NUMERICAL ANALYSIS

• INTRODUCTION TO \( \approx \)
  
  
  • Introduction
  
  
  • Floating Point Numbers
  
  
  • Computational Errors
  
  
  • Algorithm
  
  
  • Calculus Review
  
  


• ROOT FINDING
  
  
  • Bisection Method
  
  
  • Fixed Point Iteration
  
  
  • Newton-Raphson Method
  
  
  • Order of Convergence
  
  


• INTERPOLATION
  
  
  • Lagrange Polynomials
  
  
  • Cubic Spline Interpolation
  
  


• NUMERICAL DIFFERENTIATION AND INTEGRATION
  
  
  • Numerical Differentiation
  
  
  • Elements of Numerical Integration
  
  
  • Composite Numerical Integration
  
  


• DIFFERENTIAL EQUATIONS
  
  
  • Euler's Method
  
  
  • Higher-order Taylor's Method
  
  
  • Runge-Kutta Method
  
  


• LINEAR ALGEBRA
  
  
  • Introduction
  
  
  • Systems of Linear Equations: Gaussian Elimination
  
  
  • Jacobi and Gauss-Seidel Methods
  
  
  • Eigenvalues: Power Method
  
  


• ADDITIONAL TOPICS
  
  
  • Parabolic PDE: Heat Equation
  
  
  • Elliptic PDE: Laplace Equation
  
  
  • Least Squares Approximation
  
  

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