Differential Equations MTH 205

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1 A Course Title & Number MTH 205 B Pre/Co requisite(s) MTH 104 C Number of credits D Faculty Name Ayman Badawi E Term/ Year Fall 2014 F Sections CRN Days Time Location UTR 11:00 11:50 Office Hours: UTR 2 3pm, other by APPOINTMENT G Instructor Information Instructor Office Telephone H Course Description from Catalog Ayman Badawi NAB abadawi@aus.edu Covers mathematical formulation of ordinary differential equations, methods of solution and applications of first order and second order differential equations, power series solutions, solutions by Laplace transforms and solutions of first order linear systems. I J Course Learning Outcomes Textbook and other Instructional Material and Resources Upon completion of the course, students will be able to: 1. Classify a given differential equation as ordinary or partial, and determine its order and whether or not it is linear. 2. Solve first order linear ordinary differential equations. 3. Apply reduction of order to find a second linearly independent solution for a homogenous differential equation, given one solution. 4. Compute real valued linearly dependent solutions to homogenous ordinary differential equations with constant coefficients. 5. Apply variation of parameters and method of undetermined coefficients to find a particular solution. 6. Formulate and solve appropriate applied problems involving exponential growth/decay and Newton s law of cooling and series circuits as first order differential equations and solve applied problems from electrical and mechanical engineering as second order differential equations. 7. Compute power series solutions to certain differential equations with variable coefficients. 8. Apply the Laplace transform to solve a given Initial Value problem and solve systems of linear differential equations. Zill D.G., A First Course in with Modeling and Applications, 10 th edition, 2012, Brooks/Cole Thomson, U.S.A. I Learn and my personal webpage has many old quizzes/exams badawi.com

2 K L Teaching and Learning Methodologies Grading Scale, Grading Distribution, and Due Dates This is a traditional lecture based course. Students are tested and given feedback throughout the semester via regular homework, quizzes, and exams. Grading Distribution Assessment Weight Date Quizzes 20% TBA Exam % Monday, October 27, 5:30 7:30 Exam % Monday, December 15, 5:30 7:30 Final Exam 35% TBA Total 100% Grading Scale A A B B B C C C D F 0 45

3 M Explanation of Assessments There will be in class quizzes, in addition to two midterm tests, and a comprehensive final exam. All quizzes will be pre announced at least one lecture in advance. No make up quizzes will be given. However the lowest quiz will not be counted toward your final grade With a valid written excuse and making immediate arrangements with the instructor, a missed exam might be replaced with the grade of the final exam and/or the average grade of all tests (including final) and/or quizzes The final exam is common and comprehensive. The date and time of the final exam will be scheduled by the registrar s office and will be announced in class The deadline to withdraw from the course without a grade penalty (W date) is Thursday, April 17 th. N Student Academic Integrity Code Statement Student must adhere to the Academic Integrity code stated in the undergraduate catalog Turn off your cellphone before the class! SCHEDULE Note: Tests and other graded assignments due dates are set. No addendum, make up exams, or extra assignments to improve grades will be given. WEEK CHAPTER NOTES First Second Third 2: 1: Introduction to 1: Introduction to 2: First Order 1.1 Definitions and Terminology 1.2 Initial Value Problems 1.3 as Mathematical Models 2.1 Solution Curves Without the Solution 2.2 Separable 2.3 Linear

4 Eid Al Adha Holiday: October 5th October 9th Fourth 2: Fifth Sixth Seventh 3: Modeling with First Order 4: Higher Order 4: Eighth 4: 2.4 Exact 2.5 Solutions by Substitutions 3.1 Linear Models 3.2 Nonlinear Models 4.1 Preliminary Theory: Linear 4.2 Reduction of Order 4.3 Homogeneous Linear with Constant Coefficients 4.4 Undetermined Coefficients Superposition Approach 4.6 Variation of Parameters 4.7 Cauchy Euler Equation Ninth 5: Modeling with Higher Order 5.1 Linear Models: Initial Value Problems 4.7 Cauchy Euler Equation Tenth Eleventh Twelfth 6: Thirteenth Fourteenth Fifteenth 5: Modeling with Higher Order 6: Series Solutions of Linear 6: 7: The Laplace Transform 6: 8: Systems of Linear First Order Final Exam 5.1 Linear Models: Initial Value Problems 6.1 Review of Power Series 6.2 Solutions about Ordinary Points 7.1 Definition of the Laplace Transform 7.2 Inverse Transforms and Transforms of Derivatives 7.3 Operational Properties I 7.4 Operational Properties II 7.5 The Dirac Delta Function 7.6 Systems of Linear Fall Break: December 21 st January 1 st 8.1 Preliminary Theory Linear System 8.2 Homogeneous Linear Systems Review Common and Comprehensive

5 Suggested Problems Text: Zill D.G., A First Course in with Modeling and Applications, 10 th edition.

San Jose State University Department of Mechanical and Aerospace Engineering ME 230, Advanced Mechanical Engineering Analysis, Fall 2015

San Jose State University Department of Mechanical and Aerospace Engineering ME 230, Advanced Mechanical Engineering Analysis, Fall 2015 Instructor: Office Location: Younes Shabany TBD Telephone: (408)