Back

## Ordinary and Partial Differential Equations

PÎRÎ REİS UNIVERSITY

ENGINEERING FACULTY

Naval Architecture and Marine Engineering Programme

2017 - 2018 Fall-Spring Term Course catalogue Form

 Course Name : Ordinary and Partial Differential Equations Degree:  Bachelor Code Year/Semester Local Credits ECTS Credits Course Implementation, Hours/Week Course Tutorial Laboratory ENG215 2/1 (Fall-Spring) 4 5 4 - - Department Naval Architecture and Marine Engineering Programme Instructors Şengül Ersoy, Ph.D., Lecturer Contact Information Piri Reis University, Faculty of Economics and Administrative Sciences Phone: +90 216 581 00 50 Ext:1737 E-mail: sersoy@pirireis.edu.tr Office Hours Monday:  13:00-15:00 Web page http://www.pirireis.edu.tr/pruonline Course Type Compulsory Course Language English Course Prerequisites MATH122 Course Category by Content, % Basic Sciences Engineering Science Engineering Design Humanities 90 10 Course Description First Order Differential Equations, Second Order Linear Equations, Higher Order Linear Equations, Series Solutions of  Linear Equations, The Laplace Transform, Systems of First Order Linear Equations, Introduction to Partial Differential Equations Course Objectives 1. introduce the basic concepts of differential equations 2. present methods to solve differential equations of various types 3. acquire skills to apply the knowledge of differential equations to engineering  problems Course Learning Outcomes Upon succesful completion of the course students are expected to classify differential equations by order, linearity, and homogeneity know the menings of an implicit,  explicit, singular,  particular  and general solutions of  a differential equation verify that  a given function is a solution of  a differential equation use appropriate method for solutions of first, second and higher order differential equations solve a nonhomegeneous linear differential equation with constant coefficients by using annihilators or undetermined coefficients ,or variation or parameters solve linear differential equations using power series and Laplace transform methods solve  a  system of first order linear equations by using elimination or Laplace transform methods find Fourier series expansions of periodic functions know what a partial differential equation is and solve initial-boundary value  problems given for the heat, wave and Laplace equations by the method of separation of variables technique apply the knowledge of ordinary and partial differential equations in solving engineering problems Instructional Methods and Techniques Lecture, problem solving Tutorial Place Co-term Condition Textbook Differential Equations with Boundary Value Problems, Dennis G. Zill, Michael R. Cullen,  7th Edition,  Brooks Cole Publishing Company, 2009 Other References Elementary Differential Equations and Boundary Value Problems, 7th Edition, John Wiley and Sons Inc., W. E. Boyce, R. C. DiPrima, 2010. Fundamentals of Differential Equations, 8th Edition,  Addison Wesley, K. Nagle, A. B. Saff, E. D. Snider, 2011 Homework & Projects At least 5 quizzes and homeworks. Laboratory Work Computer Use Other Activities

 Assessment Criteria Activities Quantity Effects on Grading, % Attendance Midterm 1 30 Quiz 5 20 Homework Term Paper/Project Laboratory Work Practices Tutorial Seminar Presentation Field Study Final Exam 1 50 TOTAL 100 Effects of Midterm on Grading, % 50 Effects of Final on Grading, % 50 TOTAL 100

 ECTS/ WORKLOAD TABLE Activities Count Hours Total Workload Lecture 13 4 52 Midterm 1 10 10 Quiz 5 3 15 Homework 3 8 24 Term Paper/Project Laboratory Work Practices Tutorial Seminar Presentation Field Study Final Exam 1 15 15 Total Workload 115 Total Workload/25 115/25 Course ECTS Credits 5

COURSE PLAN

 Week Topics Course Outcomes 1 Definitions and Terminology, Initial-Value Problems , Differential Equations as Mathematical Models I-II-III 2 Separable Variables, Exact Equations, Linear Equations,  Solutions by Substitutions IV 3 Linear Equations,  Nonlinear Equations I-IV 4 Preliminary Theory: Linear Equations, Initial-Value and Boundary-Value Problems, Homogeneous Equations, Nonhomogeneous Equations III-IV 5 Reduction of Order, Homogeneous Linear Equations with Constant Coefficients, Undetermined Coefficients - Superposition Approach IV-V 6 Undetermined Coefficients-Annihilator Approach,Variation of Parameters V 7 Cauchy-Euler Equation,  Review of Power Series; Power Series Solutions Midterm VI 8 Solutions About Ordinary Points , Solutions About Singular Points VI 9 Definition of the Laplace Transform, Inverse Transform,Translation Theorems and Derivatives of a Transform VI 10 Transforms of Derivatives, Integrals, and Periodic Functions, Applications, Dirac Delta Function VI 11 Preliminary Theory, Homogeneous Linear Systems with Constant Coefficients, Distinct Real Eigenvalues, Repeated Eigenvalues, Complex Eigenvalues,Variation of Parameters, Matrix Exponential VII 12 Orhogonal Functions,  Fourier Series, Fourier Sine and Cosine Series VIII 13 Separable Partial Differential Equations, Classical Equations and  Boundary-Value Problems, Heat Equation IX-X 14 Wave Equation, Laplace's Equation,  Nonhomogeneous Equations and Boundary Conditions IX-X

Relationship between the Course and the Naval Architecture and Marine Engineering Programme

Curriculum

 Program Outcomes Level of Contribution 1 2 3 a An ability to apply knowledge of mathematics, science, and engineering X b An  ability to design and conduct experiments, as well as to analyze and interpret data X c An ability to design a system, component or process to meet desired needs X d Ability to function on multi-disciplinary teams X e An ability to identify, formulate, and solve engineering problems X f An understanding of professional and ethical responsibility g An ability to communicate effectively h The broad education necessary to understand the impact of engineering solutions in a global and societal context X i A recognition of the need for, and an ability to engage in life-long learning X j A knowledge of contemporary issues X k An ability to use the techniques, skills and modern engineering tools necessary for engineering practice X l An ability to apply engineering knowledge in fluid mechanics, structural mechanics, material selection and energy/propulsion systems in the context of marine vehicles and offshore structures. X

1: Small, 2: Partial, 3: Full

Programme Outcomes & Course Outcomes Connectivity Matrix

 Course Outcomes I II III IV V VI VII VIII IX X Programme Outcomes a X X X X X X X X X X b X X X c X X d X e X X X X X X f g h X X i X j X k X X X X X X X l X X X X X X X

Prepared by

Şengül Ersoy, Ph.D., Lecturer

September, 2017