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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