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brieda l introduction modern scientific programming numerical methods 2024

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Textbook in PDF format The ability to use computers to solve mathematical relationships is a fundamental skill for anyone planning for a career in science or engineering. For this reason, numerical analysis is part of the core curriculum for just about every undergraduate physics and engineering department. But for most physics and engineering students, practical programming is a self-taught process. This book introduces the reader not only to the mathematical foundation but also to the programming paradigms encountered in modern hybrid software-hardware scientific computing. After completing the text, the reader will be well-versed in the use of different numerical techniques, programming languages, and hardware architectures, and will be able to select the appropriate software and hardware tool for their analysis. It can serve as a textbook for undergraduate courses on numerical analysis and scientific computing courses within engineering and physical sciences departments. It will also be a valuable guidebook for researchers with experimental backgrounds interested in working with numerical simulations, or to any new personnel working in scientific computing or data analysis. Key Features: Includes examples of solving numerical problems in multiple programming languages, including MatLAB, Python, Fortran, C++, Arduino, JavaScript, and Verilog. Provides an introduction to modern high-performance computing technologies including multithreading, distributed computing, GPUs, microcontrollers, FPGAs, and web "cloud computing". Contains an overview of numerical techniques not found in other introductory texts including particle methods, finite volume and finite element methods, Vlasov solvers, and molecular dynamics. Preface Author Bios Scientific Computing Basics Introduction Numerical Integration Scientific Computing Programming Languages Machine Language Compiled and Interpreted Languages Example Algorithm Fortran BASIC Pascal C and C++ Java MatLAB Julia R Haskell Others Python Implementation File Output Arrays and Plotting List Initialization NumPy Arrays For-Loops Conditional Statements Functions Random Numbers Code Validation Leapfrog Method Finite Difference and Linear Algebra Taylor Series First Derivative Second Derivative Finite Difference Discretization Boundary Conditions System of Equations Gaussian Elimination Matrix Representation Matrix Algebra Matrix Inverse Matrix Types Matrix Solvers Solver Algorithms Gauss-Jordan Elimination Python Implementation Tridiagonal Algorithm Iterative Solvers Jacobi Method Gauss-Seidel Method Convergence Check Successive Over Relaxation (SOR) D Heat Equation Solver Sparse Matrix Putting it all together Iterative Solver Version Numerical Analysis Data Fitting Polynomial Fits Spline Fits Least Squares Fit Fourier Series Filtering Probability Distributions Quadrature Root Finding Additional Matrix Solver Algorithms Multigrid Conjugate Gradient LU and Cholesky Decomposition Eigenvalues Non-Linear Systems Poor Man’s Linearization Newton-Raphson Linearization Introduction to C++ C and C++ Basics Compilers and Development Environments Main Function and Basic Code Structure Variables Comments and Preprocessor Directives Functions Header Files Data Types Strings Floating Point Mathematics Integer Division Stream Input and Output Variable Scope Static Variables Conditional Statements Enumerations Conditional Operator Loops Arrays and Dynamic Memory Allocation Exceptions C++ Tennis Ball Integrator Initial Version Diffuse Reflection Random Numbers Updated Version Visualization VTK PolyData Format Structures Pointers and References Pointer Arithmetic References Call by Reference Constant Arguments Multi-Dimensional Arrays Linked Lists Object Oriented Programming Constructors and Destructors Initializer Lists Access Control Friends Operator Overloading Copy and Move Static Member Functions and Namespaces Inheritance and Polymorphism Templates Storage Containers Smart Pointers Lambda Functions and Functors Heat Equation Solver in C++ Storage Objects Matrix Solver VTK ImageData Output Main Driver Kinetic Methods Introduction Thermalization Flow Properties Knudsen Number Kinetic Methods Eulerian and Lagrangian Formulation Reduced Dimensionality Free Molecular Flow Particle Storage Computational Domain Initialization Sources Main Loop Particle Push Particle Removal Steady State Mesh-Averaged Properties Results Collisions Monte Carlo Collisions Direct Simulation Monte Carlo Particle in Cell Lorentz Force Electrostatics Integration Algorithm Hybrid Modeling Sugarcubing Initialization Implementation Eulerian Methods Introduction Advection-Diffusion Equation Diffusion Equation PDE Classification Advective Term Integration Schemes Forward Time Central Space (FTCS) Von Neumann Stability Analysis Predictor-Correct Method Multipoint Methods Runge-Kutta Methods Leapfrog and Dufort-Frankel Methods Euler Implicit Method Crank-Nicolson Method Vorticity-Stream Function Method Stream Function Vorticity Transport Equation Boundary Conditions Implementation Vlasov Methods Implementation Initial Conditions Simulation Main Loop Electric Field Interpolation Visualization Other Model Equations First-Order Wave Equation Diffusion Equation Burger’s Equation Maxwell’s Equations Finite Volume Method Surface Integral: Advection Surface Integral: Diffusion Combining Terms Axisymmetric Formulation Interactive Applications HTML Common Elements Styles Classes and Ids Dynamic Web Pages JavaScript Developer Tools Syntax Mathematics Arrays and Objects Object-Oriented Programming Accessing HTML Elements Animation Canvas User Interaction Keyboard and Mouse Interaction Adding Dynamics Colormap File Access XMLHttpRequest External JavaScript Files File Input Button Drag and Drop File Output WebGL Shader Program Shaders Drawing Elements Attributes, Varyings, and Uniforms Textures Software Engineering Debugging Common Errors Print Statements Debuggers Command Line Debugging Memory Leaks Large Projects Make Files Configuration Scripts Libraries Useful Libraries BLAS and LAPACK PETSc OpenFOAM VTK Boost Cython Graphical User Interface Frameworks Coding Standards Code Testing Verification and Validations Uncertainty Analysis Sensitivity Analysis Convergence Studies Version Control Unit Testing Code Documentation LaTeX Sections and References Environments Equations Bibliography High-Performance Computing Introduction Serial Optimization Profiling Algorithm Modification Code Optimization Cache Misses Parallel Processing Multithreading Thread Creation Parallel Vector Addition Parallel Efficiency Threads with Classes Dot Product Locks and Mutexes Atomics Message Passing Interface (MPI) MPI Dot Product Send and Receive Deadlock Reduction Domain Decomposition Remote Access Parallel Debugging CUDA Online Computational Resources Vector Addition Error Checking Blocks Timing Pinned Memory Streams Dot Product Concurrent MPI-CUDA Computation Visualization Optimization and Machine Learning Introduction Cost Function Optimization Approaches Adaptive Search Gradient Descent Examples Genetic Algorithms Machine Learning Neural Networks Activation Functions Cost Function Back Propagation Simple Neural Net in C++ Libraries Embedded Systems Single-Board Computers Microcontrollers Electrical Components Breadboards Arduino Programming Pin Interactions Using Libraries Interfacing with Python Custom Libraries FPGAs and Verilog Development Environments FPGA Hello World Schematic View Events Data Types and Assignments Clocks Control Statements IP Blocks Simulation FPGA Synergistic use with an Arduino Appendix A: Fortran Syntax References Index

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Details for: Brieda L. Introduction to Modern Scientific Programming...Numerical Methods 2024

brieda l introduction modern scientific programming numerical methods 2024