Advanced Numerical Methods for Engineering and Science
( 25 Modules )

Module #1
Introduction to Advanced Numerical Methods
Overview of numerical methods, importance of numerical analysis, and brief review of basic numerical methods

Module #2
Error Analysis and Numerical Stability
Types of errors, error propagation, numerical stability, and condition numbers

Module #3
Numerical Linear Algebra
Direct and iterative methods for solving linear systems, eigenvalue decomposition, and singular value decomposition

Module #4
Iterative Methods for Linear Systems
Gauss-Seidel, Jacobi, and successive over-relaxation (SOR) methods

Module #5
Finite Difference Methods
Introduction to finite difference methods, accuracy and stability analysis

Module #6
Finite Element Method:Basics
Introduction to finite element method, variational principles, and Galerkin method

Module #7
Finite Element Method:Applications
Applications of finite element method to solid mechanics, heat transfer, and fluid dynamics

Module #8
Boundary Element Method
Introduction to boundary element method, boundary integral equations, and applications

Module #9
Numerical Solution of Ordinary Differential Equations
Introduction to ODEs, Eulers method, Runge-Kutta methods, and multistep methods

Module #10
Numerical Solution of Partial Differential Equations
Introduction to PDEs, method of lines, finite difference methods, and finite element methods

Module #11
Computational Fluid Dynamics
Numerical methods for fluid dynamics, Navier-Stokes equations, and turbulence modeling

Module #12
Computational Heat Transfer
Numerical methods for heat transfer, conduction, convection, and radiation

Module #13
Numerical Methods for Solid Mechanics
Numerical methods for solid mechanics, stress analysis, and dynamic analysis

Module #14
Introduction to Computational Optimization
Introduction to optimization, linear and nonlinear programming, and gradient-based methods

Module #15
Advanced Optimization Techniques
Genetic algorithms, simulated annealing, and particle swarm optimization

Module #16
Uncertainty Quantification
Introduction to uncertainty quantification, sensitivity analysis, and Monte Carlo methods

Module #17
Scientific Computing with Python
Introduction to Python for scientific computing, NumPy, SciPy, and Matplotlib

Module #18
Parallel Computing for Engineering and Science
Introduction to parallel computing, parallel architectures, and parallel algorithms

Module #19
High-Performance Computing for Engineering and Science
Introduction to high-performance computing, distributed memory architectures, and MPI

Module #20
Data Visualization for Engineering and Science
Introduction to data visualization, visualization tools, and visualization best practices

Module #21
Case Studies in Engineering and Science
Real-world applications of advanced numerical methods in engineering and science

Module #22
Numerical Modeling of Multiphysics Systems
Numerical modeling of systems involving multiple physical phenomena

Module #23
Advanced Topics in Numerical Methods
Advanced topics in numerical methods, including meshless methods and Isogeometric Analysis

Module #24
Research and Development in Numerical Methods
Current research and development in numerical methods, including emerging areas and future directions

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Advanced Numerical Methods for Engineering and Science career

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Advanced Numerical Methods for Engineering and Science ( 25 Modules )

Advanced Numerical Methods for Engineering and Science
( 25 Modules )