Guide to Scientific Computing in C++

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front-matter
	Guide to Scientific Computing in C++
		Preface
		Contents
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	Chapter 1: Getting Started
		1.1 A Brief Introduction to C++
			1.1.1 C++ is "Object-Oriented"
			1.1.2 Why You Should Write Scientific Programs in C++
			1.1.3 Why You Should Not Write Scientific Programs in C++
			1.1.4 Scope of This Book
		1.2 A First C++ Program
		1.3 Compiling a C++ Program
			1.3.1 Integrated Development Environments
			1.3.2 Compiling at the Command Line
			1.3.3 Compiler Flags
		1.4 Variables
			1.4.1 Basic Numerical Variables
			1.4.2 Other Numerical Variables
			1.4.3 Mathematical Operations on Numerical Variables
			1.4.4 Division of Integers
			1.4.5 Arrays
			1.4.6 ASCII Characters
			1.4.7 Boolean Variables
			1.4.8 Strings
		1.5 Simple Input and Output
			1.5.1 Basic Console Output
			1.5.2 Keyboard Input
		1.6 The assert Statement
		1.7 Tips: Debugging Code
		1.8 Exercises
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	Chapter 2: Flow of Control
		2.1 The if Statement
			2.1.1 A Single if Statement
			2.1.2 Example: Code for a Single if Statement
			2.1.3 if-else Statements
			2.1.4 Multiple if Statements
			2.1.5 Nested if Statements
			2.1.6 Boolean Variables
		2.2 Logical and Relational Operators
		2.3 The while Statement
		2.4 Loops Using the for Statement
			2.4.1 Example: Calculating the Scalar Product of Two Vectors
		2.5 The switch Statement
		2.6 Tips: Loops and Branches
			2.6.1 Tip 1: A Common Novice Coding Error
			2.6.2 Tip 2: Counting from Zero
			2.6.3 Tip 3: Equality Versus Assignment
			2.6.4 Tip 4: Never Ending while Loops
			2.6.5 Tip 5: Comparing Two Floating Point Numbers
		2.7 Exercises
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	Chapter 3: File Input and Output
		3.1 Redirecting Console Output to File
		3.2 Writing to File
			3.2.1 Setting the Precision of the Output
		3.3 Reading from File
		3.4 Reading from the Command Line
		3.5 Tips: Controlling Output Format
		3.6 Exercises
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	Chapter 4: Pointers
		4.1 Pointers and the Computer's Memory
			4.1.1 Addresses
			4.1.2 Pointer Variables
			4.1.3 Example Use of Pointers
			4.1.4 Warnings on the Use of Pointers
		4.2 Dynamic Allocation of Memory for Arrays
			4.2.1 Vectors
			4.2.2 Matrices
			4.2.3 Irregularly Sized Matrices
		4.3 Tips: Pointers
			4.3.1 Tip 1: Pointer Aliasing
			4.3.2 Tip 2: Safe Dynamic Allocation
			4.3.3 Tip 3: Every new Has a delete
		4.4 Exercises
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	Chapter 5: Blocks, Functions and Reference Variables
		5.1 Blocks
		5.2 Functions
			5.2.1 Simple Functions
			5.2.2 Returning Pointer Variables from a Function
			5.2.3 Use of Pointers as Function Arguments
			5.2.4 Sending Arrays to Functions
			5.2.5 Example: A Function to Calculate the Scalar Product of Two Vectors
		5.3 Reference Variables
		5.4 Default Values for Function Arguments
		5.5 Function Overloading
		5.6 Declaring Functions Without Prototypes
		5.7 Function Pointers
		5.8 Recursive Functions
		5.9 Modules
		5.10 Tips: Code Documentation
		5.11 Exercises
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	Chapter 6: An Introduction to Classes
		6.1 The Raison d'Être for Classes
			6.1.1 Problems That May Arise When Using Modules
			6.1.2 Abstraction, Encapsulation and Modularity Properties of Classes
		6.2 A First Example Simple Class: A Class of Books
			6.2.1 Basic Features of Classes
			6.2.2 Header Files
			6.2.3 Setting and Accessing Variables
			6.2.4 Compiling Multiple Files
				6.2.4.1 Using Makefiles to Compile Multiple Files
			6.2.5 Access Privileges
			6.2.6 Including Function Implementations in Header Files
			6.2.7 Constructors and Destructors
			6.2.8 Pointers to Classes
		6.3 The friend Keyword
		6.4 A Second Example Class: A Class of Complex Numbers
			6.4.1 Operator Overloading
			6.4.2 The Class of Complex Numbers
		6.5 Some Additional Remarks on Operator Overloading
		6.6 Tips: Coding to a Standard
		6.7 Exercises
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	Chapter 7: Inheritance and Derived Classes
		7.1 Inheritance, Extensibility and Polymorphism
		7.2 Example: A Class of E-books Derived from a Class of Books
		7.3 Access Privileges for Derived Classes
		7.4 Classes Derived from Derived Classes
		7.5 Run-Time Polymorphism
		7.6 The Abstract Class Pattern
		7.7 Tips: Using a Debugger
		7.8 Exercises
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	Chapter 8: Templates
		8.1 Templates to Control Dimensions and Verify Sizes
		8.2 Templates for Polymorphism
		8.3 A Brief Survey of the Standard Template Library
			8.3.1 Vectors
			8.3.2 Sets
		8.4 Tips: Template Compilation
		8.5 Exercises
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	Chapter 9: Errors and Exceptions
		9.1 Preconditions
			9.1.1 Example: Two Implementations of a Graphics Function
		9.2 Three Levels of Errors
		9.3 Introducing the Exception
		9.4 Using Exceptions
		9.5 Tips: Test-Driven Development
		9.6 Exercises
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	Chapter 10: Developing Classes for Linear Algebra Calculations
		10.1 Requirements of the Linear Algebra Classes
		10.2 Constructors and Destructors
			10.2.1 The Default Constructor
			10.2.2 The Copy Constructor
			10.2.3 A Specialised Constructor
			10.2.4 Destructor
		10.3 Accessing Private Class Members
			10.3.1 Accessing the Size of a Vector
			10.3.2 Overloading the Square Bracket Operator
			10.3.3 Read-Only Access to Vector Entries
			10.3.4 Overloading the Round Bracket Operator
		10.4 Operator Overloading for Vector Operations
			10.4.1 The Assignment Operator
			10.4.2 Unary Operators
			10.4.3 Binary Operators
		10.5 Functions
			10.5.1 Members Versus Friends
		10.6 Tips: Memory Debugging Tools
		10.7 Exercises
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	Chapter 11: An Introduction to Parallel Programming Using MPI
		11.1 Distributed Memory Architectures
		11.2 Installing MPI
		11.3 A First Program Using MPI
			11.3.1 Essential MPI Functions
			11.3.2 Compiling and Running MPI Code
		11.4 Basic MPI Communication
			11.4.1 Point-to-Point Communication
				11.4.1.1 Blocking and Buffered Sends
			11.4.2 Collective Communication
				11.4.2.1 Barrier
				11.4.2.2 Combined Send and Receive
				11.4.2.3 Broadcast and Reduce
				11.4.2.4 Scatter and Gather
		11.5 Example MPI Applications
			11.5.1 Summation of Series
			11.5.2 Parallel Linear Algebra
		11.6 Tips: Debugging a Parallel Program
			11.6.1 Tip 1: Make an Abstract Program
			11.6.2 Tip 2: Datatype Mismatch
			11.6.3 Tip 3: Intermittent Deadlock
			11.6.4 Tip 4: Almost Collective Communication
		11.7 Exercises
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	Chapter 12: Designing Object-Oriented Numerical Libraries
		12.1 Developing the Library for Ordinary Differential Equations
			12.1.1 Model Problems
			12.1.2 Finite Difference Approximation to Derivatives
			12.1.3 Application of Finite Difference Methods to Boundary Value Problems
				12.1.3.1 Model Problem 1
				12.1.3.2 Model Problem 2
			12.1.4 Concluding Remarks on Boundary Value Problems in One Dimension
		12.2 Designing a Library for Solving Boundary Value Problems
			12.2.1 The Class SecondOrderOde
			12.2.2 The Class BoundaryConditions
			12.2.3 The Class FiniteDifferenceGrid
			12.2.4 The Class BvpOde
			12.2.5 Using the Class BvpOde
		12.3 Extending the Library to Two Dimensions
			12.3.1 Model Problem for Two Dimensions
			12.3.2 Finite Difference Methods for Boundary Value Problems in Two Dimensions
			12.3.3 Setting Up the Linear System for the Model Problem
			12.3.4 Developing the Classes Required
		12.4 Tips: Using Well-Written Libraries
		12.5 Exercises
back-matter
	Appendix A Linear Algebra
		A.1 Vectors and Matrices
			A.1.1 Operations Between Vectors and Matrices
			A.1.2 The Scalar Product of Two Vectors
			A.1.3 The Determinant and the Inverse of a Matrix
			A.1.4 Eigenvalues and Eigenvectors of a Matrix
			A.1.5 Vector and Matrix Norms
		A.2 Systems of Linear Equations
			A.2.1 Gaussian Elimination
				A.2.1.1 Gaussian Elimination Without Pivoting
				A.2.1.2 LU Decomposition
				A.2.1.3 Gaussian Elimination with Pivoting
			A.2.2 The Thomas Algorithm
			A.2.3 The Conjugate Gradient Method
	Appendix B Other Programming Constructs You Might Meet
		B.1 C Style Output
		B.2 C Style Dynamic Memory Allocation
		B.3 Ternary ?: Operator
		B.4 Using Namespace
		B.5 Structures
		B.6 Multiple Inheritance
		B.7 Class Initialisers
	Appendix C Solutions to Exercises
		C.1 Matrix and Linear System Classes
		C.2 ODE Solver Library
	Further Reading
		Mathematical Methods and Linear Algebra
		C++ Programming
		The Message-Passing Interface (MPI)
	Index