COMP ENG 3SK3. Computer-Aided Engineering Winter 2018 Course Outline

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COMP ENG 3SK3 Computer-Aided Engineering Winter 2018 CALENDAR/COURSE DESCRIPTION Numerical analysis; linear and nonlinear systems; least squares; polynomials, optimization; numerical integration and

1 COMP ENG 3SK3 Computer-Aided Engineering Winter 2018 CALENDAR/COURSE DESCRIPTION Numerical analysis; linear and nonlinear systems; least squares; polynomials, optimization; numerical integration and differentiation; interpolation; engineering applications. Three lectures, one tutorial. PRE-REQUISITES AND ANTI-REQUISITES Prerequisite(s): ELEC ENG 2CJ4 or 2CJ5; and MATH 2P04 or MATH 2Z03 Antirequisite(s): COMP ENG 3SK4, SFWR ENG 3X03 SCHEDULE Lectures: Tuesdays, Wednesdays & Fridays 12:30-1:20pm in ABB-102 Tutorial: Thursdays 5:30-6:20pm in KTH-B135 Labs: (None) INSTRUCTOR OFFICE HOURS AND CONTACT INFORMATION Dr. Dongmei Zhao ITB-A Ext Office Hours: TBA TEACHING ASSISTANT OFFICE HOURS AND CONTACT INFORMATION Name (First Last) Address Room Ext. Office Hours Maryam Jenab ITB-A TBA Peyvand Teymoori ITB-A TBA Abdallah Ghazy TBA Dania Elzouki ITB-A TBA COURSE WEBSITE/ALTERNATE METHODS OF COMMUNICATION COURSE OBJECTIVES Page 1 of 6

2 By the end of this course, students should be able to: Learn computer-aided techniques (numerical methods) Apply computer-aided techniques to practical engineering problems Reinforce programming skills (in C, MATLAB, and Python) by implementing computer-aided techniques ASSUMED KNOWLEDGE Calculus, basic matrix operations, ordinary differential equations, and circuit analysis. COURSE MATERIALS Required Text: [Chapra] Steven Chapra and Raymond Canale, Numerical Methods for Engineers, 7th Edition, McGraw-Hill, Calculator: Only the McMaster Standard Calculator (CASIO FX-991 MS or MS Plus) is permitted in tests and examinations. This is available at the Campus Bookstore. Other: Suggested Reference Books [Heath] Michael Heath, Scientific Computing: An Introductory Survey, Second Edition, McGraw-Hill, [Rao] Singiresu S. Rao, Applied Numerical Methods for Engineers and Scientists, Prentice Hall, COURSE OVERVIEW Week Topic Readings 1 Computer representation of numbers and errors Text Ch. 3 2 Taylor series Text Ch. 4 Objectives: represent a decimal number into IEEE standard format, find truncation error of floating point representation, understand concept of machine precision and its effect on floating point calculations, familiar with Taylor series expansion and relationship of its convergence and floating point calculation errors. 3 Roots of nonlinear equations Text Ch Roots of polynomials Text Ch. 7 Page 2 of 6

3 Objectives: find roots of continuous function with single unknown variable using one of the numerical methods covered in class in order to achieve required accuracy and perform simple error analysis, find repeated roots of polynomials, can use Taylor serious to derive iterative formula and convergence rate for Newton s method, understand pros and cons of each numerical method in terms of convergence and applied conditions. 5 One-dimensional unconstrained optimization Text Ch. 13 sections 1 & 3 Objectives: solve one-dimensional unconstrained optimization problems using Newton s method and Golden search method, understand convergence problem of Newton s method and the Golden ratio. 6 Multi-dimensional unconstrained optimization Text Ch. 14 Objectives: solve multi-dimensional unconstrained optimization problems analytically and numerically using Newton s method and steepest ascent method. Project 1 Trilateration for localization 7 Numerical integration Text Ch.21 sections 1 & 2, Ch 22 section 2 Objectives: numerically integrate a function and estimate truncation error; numerically integrate a function in order to achieve a preset accuracy. 8 Numerical differentiation Text Ch.23 section 1 Objectives: numerically estimate first and second order derivative of functions. Project 2 Recognizing handwritten digits using deep learning and neural networks 9 Numerical solutions of ordinary differential equations Text Ch.25 sections 1-4 and 26 Objectives: numerically solve first order and second order ordinary differential equations using Runge-Kutta methods, and estimate errors, numerically solve a set of ordinary differential equations, can use multistep methods to refine solutions. 10 Linear algebraic equations Text Ch Singular value decomposition Posted reading material. Page 3 of 6

4 Objectives: solve 2x2 and 3x3 linear equation sets analytically using Cramer s rule, apply Gauss elimination to solve a set of linear equations (using computer and by hand) and apply pivoting if necessary, perform LU decomposition and apply it to solve a set of linear equations, perform Cholesky decomposition and apply it to solve a set of linear equations, understand the limitation of Cholesky decomposition, apply Gauss-Seidel iteration to solve a set of linear equations and know the convergence condition; understand concept of condition number and can use it to do error analysis for solving a set of linear equations. Project 3 SVD for image compression 12 Least-squares regression Text Ch. 17 sections 1-4 Objectives: fit a curve using least square criterion, evaluate fitted model, and estimate data based on fitted model. 13 Interpolation Text Ch.18 sections 1 3 and 6 Objectives: apply Newton s and Lagrange interpolating polynomials to estimate data. ASSESSMENT Component Weight Projects (3) In-class tests (3) 25% 15% (each test will be 30 minutes long; the best 2 marks will be used) Final Exam 60% (a passing grade is required for the exam in order to pass the course) Total 100% Late submissions of assignments and projects are subject to 20% penalty per day (less than one day is counted as one day). Please note that announcements concerning any type of graded material may be in any format (e.g., announcements may be made only in class). Students are responsible for completing the graded material regardless of whether they received the announcement or not. What this means is that if you skip class and an announcement for a lab, test etc. is made in that class, then you are still responsible for that material. If you miss it, you get zero. ACCREDITATION LEARNING OUTCOMES Note: The Learning Outcomes defined in this section are measured throughout the course and form part of the Department s continuous improvement process. They are a key component of the accreditation process for the program and will not be taken into consideration in determining a student s actual grade Page 4 of 6

5 in the course. For more information on accreditation, please ask your instructor or visit: Outcomes Indicators Measurement Method(s) Demonstrate an ability to identify a range of suitable engineering fundamentals (including mathematical techniques) that would be potentially useful for analyzing a technical problem. For example, use appropriate numerical methods for unconstrained optimization to solve the trilateration problem in localization; and use the concept of SVD for image compression. Can estimate outcomes, uncertainties and determine appropriate data to collect. For example, can estimate accuracy and errors in numerical calculations, truncation errors in numerical integration and differentiation, absolute and relative errors in an estimated root of a nonlinear equation, and apply appropriate numerical methods to achieve required accuracy. Proposes solutions to open-ended problems. For example, propose solutions to reduce computational complexity in recognizing handwritten digits. Critically evaluates and applies knowledge, methods and skills procured through self-directed and self-identified sources, including those that lie outside the nominal course curriculum, so that to apply appropriate numerical methods in solving practical electrical and computer engineering problems. For example, students will be guided to learn some basic concepts of back propagation, deep learning, and neural networks. 2.2 test/project/exam 3.3 test/project/exam 4.3 test/project/exam 12.1 test/project/exam ACADEMIC INTEGRITY You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity. Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: Grade of F assigned for academic dishonesty ), and/or suspension or expulsion from the university. It is your responsibility to understand what constitutes academic dishonesty. For information on the various types of academic dishonesty please refer to the Academic Integrity Policy, located at Page 5 of 6

6 The following illustrates only three forms of academic dishonesty: 1. Plagiarism, e.g. the submission of work that is not one s own or for which other credit has been obtained. 2. Improper collaboration in group work. 3. Copying or using unauthorized aids in tests and examinations. ACADEMIC ACCOMMODATIONS Students who require academic accommodation must contact Student accessibility Services (SAS) to make arrangements with a Program Coordinator. Academic accommodations must be arranged for each term of study. Student Accessibility Services can be contact by phone at ext or at sas@mcmaster.ca. For further information, consult McMaster University s Policy for Academic Accommodation of Students with Disabilities. NOTIFICATION OF STUDENT ABSENCE AND SUBMISSION OF REQUEST FOR RELIEF FOR MISSED ACADEMIC WORK In the event of an absence for medical or other reasons, students should review and follow the Academic Regulation in the Undergraduate Calendar "Requests for Relief for Missed Academic Term Work": NOTICE REGARDING POSSIBLE COURSE MODIFICATION The instructor and university reserve the right to modify elements of the course during the term. The university may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster and course websites weekly during the term and to note any changes. Page 6 of 6

ME 4495 Computational Heat Transfer and Fluid Flow M,W 4:00 5:15 (Eng 177)

ME 4495 Computational Heat Transfer and Fluid Flow M,W 4:00 5:15 (Eng 177) Professor: Daniel N. Pope, Ph.D. E-mail: dpope@d.umn.edu Office: VKH 113 Phone: 726-6685 Office Hours:, Tues,, Fri 2:00-3:00 (or