CME 261F - Engineering Mathematics I
Detailed Syllabus
Academic Year ‘13/’14
September 9, 2013
Instructor Prof. Kaiwen Xia, Department of Civil Engineering
Office GB 314A
Teaching Assistants
Tamer Abdulazim ()
Glareh Amirjamshidi ()
MohamedElshenawy ()
Patrick PaskalisKanopoulos ()
Mona A. Qouqa ()
Bangbiao Wu ()
Wei Yao ()
Course Schedule
Monday / Tuesday / Wednesday / Thursday / FridayLecture / 13:00-14:00
LM159 / 9:00-11:00
SF1105
Practice* / 11:00-12:00
WB255/GB150 / 10:00-11:00
GB150/GB144
Tutorial** / 14:00-15:00
BA1130
* Practice sessions will be used for office hour and practice with Matlab.
** Tutorial sessions will be used for quizzes (in examination center) or general assistance to students.
Course Website
Blackboard will be used for announcements, posting problems, handouts, grades and any other information for the course. See for login instructions.
Course Description
This course deals with both numerical methods for engineering analysis and advanced topics in analytical calculus. Within the numerical methods portion of the course emphasis is placed on problem formulation, solution algorithm design and engineering applications. Within the analytical calculus portion emphasis is placed on the vector calculus.
Evaluation Scheme
Component / PercentageMatlabProjects / 20%
Two Quizzes / 30%
Final / 50%
Exams
All exams will be Type A (close book, no aids other than the information supplied on the examination paper) and calculators must be nonprogrammable.
Classroom Rules
Late appearance and early leave are discouraged.
Cell phones should be always off or set in the quiet mode during the lecture.
No noise should be made in the classroom except for the discussion periods.
Questions during the lecture are encouraged.
Repeated disruptive behaviors will be reported to the appropriate authorities.
Textbook
S.C. Chapra, Applied Numerical Methods with MATLAB, (3rded.), McGraw Hill
C.H. Edwards & D.E. Penney, Calculus: Early Transcendentals (7thed.), Prentice Hall
Table of Contents
The references to Chapters (Ch) and Sections (Sec) are from the following texts:
C= S.C. Chapra, Applied Numerical Methods with MATLAB, (3rded.), McGraw Hill
E&P = C.H. Edwards & D.E. Penney, Calculus: Early Transcendentals (7thed.), Prentice Hall
Topic I: Basics of Matlab and Sources of Numerical Errors (1 week)
(C, 2.1 – 2.4, 3.1 – 3.5, 4.1 – 4.3)
Covered:Matlab Fundamentals, programming in Matlab, data uncertainty, round off and truncation errors
Discussed:Model errors
Topic II: Solution of Nonlinear Equations in One Variable (2 weeks)
(C, 5.1 – 5.5, 6.1 - 6.4)
Covered: Graphic method, Bisection, Fixed-Point Iteration, Newton’s Method, convergence characteristics, assessing precision of answer at each iteration
Discussed: Engineering motivations for nonlinear equations, False Point and Secant methods, solving nonlinear equations with Matlab
Examples: Design of a model submarine and a dam
Topic III: Solution of Systems of Equations (2 weeks)
(C, 9.1 – 9.3, 10.1 – 10.2, 11.1-11.2, 12.1)
Covered: Building on material from MAT188 (intro to Gauss and LU), Naïve Gauss Elimination, LU Decomposition, Gauss-Seidel iteration
Discussed: engineering motivations for systems of equations (e.g., stiffness matrices for plane frame structures), Gauss with pivoting, system conditioning and methods for assessing reliability of computed answer, solution of nonlinear systems using iterative techniques
Example: Structural mechanics and pollution of the five lakes
Topic IV: Partial Differentiation (2 weeks)
(E&P, Ch 12)
Covered: Building on material from MAT187, Functions of several variables; functions of two variables and contour maps over a base plane; limits and continuity; partial derivatives in the ordinate directions, directional derivative in a specified direction, gradient (maximum directional derivative) and normal vectors
Discussed: engineering motivations
Examples: Vibration of strings and wave propagation in bars
Topic V, Part I: Least-Squares Approximation (1.5 weeks)
(C, 14.1 -14.3, 15.1, 15.3, 15.5)
Covered: Building on material in MAT188, Error measure for a given data point [ei = yi – f(xi)] and entire data set [Sr = (ei)2]; linear regression (with and without intercept), linearization of nonlinear functions, nonlinear regression
Discussed: engineering motivations (e.g., best-fit predictive models for data with uncertainty such as compressive strength data, exponential growth/decay models, power laws, saturation growth rate models, traffic data)
Example: Fitting of rock fracture data
Topic V, Part II: Interpolation and Polynomial Approximation (1.5 weeks)
(C, 17.1, 17.3, 17.5, 18.1 - 18.4)
Covered: Building on material in MAT188, method of undetermined coefficients (set of linear equations to determine polynomial coefficients), Lagrange Polynomials, problems with oscillations and extrapolation; linear, quadratic and cubic splines, implications of extrapolating spline fits beyond the given range of data
Discussed: engineering motivation (e.g., curve fits for use as predictive models for data such as stream flow and population change)
Example: Annual temperature change
Topic VI: Numerical Integration (2 weeks)
(C, 19.1 – 19.6, 20.1 – 20.4)
Covered: Building on material from MAT186 (intro to Trapezoid and Simpson’s rules), Trapezoid Rule, Simpson’s 1/3 and 3/8 rules, Gauss 2-point Quadrature, Error estimates and “n-2n” (Richardson) extrapolation for improved estimates
Discussed: engineering motivations (e.g., numerical analogues to the analytic approach described in the previous section Multiple Integrals, such as surface areas and volumes of slopes described by point-wise data coming from a land surveying program)
Topic VII: Ordinary Differential Equation (1 week)
(C, 23.1 – 23.6)
Covered: Euler’s method, Improvements of Euler’s method, Runger-Kutta methods
Discussed: Systems of equations
CME261 Syllabus Page 1 of 3 Prof. Kaiwen Xia