By DORON ZEILBERGER

These are the handouts I gave out when I taught "Advanced Calculus for Engineers", a.k.a. as "Calc5".

- Lecture 1: Definition of the Laplace Transform
- Lecture 2: The Inverse Laplace Transform and Derivatives
- Lecture 3: Translation Theorems for the Laplace Transform
- Lecture 4: Operational Properties of the Laplace Transform
- Lecture 5: The Dirac Delta Function
- Lecture 6: Solving Systems of Linear Differential Equations using the Laplace Transfrom
- Lecture 7: Orthogonal Functions
- Lecture8 : Fourier Series
- Lecture 9: Fourier Cosine and Sine Series
- Lecture 10: Complex Fourier Series
- Lecture 11: The Sturm-Liouville Problem
- Lecture 12: Fourer-Legendre Series and Linear Recurrences
- Lecture 13: Separable Partial Differential Equations
- Lecture 14: Classical PDEs and Boundary-Value Problems
- Lecture 15: The Heat Equation
- Lecture 16: The Wave Equation
- Lecture 17: Laplace's Equation
- Lecture 18: Laplace's Equation in Polar Coordinates
- Dr. Z.'s amazing method for solving Boundary Value Problems
- Lecture 19: Applications or the Laplace Transform for solving BVP PDEs
- Lecture 20: The Fourier Integral
- Lecture 21: Fourier Transforms
- Lecture 22: Numerical Solutions of Ordinary Differential Equations
- Lecture 23: Numerical Solutions of Laplace's Equation
- Lecture 24: The Art of Checking and avoiding Dumb mistakes

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