Course No. Title Classification Credits Prerequisites Semester COE351 Engineering Mathematics 1 required 3-3-0 None 1st Lecturer Department Name Phone E-MAIL Automotive Engineering Srungjae Min ☎2220-0457 seungjae@hanyang.ac.kr Course Description This course introduces students to the ideas and techniques for solving ordinary differential equations. It will emphasize both mathematical methods and conceptual understanding of engineering disciplines. The principal topics covered will include 1st-order ODEs, 2nd-order linear ODEs, series solutions of ODEs and Laplace transforms. Applications of these techniques for the solution of boundary value and initial value problems will be given. Goal The main objectives of this course are twofold: the study of ordinary differential equations and their most important methods for solving them and the study of modeling. Textbook Erwin Kreyszig, Advanced Engineering Mathematics (10th ed), 2011, Wiley Reference Clevw B. Moler, Numerial Computing with MATLAB, 2004, SIAM Evaluation Midterm Final Attendence Homework Participation etc Total 40 40 0 20 0 0 100 Week Lecture Textbook 1 Introduction 1st-order ODEs: basic concepts, modeling, separable ODEs 1.1~1.3 2 1st-order ODEs: exact ODEs, integrating factors, linear ODEs, Bernoulli equation 1.4~1.5 3 2nd-order linear ODEs: homogeneous linear ODEs of 2nd order 2.1 4 2nd-order linear ODEs: homogeneous linea ODEs with constant coefficients 2.2 5 2nd-order linear ODEs: Euler-Cauchy equation, existence and uniqueness of solutions, Wronskian 2.5~2.6 6 2nd-order linear ODEs: nonhomogeneous ODEs, solution by variation of parameters 2.7~2.10 7 Midterm Exam 8 series solutions of ODEs: power series method 5.1 9 series solutions of ODEs: extended power series method, Frobenius method 5.3 10 series solutions of ODEs: Bessel’s equation, Bessel functions 5.4~5.5 11 Laplace transforms: linearity, first shifting theorem 6.1 12 Laplace transforms: transforms of derivatives and integrals, unit step function, second shifting theorem 6.2~6.3 13 Laplace transforms: short impulses, Dirac’s delta function, convolution 6.4~6.5 14 Laplace transforms: differentiation and integration of transforms, systems of ODEs 6.6~6.7 15 Final Exam