressed to me as soon as possible.  Attach any documentation with it (no e-mails will be accepted).


Do not presume that your reasons for missing an examination or test are acceptable unless authorization is given to you.


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Students who need to be absent under this rule must provide written notice of date(s) to me by the second-class meeting.  The request needs to be reasonable under university rules.



“Students in need of academic accommodations for a disability may consult with the office of Students with Disabilities Services to arrange appropriate accommodations. Students are required to give reasonable notice prior to requesting an accommodation.” The website is

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If you are found cheating on any of the tests, exams, graded HWs, projects, you will get a 'FF’ for the whole course, and referred to the Dean's office for further process or appeal.

Academic disruption includes excessive side talking, lack of respect for your fellow classmates and the instructor, listening to music, cell phone distractions, solving crossword puzzles. These will be handled as per the undergraduate catalog of 2012-13.

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The following restates portions of USF Academic Policy from the USF Undergraduate Manual concerning the “incomplete” grade, academic dishonesty, and disruption of academic process.  The faculty of the Department of Mechanical Engineering requests all students in the department to be informed of these policies.


Incomplete Grade Policy

“It may be awarded to an undergraduate student only when a small portion of the students work is incomplete and only when the student is otherwise earning a passing grade.”


Academic Dishonesty

“Each individual is expected to earn his/her degree on the basis of personal effort.  Consequently, any form of cheating on examinations or plagiarism on assigned papers constitutes unacceptable deceit and dishonesty.”


Penalties for Academic Dishonesty

“Penalties for academic dishonesty will depend on the seriousness of the offense and may include assignment of an “F” or a numerical value of zero on the subject paper, lab report, etc., an “F” or an “FF” grade (the latter indicating academic dishonesty) in the course, suspension or expulsion from the University.”  In this course, a FF is assigned for any cheating in the assigned HW, quizzes and/or competency tests.


Disruption of Academic Process

“Disruption of the classroom or teaching environment is also unacceptable.  This cannot be tolerated in the University community, and will be punishable, according to the seriousness of the offense.”


Punishment Guidelines for Disruption of Academic Process

“Punishment for disruption of academic process will depend on the seriousness of the disruption and will range from a private verbal reprimand to dismissal from class with a final grade of “W,” if the student is passing the course.  If the student is not passing, a grade of “F” will be shown on the student record.  Particularly serious instances of disruption of the academic process may result in suspension or permanent expulsion from the University.”



All unauthorized recordings of class are prohibited.  Recordings that accommodate individual student needs must be approved in advance and may be used for personal use during the semester only; redistribution is strictly prohibited.

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In response to student requests and instructor observations, the following class rules will apply in this course:

  1. Put the cell phones on silent or vibrate.  Cell phones should be out of sight and not answered inside the classroom.
  2. No checking of e-mail or internet surfing in the class or during the breaks.
  3. No food or drink in the lab, a drink is allowed during the lecture.
  4. No talking during lecture (except for questions to instructor or discussion time).
  5. No reading newspapers or magazines or solving crossword puzzles, etc.
  6. No working on other coursework during lecture.
  7. No use of laptops.
  8. No use of portable electronic music devices (mp3 players, iPods, etc).


The purpose of these class rules is to eliminate activity that is disruptive to the academic process.  Most students view these as a common courtesy to the instructor and fellow students.  Failure to comply with a class rule will be viewed as a Disruption to the Academic Process.  The penalty for such disruption is given in the syllabus.

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