Computational Techniques in Numerical Analysis
( 25 Modules )

Module #1
Introduction to Numerical Analysis
Overview of numerical analysis, its importance, and applications

Module #2
Floating Point Representation
Binary representation of numbers, rounding errors, and IEEE floating point standard

Module #3
Numerical Errors and Stability
Types of numerical errors, error propagation, and stability of algorithms

Module #4
Root Finding Methods
Bisection method, Newton-Raphson method, and Secant method for finding roots of equations

Module #5
Linear Algebra Review
Review of linear algebra concepts:vectors, matrices, determinants, and linear systems

Module #6
Gaussian Elimination
Gaussian elimination method for solving systems of linear equations

Module #7
LU, Cholesky, and QR Decompositions
Factorization methods for matrix decomposition and their applications

Module #8
Iterative Methods for Linear Systems
Jacobi, Gauss-Seidel, and SOR methods for solving systems of linear equations

Module #9
Eigenvalue Decomposition
Eigenvalue decomposition, power method, and QR algorithm

Module #10
Numerical Differentiation
Finite difference methods for numerical differentiation and error analysis

Module #11
Numerical Integration
Rectangle rule, trapezoidal rule, and Simpsons rule for numerical integration

Module #12
Interpolation
Polynomial interpolation, Lagrange interpolation, and spline interpolation

Module #13
Curve Fitting
Least squares method, polynomial regression, and nonlinear regression

Module #14
Numerical Solution of Ordinary Differential Equations
Eulers method, Runge-Kutta methods, and multistep methods for ODEs

Module #15
Finite Difference Methods for PDEs
Finite difference methods for parabolic, hyperbolic, and elliptic PDEs

Module #16
Finite Element Method
Introduction to finite element method for solving PDEs

Module #17
Numerical Solution of Partial Differential Equations
Method of lines, finite volume method, and boundary element method for PDEs

Module #18
Computational Linear Algebra
Computational aspects of linear algebra:QR factorization, SVD, and eigenvalue decomposition

Module #19
Optimization Techniques
Linear and nonlinear optimization techniques:gradient descent, Newtons method, and quasi-Newton methods

Module #20
Monte Carlo Methods
Introduction to Monte Carlo methods for solving numerical problems

Module #21
Parallel Computing
Introduction to parallel computing, parallel algorithms, and parallel programming models

Module #22
Numerical Analysis of Big Data
Numerical analysis of big data, data mining, and machine learning

Module #23
Applications of Numerical Analysis
Applications of numerical analysis in physics, engineering, economics, and computer science

Module #24
Case Studies and Projects
Real-world case studies and project development in numerical analysis

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Computational Techniques in Numerical Analysis career

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Computational Techniques in Numerical Analysis ( 25 Modules )

Computational Techniques in Numerical Analysis
( 25 Modules )