MA 382 - Laplace and Fourier Transforms

• Find Laplace and inverse Laplace transforms using a table
• Find Fourier transforms
• Solve linear differential equations and systems of equations with input functions, such as: continuous, piecewise continuous, unit step, impulse and periodic
• Solve certain types integral, and integro-differential equations
• Solve certain classes of linear partial differential equations

• Improper integrals
• Infinite series
• Linear differential equations

• Basic properties of Laplace transforms and transforms of special functions (3 classes)
• Transforms of derivatives and integrals and derivatives of transform (2 classes)
• Application to differential equations (2 classes)
• The unit step function (1 class)
• The Dirac delta function (1 class)
• Applications of step and impulse functions (1 class)
• Periodic functions and their applications (2 classes)
• Convolution and applications (2 classes)
• Solving integral equations (1 class)
• Fourier series (3 classes)
• Fourier integral representation (1 class)
• Fourier transforms and its properties (2 classes)
• Fourier sine and cosine transforms (1 class)
• Application of Fourier transforms to partial differential equation (2 classes)
• Exams and review for exams (6 classes)