LAPLACE TRANSFORMS & INVERSE

• Solve 2. order Differential Equation using Laplace Transforms
• Find Transfer Function via Laplace Transforms
• Solve 3. order Differential Equation using Laplace Transforms
• Solve Integral Equation using Laplace Transforms
• Laplace Transform – Step by Step
• Laplace Transform of Piecewise Defined Functions
• Laplace Transform of Dirac Delta
• Laplace Transform of Unit Step
• Laplace Transform over given Interval
• Laplace Transform and RLC Circuit Analysis
• Table of Laplace Transforms
• Laplace Transform of Unit Step and Heavyside Functions
• Inverse Laplace Transform
• Inverse Laplace and Partial Fractions
• Table of Laplace Transforms

FOURIER SERIES, TRANSFORMS & INVERSE

• Fourier Transform – Step by Step
• Fourier Transform – Basic Signals
• Fourier Transform – Unit Step Function
• Fourier Transform – Convolution
• Fourier Transform – Piecewise Functions
• Contour Integrals (Circle, SemiCircle)
• Inverse Fourier Transform – Step by Step
• Inverse Fourier Transform – Step by Step
• Table of Fourier Transforms
• Usual Fourier Series of Function over [-pi,pi]
• Fourier Series of Function over [a,b]
• Fourier Series of Function with 2 Pieces
• Fourier Series of Function with 3 Pieces
• Fourier Series of Function with 4 Pieces
• Fourier Series of Step Function

Z TRANSFORMS & INVERSE

• Table of Z-Transforms
• Z Transform – Step by Step
• Z-Transform of u(n), a^n*u(n), n*a^n*u(n)
• Z-Transform of δ(n), -a^n*u(-n-1), a^n*u(n)+b^n*u(-n-1)
• Z-Transform of X(n)=n
• Z-Transform of X(n)=n^2
• Z-Transform of X(n)=a^n*u(n)
• Z-Transform of X(n)=a^n*u(n-1)
• Z-Transform of X(n)=a^n*u(n-2)
• Z-Transform of X(n)=n*a^n*u(n)
• Z-Transform of X(n)=b^n*u(-n-1)
• Z-Transform of X(n)=-b^n*u(-n-1)
• Z-Transform of X(n)= a^n*u(n)-b^n*u(-n-1)
• Z-Transform of X(n)= e^(a*x)*u(n)
• Z-Transform of X(n)= n*e^(a*x)*u(n)
• Z-Transform of X(n)= n^2*e^(a*x)*u(n)
• Z-Transform of X(n)= sin(a*x)*u(n)
• Z-Transform of X(n)= cos(a*x)*u(n)
• Z-Transform of X(n)= e^(a*x)*sin(w*n)*u(n)
• Z-Transform of X(n)= e^(a*x)*cos(w*n)*u(n)
• Inverse Z-Transforms – Step by Step
• Inverse Z-Transforms – via Partial Fractions
• Inverse Z-Transforms – via Polynomial Division
• Inverse Z-Transforms – via Residue/Contour Integral
• Inverse Z-Transforms of kz/(z-a), z^(-n), k*a*z/(z-a)^2, ..

DISCRETE TIME FOURIER TRANSFORMS (DTFT)

• of Number Sequence x[n]
• x[n]=b^n*u[n]
• x[n]=u[n]
• x[n]=u[n-k]
• x[n]=δ(n)

TRANSFER FUNCTIONS

• Find Transfer Function
• Convert: State Space to Transfer Function
• Find Magnitude (Amplitude) Response (LTIC)
• Find Phase Response (LTIC)
• Find System Output (Input x(t)=cos(a*t) )

EXTRAS

• Partial Fraction Decomposition
• Polynomial Division
• Find Poles, Residues and their Sums
• Find Order of Poles
• Pole-Zero Plot
• Find Transfer Function
• State Space to Transfer Function
• Beta Function
• Gamma Function
• Gamma Distribution