Department of Mathematics and Physics College of Arts and Sciences University of Qatar Course Syllabus Components By Dr. Safeer Hussain Khan 2009/2010 Academic Year Dr. Safeer Hussain Khan Mathematics for Engineers Faculty Information Name: Safeer Hussain Khan Program: Math & Physics Telephone: 4852200 E- Mail: safeer@qu.edu.qa Office Number: C216 Corridor # 3 2 Dr. Safeer Hussain Khan Mathematics for Engineers Course Information Course Name: Mathematics for Engineers Course Number: 20967-MATH 217 – L01 Credit Hours: 3 Class Timings: Contact Hours: 4 8:00-9:15 on Mondays,Wednesdays and 2:00-3:15 Wednesdays Office Hours: Tue 10:00-11:00 Wed 1:00-2:00, First Day of Classes: Sunday, Feb 21, 2010 Last Day of Classes: Thursday, June 3, 2010 Location of Class Room: BCR-C201 Prerequisites: Calculus 3 Required Textbook: Fundamentals of Differential Equations bound with IDE CD (5th Edition) by Nagle, Saff and Snider Reference Books 1. Advanced Engineering Mathematics, by Peter V.O'Neil 2. Differential Equations with boundary problems: Dennis G. Zill and Michael R. Cullen. 3. Advanced Engineering Mathematics, Kreyszig, 7th ed., 1993, John Wiley. 3 Dr. Safeer Hussain Khan Mathematics for Engineers Course Description Mathematics for Engineers is a course which introduces some mathematical tools for solving and analyzing the problems arising in the mathematical modeling in engineering. A specified differential equation endeavors to match the known features of the application being modeled, as well as to be able to predict the systems' behavior in other circumstances. The course integrates theory and application using a problem-based approach. This course prepares the students for future learning in relation to problem solving and decision-making, technical competence, teamwork and leadership. First-Order Differential Equations: Initial-value problem. separable variables. Homogeneous equations. Exact equations. Linear equations. Integrating factor. Bernoulli equation. Applications. Second-Order Differential Equations: Initial-value and Boundary-value problems. Linear differential operators. Reduction of order. Homogeneous equations with constant coefficients. Nonhomogeneous equations. Method of undetermined coefficients. method of variation of parameters. some nonlinear equations. Applications. Higher order Differential Equations. Series Solutions: Cauchy-Euler equation method. Solutions about ordinary points. Solutions about singular points. Method of Frobenius. Second Solutions and Logarithm terms. System of Linear Differential Equations: Definitions. Elimination method. Application of Linear Algebra. Homogeneous linear systems. Nonhomogeneous linear systems. Solving systems by Laplace transforms. Laplace Transforms: Definitions. Properties. Inverse Laplace transforms. Solving initialvalue problems. Special functions: Heavyside unit step function. Convolution theorem. Partial Differential Equations: Some mathematical models. Fourier series solutions. Method of seperation of variables. The D’Alembert solution of the wave equation. Applications. 4 Dr. Safeer Hussain Khan Mathematics for Engineers Course Objectives To acquaint students with the necessary basic theories and methods both in Ordinary and Partial Differential Equations. To acquaint students with the Differential Equations and their applications. To introduce, among others, the Laplace Transform method which is an efficient tool for solving Engineering problems in an elegant way. To present students with some realistic problems. To equip the students with a number of methods for solving differential equations, concentrating on those which are of practical importance. To make use of softwares like Mathematica wherever required. 5 Dr. Safeer Hussain Khan Mathematics for Engineers Content Distribution The distribution of the textbook units over one semester (14 weeks) Topics Weeks Basic Definitions and Terminology: Motivation, ½ Definitions, Classification by type, Classification by order, Linearity, Solutions. First-Order Differential Equations: Initial-value problem, ½-3 Separable variables, Homogeneous equations, Exact equations. Linear equations, Integrating factor, Bernoulli equation, Applications. Second-Order Differential Equations: Initial-value and 3-6 Boundary-value problems, Linear differential operators, Reduction of order, Homogeneous equations with constant coefficients, Nonhomogeneous equations, Method of undetermined coefficients, Method of variation of parameters, Some non-linear equations, Applications, Higher order Differential Equations. Series Solutions: Cauchy-Euler equations, Solutions about 6-8 ordinary points, Solutions about singular points. Method of Frobenius, Second solutions and Logarithm terms. Systems of Linear Differential Equations: Definitions, 8-9½ Elimination method, Application of Linear Algebra, Homogeneous linear systems, Nonhomogeneous linear systems, Solving systems by Laplace transforms. Laplace Transforms: Definitions, Properties, Inverse 9½-11 Laplace transforms, Solving initial-value problems. Special functions: Heavyside unit step function, Periodic function, Dirac delta function, Convolution theorem. Partial Differential Equations: Some mathematical models, 11-14 Fourier series solutions, Method of separation of variables, The D’Alembert solution, Applications. Notice: This schedule is only a rough guideline and changes may occur as and when deemed necessary by the instructor. These changes will be notified to the students. 6 Dr. Safeer Hussain Khan Mathematics for Engineers Methods of Teaching The following teaching methods are followed in the class: 1) Lectures give the basic concepts and examples show how these concepts are related to each other. 2) Some quizzes and/or assignments will be given. 3) Two major exams will be given. 4) Meaningful emails are responded. Methods of Students Evaluation: First Exam: 31-3-09 (Wednesday) 8 AM-9:00 AM 20 Marks Second Exam: 12-5-10 (Wednesday) 8 AM-9:00 AM 20Marks Final Exam: 8 -6-10 (Tuesday) Quizzes In the class. 11:00 PM-1:00 PM 40 Marks 10 Marks Assignments 10 Marks Marks are awarded on the basis of both presentation and concept. The place for the final examination will be communicated later on. 7 Dr. Safeer Hussain Khan Mathematics for Engineers Instructions for the students � Attendance: According to the University of Qatar policy, a student has to attend more than 75 % of the lectures; otherwise the student will not be able to enter the final exam and consequently can not pass this course. � Only a limited use of calculators is allowed in the examinations. � Of course, cell phones must not be used during the classes and the examinations. � The final exam is comprehensive. � Possibly three quizzes and assignments will be given. � Assignments are to be returned on time. Late submission will result in loss of marks. � Marks are awarded on the basis of both presentation and concept. � Homework/Practice Problems will be assigned by the instructor, and students are strongly urged to solve much more problems than indicated by the instructor. 8 Dr. Safeer Hussain Khan Mathematics for Engineers Learning Activities and Tasks Students are responsible for their own ongoing learning process. They need to do their assignments independently unless they are allowed to work in groups. Course Regulations Student Responsibilities and Attendance Policies and Procedures Class attendance is compulsory. In accordance with University regulations, a student’s absence cannot exceed 25% of the total number (entire semester) of class meetings. If your absence rate exceeds 25%, including both excused and unexcused absences, you will NOT be allowed to take the final examination and will receive an ‘F barred’ grade for the course. Students are expected to be punctual (every 3 late class arrivals will be counted as 1 class absence) in class attendance and to conduct themselves in an adult and professional manner. Homework assignments and library assignment should be worked independently. Exchanging ideas are permitted orally but don't require any kind of copying. Homework assignment should be submitted in organized way and any late assignments may be assessed and corrected but the grade will be zero. Plagiarism (Academic Dishonesty) All students are expected to turn in work that is their own. Any attempt to pass off another's work as your own will constitute an "F" in the entire course. Using part of, or the entire work, prepared by another or turning in a homework assignment prepared by another student or party are examples of plagiarism. You may discuss assignments and projects with each other, but you should do the work yourself. In the case of group projects, you will be expected to do your share of the work. If you use someone else's words or ideas, you must cite your sources. Plagiarism is considered a serious academic offence and can result in your work losing marks or being failed. QU expects its students to adopt and abide by the highest standards of conduct in their interaction with their professors, peers, and the wider University community. As such, a student is expected not to engage in behaviours that compromise his/her own integrity as well as that of QU. You may discuss assignments and projects with each other, but you should do the work yourself. In the case of group projects, you will be expected to do your share of the work. If you use someone else's words or ideas, you must cite your sources. Plagiarism includes the following examples and it applies to all student assignments or submitted work: 9 Dr. Safeer Hussain Khan Mathematics for Engineers Use of the work, ideas, images or words of someone else without his/her permission. Use of someone else's wording, name, phrase, sentence, paragraph or essay without using quotation marks. Misrepresentation of the sources that were used. For further information see: http://www.plagiarism.org/ The instructor has the right to fail the coursework or deduct marks where plagiarism is detected 10 Dr. Safeer Hussain Khan Mathematics for Engineers Classroom Discipline The use of mobile telephones inside the classroom is NOT allowed. Any student disciplinary issues, which may arise, will be referred to the head of the Department. Additional Sources: Printed Sources 1. Differential Equations with boundary problems: Dennis G. Zill and Michael R. Cullen. 2. Advanced Engineering Mathematics, Kreyszig, 7th ed., 1993, John Wiley. 3. Calculus, by Swokowski, Sixth Edition 1994,PWS Publishing Company, Boston. 4. Calculus with Analytic Geometry, by H. Edwards and D. E. Penny, 5th Edition, 1998, Prentice Hall. 5. Calculus, by R.T. Smith and R.B. Minton, 2nd Edition, 2002, McGraw-Hill. 6. Calculus: One and Several Variables by S. L. Salas, G. J. Etgen and E. Hille; 10th Edition, 2007, John Wiley & Sons. 7. Calculus, Early Transcendentals by J. Stewart, 6th Edition, 2008, Brooksw/Cole. Non-Printed Sources Check blackboard site http://mybb.qu.edu.qa for class notes and exams solutions, etc. Online Sources Some Useful Resources and Media Address -Differential Equations, Paul Dawkins, http://tutorial.math.lamar.edu/index.aspx - http://www.efunda.com - http://www.sosmath.com/diffeq - http://www.mathword.wolfram.com - http://tutorial.math.lamar.edu/ 11 CATEGORY 5 4 3 Dr. Safeer Hussain Khan 2 1 0 Score y/7 Mathematics for Engineers Course Matrix Objectives Objective 1: To introduce Outcomes Identify and classify differential equations by type, order and linearity. different fundamental methods to Define an initial-value problem and state the theorem of existence and solve first order differential uniqueness of its solution. equations and their applications Solve equations by the method of separation of variables. Find the general solution of a homogeneous equation Solve exact differential equations Find integrating factors. Solve linear equations and non-exact equations. Solve Bernoulli’s equation. Solve problems involving rates of growth, decay, and physical reaction. Solve equations solvable for y (dependent variable) and equations solvable for x (independent variable). Recognize initial- and boundary-value problems. Objective 2 To familiarize students with the fundamental Recognize a linear differential operator. methods in linear differential Reduce the order of a differential equation. equations of the second (and Solve equations whose characteristic equation has distinct or repeated higher) order(s) with constant real roots or imaginary roots. coefficients and their Solve non-homogeneous differential equations using the method of applications. undetermined coefficients. Solve non-homogeneous differential equations using the method of variation of parameters. Solve some non-linear differential equations. Solve some vibration models. Solve higher order equations with constant coefficients. Objective 3: To acquaint Find the general solution of the Cauchy-Euler equations students with the basic methods in Identify singular points and ordinary points. differential equations of the Identify regular singular points and irregular singular points. second order with non-constant Solve nonsingular differential equations by the power series method. coefficients. Identify the interval of convergence of a power series solution. Find the indicial equation of a differential equation. Determine solutions of differential equations for various values of the roots of the indicial equation Objective 4: To learn the steps Set up systems of equations from given situations. of solving more than one Use elementary elimination techniques to solve systems of equations. differential equation. Solve homogeneous linear systems by the Eigenvalues-Eigenvectors method. Objective 5: E. To develop the ability to apply Laplace transforms method to solve differential equations and systems of differential equations Find the Laplace transform of elementary functions and their derivatives. Solve differential equations using the Laplace transform. Use the convolution integral to find inverse transforms. Solve initial-value problems. Solve systems of differential equations. Objective 6: . To develop basic methods for solving problems involving partial differential equations. Find a Fourier series solution of a function. Recognize Heat, Wave and Laplace operators. Find the general solution of second order PDEs by assuming a trial solution of the form u(x, y) = f (mx + y). Use the method of separation of variables to solve boundary value problems for the wave, heat and Laplace’s equations. Determine the D’Alembert solution of the second order PDEs. 12 Assessment Tools Exams Quizzes Assignments Presentations Exams Quizzes Assignments Presentations Exams Quizzes Assignments Presentations Exams Quizzes Assignments Presentations Exams Quizzes Assignments Presentations Exams Quizzes Assignments Presentations Dr. Safeer Hussain Khan Mathematics for Engineers Assignment Rubrics (Written Part 5 Points) Student name and ID:………………………… Group# 5 Organization Amount of Information Quality of Information Sources Diagrams & Illustrations 4 Information is very organized with wellconstructed paragraphs and subheadings. All topics are addressed and all questions answered with at least 2 sentences about each. Information clearly relates to the main topic. It includes several supporting details and/or examples. All sources (information and graphics) are accurately documented in the desired format.References clearly stated. Diagrams and illustrations are neat, accurate and add to the reader's understanding of the topic. 3 2 1 Information is organized with wellconstructed paragraphs. All topics are addressed and most questions answered with at least 2 sentences about each. Information clearly relates to the main topic. It provides 1-2 supporting details and/or examples. All sources (information and graphics) are accurately documented, but a few are not in the desired format. Refernces clearly stated Diagrams and illustrations are accurate and add to the reader's understanding of the topic. Information is organized, but paragraphs are not wellconstructed. All topics are addressed, and most questions answered with 1 sentence about each. Information clearly relates to the main topic. No details and/or examples are given. The information appears to be disorganized. All sources (information and graphics) are accurately documented, but many are not in the desired format. Not all refernces are included Diagrams and illustrations are neat and accurate and sometimes add to the reader's understanding of the topic. Some sources are not accurately documented or there are no references included. 13 0 One or more topics were not addressed. Information has little or nothing to do with the main topic. Diagrams and illustrations are not accurate OR do not add to the reader's understanding of the topic. Score= y/5 Dr. Safeer Hussain Khan Mathematics for Engineers Assignment Rubrics (Oral PresentationPart 5 Points) Student name and ID:………………………… Group # 5 4 3 2 1 0 There is a logical There is some There is little or no sequence of logical sequence of logical sequence of information. information. information. Organization Title slide and closing Title slide and Title slide and/ or slide are included closing slides are closing slides are not appropriately. included. included.. Slide Design (text, colors, Presentation is background, attractive and illustrations, size, appealing to viewers. titles, subtitles) Content Delivery Presentation is somewhat appealing to viewers. Presentation includes some Presentation covers essential topic completely and information. in depth. Some information Information is clear, is somewhat appropriate, and confusing, accurate. incorrect, or flawed. There was some Ideas were difficulty communicated with communicating enthusiasm, proper ideas due to voice voice projection and projection, lack of clear delivery. preparation, There was sufficient incomplete work, eye contact with and/or insufficient audience. eye contact. There were sufficient Insufficient use of use of other nonnon-verbal verbal communication communication skills. skills. Appropriate delivery Delivery pace is pace was used. somewhat appropriate. Little to no attempt has been made to make presentation appealing to viewers. Presentation includes little essential information. Information is confusing, inaccurate, or flawed. There was great difficulty communicating ideas due to poor voice projection, lack of preparation, incomplete work, and/or little or no eye contact. No use of non verbal communication skills. Inappropriate delivery pace was used. 14 Score y/5 Dr. Safeer Hussain Khan Interaction with Audience Mathematics for Engineers Ideas were There was some communicated with difficulty enthusiasm, proper communicating voice projection and ideas due to voice clear delivery. projection, lack of There was sufficient preparation, eye contact with incomplete work, audience. and/or insufficient There were sufficient eye contact. use of other non Insufficient use of verbal non-verbal communication skills. communication Appropriate delivery skills. pace was used. Delivery pace is somewhat appropriate. 15 There was great difficulty communicating ideas due to poor voice projection, lack of preparation, incomplete work, and/or little or no eye contact. No use of non verbal communication skills. Inappropriate delivery pace was used. Dr. Safeer Hussain Khan Mathematics for Engineers Practice Problems "Practice makes a man perfect" is a well-known saying. It is particularly true for mathematics students. Following are the Recommended Practice Problems from the text book. It is expected that the students will solve all of them, but shall not restrict themselves to these problems only. Section 1.1 1.2 2.2 2.3 2.4 2.6 Page 82 3.3 3.5 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.9 4.10 Page 250 6.1 6.2 6.3 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Page 444 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 9.5 9.6 9.7 10.2 10.6 10.7 Question Numbers 1, 2, 3, 4,5,8,11 3,8,17,18,23,25,28 1-15 odd,19-23 odd,29 7-21 odd, 30*,32* 1-17 odd,23,25 1-15 odd,17-27 odd 1-39 odd 1*,2*,3*,6*,7* 1*,2*,3* 1-9 odd 1-19 odd,34 1-27 odd,34 9-35 odd 3-7 odd,17-21 odd,23-27 odd 1-17 odd 9-17 odd 1-9 odd 1-5 odd,11,13 1-35 odd 1-13 odd 1-13 odd 1-9 odd 1-29 odd 1-27 odd 1-29 odd,33-36 1-23 odd 1-39 odd,51,52 1-21 odd 1-19 odd 1-13 odd 1-31 odd 1-9 odd 1-9 odd 1-23 odd,35* 1-11 odd 1-9 odd 1-9 odd,19-33 odd 1-9 odd 13-18 1-15 odd,31-33 1-7 odd 1-15 odd,33* 1-21 odd 1-8 1-5 16 Dr. Safeer Hussain Khan Mathematics for Engineers Some general instructions for the students � Feel free to ask any question related to the material presented in the class during the class time. � Check blackboard site http://mybb.qu.edu.qa for announcements and some class material like class notes, assignments, syllabus, assignments and exams solutions, etc. � Only a limited use of calculators is allowed in the examinations. � Of course, cell phones must not be used during the class and the examinations. � Homework Problems will be assigned by the instructor, and students are strongly urged to solve much more problems than indicated by the instructor. � Mathematics Department provides syllabi very close to the ones of the most international universities. Deducting and cutting short this syllabus is impossible and the students should understand this in advance. ------One can get only for what (s)he works.---------------------------GOOD LUCK-------------------------- 17