Course Details

Title Engineering Mathematics 1
Field of Study Mathematics
Professor hanyang (
Type Academic course
Delivery Method Offline (100% offline course):
Credits 3
Contact hours 45
Course code COE3051
Course number

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.


Linear Algebraic Equation, Ordinary Differential Equation(ODE), Linear Differential Equation, Series Solutions of ODEs, Laplace Transforms


Materials: Advanced Engineering Mathematics (Erwin Kreyszig)

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
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