### Course Details

 Title Engineering Mathematics 1 Field of Study Mathematics Professor hanyang (summerschool@hanyang.ac.kr) Type Academic course Delivery Method Offline (100% offline course): Credits 3 Contact hours 45 Schedule Course code COE3051 Course number Description In this course, we learn ordinary differential equation(O.D.E.), linear differential equation(L.D.E.), series, series solution in differential equations and Laplace transformation systematically based on differential and integral calculus (fundamental prerequisite), and the linear algebraic equations by use of matrix analysis. Objective Linear Algebraic Equation, Ordinary Differential Equation(ODE), Linear Differential Equation, Series Solutions of ODEs, Laplace Transforms Preparations None Materials: Advanced Engineering Mathematics (Erwin Kreyszig) Materials Evaluation Assignment 0% Lesson Plan Class 1: §7.1 ~ §7.3 Linear Systems of Equations. Gauss Elimination §7.4 Linear Independence. Rank of a Matrix. Vector Space Class 2: §7.5 ~ §7.7 Determinants. Cramer's Rule §7.8 Inverse of a Matrix. Gauss-Jordan Elimination Class 3: §8.1 Eigenvalues & Eigenvectors §1.3 Separable ODEs Class 4: §1.4 Exact ODEs. Integrating Factors §1.5 Linear ODEs. Bernoulli Equation Class 5: §2.1 Homogeneous Linear ODEs of 2nd Order §2.2 Homogeneous Linear ODEs wth Constant Coefficients Class 6: §2.5 Euler-Cauchy Equations §2.6 Existance & Uniqueness of Solutions. Wronskian. §2.7 Nonhomogeneous ODEs §2.10 Solution by Variation of Parameters Class 7: Midterm exam Class 8: §3.1-§3.2 Homogeneous Linear ODEs §3.3 Nonhomogeneous Linear ODEs Class 9: §5.1 Power Series Method Class 10: §5.3 Extended Power Series Method: Frobenius Method Class 11: §5.4 Bessel's Equation. Bessel Functions J(x) (except Th1 & Ex2,3) §5.5 Bessel Function of the Y(x). General Solutions (Th1 is included only) Class 12: §6.1 Laplace Transform. First Shifting Theorem(s-Shifting) Class 13: §6.2 Transforms of Derivatives and Integrals. ODEs §6.3 Unit Step unction (Heaviside Function). Second Shifting Theorem(t-Shifting) §6.4 Short Impulses. Dirac's Delta Function. Partial Functions Class 14: §6.5 Convolution. Integral Equations §6.6 Differentiation and Integration of Transforms. ODEs wth Variable Coefficients Class 15: Final Exam Last Updated November 1, 2021 Print