MA 3502 - Engineering Mathematics II

• Determine the solution of a first order differential equations by the method of separation of variables
• Solve exact equations
• Determine appropriate integrating factors for first order linear equations
• Determine the general solution of higher order linear homogeneous equations with constant coefficients
• Determine the general and particular solutions of certain linear non-homogenous equations using the methods of undetermined coefficients and variation of parameters
• Determine the Laplace transform and inverse Laplace transform of certain elementary functions
• Solve certain linear differential equations using Laplace transforms

• Differentiation of elementary functions for all topics
• Integration techniques for solving differential separable and exact equations and for variation of parameters
• Improper integrals for Laplace transforms

• Basic concepts of differential equations
• Solution of first order equations by separation  of variables
• Solution of exact equations
• Solution of first order linear non-homogeneous equations
• Solution of higher order linear homogeneous differential equations with constant coefficients
• Solution of higher order linear non-homogeneous differential equations using the method of undetermined coefficients
• Solution of higher order linear non-homogeneous differential equations using the method of variation of parameters
• Introduction to Laplace transforms
• Laplace transforms of elementary functions
• Inverse Laplace transforms
• Operational properties: Laplace transforms and inverse Laplace transforms involving transforms of derivatives, derivatives of transforms, exponential shift (translation on the s-axis) and Heaviside function (translation on the t-axis), Dirac delta function and periodic functions
• Solution of linear differential equations using Laplace transforms