دانلود کتاب Introduction to the Tools of Scientific Computing

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Preface
Preface to the Second Edition
Acknowledgments
Preface to the First Edition
Acknowledgments
Contents
Chapter 1 Introduction
Background
Pitfalls and Limitations
Programming Languages
The C Language
Program Packages Matlab, Maple, Mathematica
The Golden Middle Course: Python
Part I Background
Part II Core Languages
Part III Commercial Computing Environments
Part IV Distributed Computing
Part V Specialized Programming Frameworks
Part I Background
Chapter 2 Mathematical Foundations of Programming
2.1 A Simple Machine Model
Machine Language and Higher-Level Programming Languages
Church’s Thesis
The Turing Machine
Limits of Computability
Repercussions in Mathematics
Extended Number Ranges
2.2 Digital Computers
Number Representation
Natural Numbers
Integer Numbers
Real Numbers, Floating Point Numbers
Higher-Level Programming Languages
Part II Core Languages
Chapter 3 Python, the Fundamentals
3.1 Python Interpreter
A First Example
Interactive Mode
3.2 Elementary Data Types
Numbers and Arithmetic
Integer Numbers
Real Numbers, Floating Point Numbers
Arithmetical Operations
Error Propagation in float Computations
The Types complex and bool
Complex Numbers
Boolean Operators, Comparisons
3.3 Variables and Value Assignments
Basic Rule
3.4 Control Structures
Loops
While Loops
For Loops
Interlude: the range Function
The break and continue Statements
Conditional Statements
Floating Point Precision Revisited: Machine Epsilon
3.5 Collection Types: Lists, Tuples, Dictionaries and Sets
Lists
list is a Reference Type
Sieve of Eratosthenes
Sublists
Concatenation
List Comprehensions
Tuples
Dictionaries
Sets
3.6 Functions
Anonymous Functions, Lambda Expressions
Functions as Arguments
Functions as Return Values
Recursion
The Quicksort Algorithm
3.7 String Interpolation and Formatting
3.8 Writing and Reading Files
Writing Strings
Interlude: Access Paths
Reading
Numbers
Binary Files and pickle
3.9 Object-Oriented Programming and Classes
Polynomials
Inheritance
Exercises
Machine Epsilon
Polynomial Class
Linear Algebra
Numerical Integration with the Trapezoidal Rule
The Taylor Series
The Newton Method
Fermat’s Last Theorem
Chapter 4 Python in Scientific Computation
4.1 NumPy
NumPy Arrays
Vectors and Matrices
Vectors
Matrices
Access to Matrix Components
Flatten and Reshape
Standard Matrices
Advanced Construction Methods
The Methods diag and kron, the Poisson Matrix
4.2 Conjugate Gradient Method
Quadratic Form
The Method
4.3 SciPy
4.4 Linear Algebra
Matrix Algorithms
Linear Equations
LU Decomposition
Cholesky Decomposition
Application: Method of Least Squares
QR Decomposition
QR Decomposition in Rectangular Matrices
The Gaussian Normal Equation
Eigenvectors and Eigenvalues
Sparse Matrices
Sparse Poisson Matrix
4.5 Graphics with Matplotlib
4.6 Nonlinear Equations, Optimization
Single Equations
Equation Systems
Minimization
4.7 Numerical Integration, Ordinary Differential Equations
Integration
Ordinary Differential Equations ODEs
Initial Value Problems, solve_ivp
The Solver solve_ivp
Lotka–Volterra Equations
Pendulum
Boundary Value Problems BVPs, solve_ivp
4.8 Partial Differential Equations
Discretization
Solution Program
Sparse Poisson Matrix
Nonhomogeneous Boundary Conditions
The SciPy Program
Verification
4.9 Round off: Random Numbers
Monte Carlo Method for the Computation of