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## Applied Engineering Mathematics

PÎRÎ REİS UNIVERSITY

ENGINEERING FACULTY

Naval Architecture and Marine Engineering Programme

2017 - 2018 Fall-Spring Term Course catalogue Form

 Course Name : Applied Engineering Mathematics Degree:  Bachelor Code Year/Semester Local Credits ECTS Credits Course Implementation, Hours/Week Course Tutorial Laboratory ENG225 2/2 (Fall-Spring) 3,5 5 3 1 - Department Naval Architecture and  Marine Engineering 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 ENG215 Course Category by Content, % Basic Sciences Engineering Science Engineering Design Humanities 50 50 - - Course Description Vector differential Calculus. Grad, div, curl. Vector integral Calculus. Integral theorems. System of ODEs. Series solutions of ODEs. Special functions. Fourier analysis. Partial differential equations. Course Objectives To give an ability to apply knowledge of mathematics on engineering problems, especially how to study and solve differential equations, which model physical systems varying in space and/or time. Course Learning Outcomes Upon successful completion of the course students should be able to: apply the knowledge of the vector calculus in solving engineering problems solve  a linear   system by using elimination or operator or Laplace transform methods solve linear differential equations using power series methods knows the relations between the special functions and applications of special functions in engineering 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 Books, lecture and  problem solving Tutorial Place Classroom Co-term Condition Textbook Advanced Engineering Mathematics, Erwin Kreyszig, John Wiley&Sons, 10th Edition, 2014. Other References Advanced Enginering Mathematics, 7th Edition, Cengage, Peter O’Neil,  2011. Fundamentals of Differential Equations, 8th Edition, Addison Wesley, K. Nagle, A. B. Saff, E. D. Snider, 2011. Thomas’ Calculus, 12th Edition, Pearson, Global Edition, George B. Thomas, Jr., Maurice D. Weir, Joel Hass. Homework & Projects Homework assignments based on lectures will be given regularly and quizzes  will be held. 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 3 39 Midterm 1 16 16 Quiz 5 3 15 Homework 3 5 15 Term Paper/Project Laboratory Work Practices Tutorial 13 1 13 Seminar Presentation Field Study Final Exam 1 24 24 Total Workload 122 Total Workload/25 122/25 Course ECTS Credits 5

COURSE PLAN

 Week Topics Course Outcomes 1 Vectors in 2-Space and 3-Space. Inner product. Vector Product. Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives. Curves. Arc Length. Curvature. Torsion. I 2 Gradient of a Scalar Field. Directional Derivative. Divergence of a Vector Field. Curl of a Vector Field. I 3 Line Integrals. Green’s Theorem in the Plane. Surface Integrals. I 4 Triple Integrals. Divergence Theorem and its Applications. Stokes’s Theorem. I 5 Basic Theory of System of ODEs. Wronskian. Constant-Coefficient Systems. Phase Plane Method. Criteria for Critical Points. Stability. II 6 Differential  Operators and the Elimination Method for Systems.Solving Linear Systems with Laplace Transforms.  Nonhomogeneous Linear Systems of ODEs. II 7 Power Series Method. Legendre’s Equation. Legendre Polynomials  . III-IV 8 Frobenius Method. Bessel’s Equation. Bessel Functions of the first kind, . Bessel Functions of the second kind, .                                                                             MIDTERM III-IV 9 Fourier Series. Even and Odd Functions. Half-Range Expansions. Sturm-Liouville Problems. Orthogonal Functions and Series. Generalized Fourier Series. Fourier Integral. Fourier Cosine and Sine Transforms. Fourier Transform. V 10 Basic Consepts of PDEs. Wave equation: Solution of the Wave Equation, Characteristics. Solution by Separating Variables. Use of Fourier Series. Heat Equation: Solution by Fourier Series. Solution by Fourier Integrals and Transforms. V-VI 11 Rectangular Membrane, Two Dimensional Wave Equation.  Double Fourier Series. V-VII 12 Laplacian in Polar Coordinates. Circular Membrane. Fourier-Bessel Series. Laplace’s Equation in Cylindrical and Spherical Coordinates. V-VII 13 Solution of PDEs by Laplace Transforms. VI-VII 14 Review

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 Programme Outcomes a X X X X X X X b X X X c X X d X X e X X X X X f g h X X X i X X X j X X X k X X X X X X l X X X X X X X

Prepared by

Şengül Ersoy, Ph.D., Lecturer

February, 2018