College of Arts & Science Department of Math, Statistics & Physics Fall 2009 Mathematics for Engineers (MATH 217) Course Syllabus Components COLLEGE OF ARTS & SCIENCES Department of Mathematics & Physics "Among all of the mathematical disciplines the theory of differential equations is the most important it furnishes the explanation of all those elementary manifestations of nature which involve time". (Sophus Lie) (1) Faculty Information Dr. Kenzu Abdella Name Program Mathematics Office Science Building SC 215, or Corridor 3, Men's Building, C215 Phone 485-2199 Email Kenzua@qu.edu.qa Website TBA Monday: 11:00-12:00 & Thursday: 11:00-12:00 Office Hours By appointment. Questions submitted via blackboard and emails are welcome at any time. (2) Course Information Course Number MATH 217 Course Name Mathematics for Engineers Credit Hours Three C.H. Catalogue Description First-Order Differential Equations: Initial-value problem. separable variables. Homogeneous equations. Exact equations. Li-near 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. Ap-plications. Higher order Differential Equations. Laplace Transforms: Definitions. Properties. Inverse Laplace transforms. Solving initial-value problems. Special functions: Heavyside unit step function. Convolution theorem. System of Linear Differential Equations: Definitions. Elimination method. Application of Linear Algebra. Homogeneous linear systems. Nonhomogeneous linear systems. Solving systems by Laplace transforms. Series Solutions: Cauchy-Euler equation method. Solutions about ordinary points. Solutions about singular points. Method of Frobenius. Second Solutions and Logarithm terms.? Partial Differential Equations: Some mathematical models. Fourier series solutions. Method of seperation of variables. The D Alembert solution of the wave equation.
Resources Course Schedule Pre-Requisites Sunday: Tuesday: Thursday: Calculus III 14:00-15:15, Lecture Room SD212 14:00-15:15, Lecture Room SD212 14:00-15:15, Lecture Room SD212 Textbook Differential Equations with Boundary Problems, by D. G. Zill & M.R. Cullen. 6 th Edition, Brooks/Cole Publishing Company, 2005. ISBN: 0-534-41887-2 References and Additional Resources Learning Resources and Media Advanced Engineering Mathematics, by Peter V. O Neil - Thomson 2007. Advanced Engineering Mathematics, by Erwin Kreyszig John Wiley & Sons. Inc. 9 th Edition, 2006. http://www.efunda.com http://www.sosmath.com/diffeq http://www.mathword.wolfram.com Exam Schedule (3) Course Description If you find an interesting mathematics link let me know and I will add it to the list. Exam Date Midterm Exam1 Saturday, April, 3, 2010. Midterm Exam2 Saturday, May, 15, 2010. Final Exam As in the schedule, Comprehensive Mathematics for Engineers is a single semester course introducing the student to a tools used in analyzing a range of problems arising in the modeling of engineering problems. 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 learning integrates theory and application using a problem-based approach. This will relieve the student of performing, by hand, many of the detailed calculations needed. This course prepares the student for future learning in relation to problem solving and decision-making; technical competence; teamwork and leadership; and reflection. (4) Objectives & Learning Outcomes (4.1) Course Objectives The main objective of this course is to develop understanding of the basic concepts of ordinary and partial differential equations. Specific objectives include: Acquainting students with the necessary theories and methods in both Differential and Partial Differential Equations. Acquainting students with Differential Equations and their applications. Introducing among others, the Laplace Transform method which is an efficient tool for solving Mathematics for Engineers Course Syllabus. Spring 2010 2/6 Professor Kenzu Abdella
Engineering problems in an elegant way Presenting students with some realistic problems Equipping students with a number of methods for solving differential equation, concentrating on those which are of practical importance. (4.2) Student Learning Outcomes Upon completion of this course, a student is expected to be able to: Classify differential equations by type, order and linearity Determine the general solution of different types of differential equations by using different techniques Solve non-homogeneous differential equations by using the method of undetermined coefficients and the method of variation of parameters Solve some non-linear differential equations Solve differential equations by using the Laplace transform Solve systems of differential equations by using the eigenvalue-eigenvector method Solve problems involving rates of growth, decay, and physical reaction Solve some vibrational models based on real life problems Solve differential equations by the power series method at regular and singular points Solve some mathematical models by using the method of separation of variables. (5) Content Distribution Topics to be covered Chapter One. Basic Definitions and Terminology: Motivation, Definitions, Classification by type, Classification by order, Linearity, Solutions. Chapter two. First-Order Differential Equations: Initial-value problem, Separable variables, Homogeneous equations, Exact equations. Linear equations, Integrating factor, Bernoulli equation, Applications. Chapter three. 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 non-linear equations, Applications, Higher order Differential Equations. Weeks Learning Outcomes 1 A1 2-3 A2.D1 4-6 B1.B2 Assessment Tools Case Studies Mathematics for Engineers Course Syllabus. Spring 2010 3/6 Professor Kenzu Abdella
Chapter Four. Laplace Transforms: Definitions, Properties, Inverse Laplace transforms, Solving initial-value problems. Special functions: Heavyside unit step function, Periodic function, Dirac delta function, Convolution theorem. Chapter Five. Systems of Linear Differential Equations: Definitions, Elimination method, Application of Linear Algebra, Homogeneous linear systems, Solving systems by Laplace transforms. Chapter six. Series Solutions: Cauchy-Euler equations, Solutions about ordinary points, Solutions about singular points. Method of Frobenius, Second solutions and Logarithm terms. Chapter seven. Partial Differential Equations: Some mathematical models, Fourier series solutions, Method of separation of variables, The D Alembert solution, Applications. (6) Course Format & Regulations 7-9 C1.D2 9-10 C2 11-12 E1 13-14 D2.E2 Case Studies (6.1) General Course Format and Activities Various teaching strategies and learning activities will interspersed throughout the sessions. For teaching this course the following learning activities will be used: Assigning reading material before and after we take it up in class. There will be regular quizzes. Engaging students in solving problems via assignments. Encouraging small-group discussions on homework problems. Engaging students in preparing the course portfolios. Requiring students to write technical papers or projects (Case studies). (6.2) Assignments Students will have frequent assignments with regard to the course material; specifically, reading each section before we take it up in class, reading your notes after every class, and performing your homework. The first two tasks will serve to keep your attention and interest up whilst the last task will help you to powerfully comprehend the material and build up your problem solving techniques. In fact working through problems is crucial to your understanding of Mathematics for Engineers and getting passing grade. Assignments are essential to learn most of techniques for solving differential equations, so please take the assignments very seriously. Performance of homework assignments is subjected to the following guidelines and rules: For team and non-team problems, these are not acceptable: Mathematics for Engineers Course Syllabus. Spring 2010 4/6 Professor Kenzu Abdella
Handing your homework to your friends. Copying your friend s homework. For non-team problems, before participating in group discussions I suggest that you initially attempt to solve the problems by yourselves, as this will help you to explore honestly your weaknesses. You will receive written solutions when problem sets are collected. Any question concerning the assignments can be directed to me in the office hours. (6.3) It is critical to constantly measure the follow-up of the students regarding the class material. Thus I use quiz strategy. Besides it will help students to do not fall behind, quizzes will help the instructor to recognize early the student s weakness points. Approximately 3-4 quizzes shall be given during the semester. (6.4) Technical Paper (Case Studies) Preparing and presenting a technical paper aim to improve the students communication skills, introduce them to the realistic application of class material, and motivate them to learn more about multimedia facilities. Organization of your technical paper must follow the following rules: The technical paper must be on a topic relevant to the material we cover; it should explain the approach used in solving differential equations for a real live problems or natural phenomenon. Technical papers must include a table of contents, introduction, main body, conclusion, and references. No more than two students should share the same project. In preparing their technical paper students should make use of multiple types of references e.g. text books, published Journal papers, and appropriate web resources. A single, one type reference term paper will not be accepted. Presenting your work to the class will be included in the final grade for the term paper. (6.5) Problem Solving Sessions Student s problem solving skill can be enhanced through the organization of problem solving sessions. In such sessions the class will be broken into small working groups whose goal will be to solve challenging real-life problems. (6.6) Student Portfolio The student portfolio is a collection of student notes, ideas, questions, and perspectives of the course material. The main purpose of the portfolio is to allow students to demonstrate what they have learned in class and to identify and assess their personal scientific growth in the subject. Further, preparation of the portfolio will help students to gain experiences in keeping record of the material covered in class in an organized manner. Encouraging students to reproduce and organize the class material can be served as an instrument to improve dramatically their study procedure and consequently complete their preparation for quizzes and exams. Finally, I believe that the major objective of having the portfolio is to document that all of the above learning outcomes have been met. The portfolio should include the following entries: Table of contents. All in-class handouts. Class notes. Homework assignments... General media articles relevant to the course topics Term paper (Case Studies). Mathematics for Engineers Course Syllabus. Spring 2010 5/6 Professor Kenzu Abdella
(6.7) Exam Rules Exam is a vital evenhanded learning instrument to gauge students, qualitatively and quantitatively, on the course foremost theoretical concepts. The regulations regarding the conduct of examinations are summarized in the following points: There will be three exams during the semester. All exams are closed notes. Prior to each exam, special review sessions will be arranged. There will be no makeup exams and no grade will be dropped. Grades will be final and fair. They cannot be negotiated. A missed quiz or exam counts as a zero. If an exam is missed verifiable circumstances will be considered. For further information regarding academic honesty on conduct of examination see the Deanship Of student Affairs website at http://www.qu.edu.qa/doc/stdaffairs/qustudenthandbook (6.8) Classroom Regulations In order for you to successfully complete the Mathematics for Engineers course, you must pay strict attention to your work and attendance. The regulations regarding attendance, and classroom discipline are summarized in the following points: Class attendance is compulsory. 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. Every three late class arrivals will be counted as one class absence. The use of mobile telephones inside the classroom is prohibited. (7) Marking Scheme The grading policy for the course will have the following bounds: Learning Activity Bounded Grade Weight Midterm Exam 1 20% Midterm Exam 2 20% Assignments, and Case Studies 20% Final Exam 40% Total 100% Mathematics for Engineers Course Syllabus. Spring 2010 6/6 Professor Kenzu Abdella