Introduction
  • Introduction
Roots of High-Degree Equations
  • Introduction and Simple Iterations Method
  • Simple Iterations Method: Code I (for Loop)
  • Simple Iterations Method: Code II (while Loop)
  • Convergence vs Divergence
  • Newton-Raphson Method
  • Bisection Method: Algorithm
  • Bisection Method: Code
  • False Position (Regula Falsi) Mehtod
  • Secant Method
  • User-Defined Functions & Run-Time Input
  • Root Finding in SciPy & Summary
Interpolation and Curve Fitting
  • Introduction and Linear Interpolation Method
  • Lagrange's Method: Algorithm
  • Lagrange's Method: Code
  • Newton's Method: Algorithm
  • Newton's Method: Code
  • Linear Regression: Algorithm
  • Linear Regression: Code I (for Loop)
  • Linear Regression: Code II (NumPy Arrays)
  • Polynomial Fit: Algorithm
  • Polynomial Fit: Code
  • Interpolation Functions of SciPy
  • Curve Fitting Functions of SciPy & Summary
Numerical Differentiation
  • Introduction and Finite Differences Method
  • Finite Differences Method: Code I
  • Finite Differences Method: Code II
  • Plotting Derivative Curves
  • Numerical Differentiation Function in SciPy & Summary
Numerical Integration
  • Introduction & Trapezoidal Rule: Algorithm
  • Trapezoidal Rule: Code
  • Simpson's 1/3 Rule: Algorithm
  • Simpson's 1/3 Rule: Code
  • Simpson's 3/8 Rule: Algorithm
  • Simpson's 3/8 Rule: Code
  • Double Integration: Algorithm
  • Double Integration: Code
  • Quadrature in SciPy & Summary
Systems of Linear Equations
  • Introduction & Gauss Elimination Method: Algorithm
  • Gauss Elimination Method: Code I (Elimination)
  • Gauss Elimination Method: Code II (Back-Substitution)
  • Gauss Elimination Method: Code III (Modifications)
  • Jacobi's Method: Algorithm
  • Jacobi's Method: Code
  • Gauss-Seidel's Method
  • Diagonal Dominance
  • Linear System Solution in NumPy and SciPy & Summary
  • Gauss-Jordan Method: Procedure
  • Gauss-Jordan Method: Algorithm & Code
Ordinary Differential Equations
  • Introduction & Euler's Method
  • Second Order Runge-Kutta's Method
  • Fourth Order Runge-Kutta's Method
  • Fourth Order Runge-Kutta's Method: Plot Numerical and Exact Solutions
  • Higher-Order ODE's: Algorithm
  • Higher-Order ODE's: Code
  • Higher-Order ODE's: Plotting Solutions
  • ODE Solution in SciPy & Summary