Numerical C: Applied Computational Programming with Case Studies

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Learn applied numerical computing using the C programming language, starting with a quick primer on the C programming language and its SDK. This book then dives into progressively more complex applied math formula for computational methods using C with examples throughout and a larger, more complete application towards the end.
Numerical C starts with the quadratic formula for finding solutions to algebraic equations that model things such as price vs. demand or rise vs. run or slip and more. Later in the book, you'll work on the augmented matrix method for simultaneous equations.
You'll also cover Monte Carlo method model objects that could arise naturally as part of the modeling of a real-life system, such as a complex road network, the transport of neutrons, or the evolution of the stock market. Furthermore, the Monte Carlo method of integration examines the area under a curve including rendering or ray tracing and the shading in a region.
Furthermore, you'll work with the product moment correlation coefficient: correlation is a technique for investigating the relationship between two quantitative, continuous variables, for example, age and blood pressure. By the end of the book, you'll have a feeling for what computer software could do to help you in your work and apply some of the methods learned directly to your work.
What You Will Learn

Gain software and C programming basics
Write software to solve applied, computational mathematics problems
Create programs to solve equations and calculus problems
Use the trapezium method, Monte Carlo method, line of best fit, product moment correlation coefficient, Simpson's rule, and matrix solutions
Write code to solve differential equations


Apply one or more of the methods to an application case study

Who This Book Is For
Those with an existing knowledge of rudimentary mathematics (school level) and some basic programming experience. This is also important to people who may work in mathematics or other areas (for example, life sciences, engineering, or economics) and need to learn C programming.

Author(s): Philip Joyce
Year: 2019

Language: English

Table of Contents
About the Author
About the Technical Reviewer
Acknowledgments
Introduction
Chapter 1: Introduction to C
First Program
Get and Print a Character
Add Two Numbers
Add Two Decimal Numbers
Multiply Two Numbers
Divide Two Numbers
Forloops
Flowcharts
Do Loops
Switch Instruction
If Then Else
If Then Else If
Data Arrays
Functions
Strings
Mathematical Functions
Structures
Size of Variables
Goto Command
Common Mathematical and Logical Symbols
Chapter 2: Solving Equations
Quadratic Equations
Factorizing
Completing the Square
Quadratic Formula
Equations of Higher Powers
Trial and Improvement
Which Solution Are We Finding?
Three Solutions
User-Entered Function
Chapter 3: Numerical Integration
Trapezium Integration
Simplification of Formula
Inverse Power
Combined Powers
Problem with Negative Areas
Simpson’s Rule Integration
Chapter 4: Monte Carlo Integration
Finding an Odd-Shaped Area
Monte Carlo Area of Graph
Area of a Circle
Higher Dimension Graphs
Even Higher Dimensions
Chapter 5: Matrices
Matrix Arithmetic
Matrix Addition and Subtraction
Matrix Multiplication
Matrix Inverse
Coding a Matrix Inverse
Testing the Code
Chapter 6: Correlation and PMCC
Scatter Graphs and Correlation
Product Moment Correlation Coefficient
Chapter 7: Monte Carlo Methods
Radioactive Decay Simulation
Buffon’s Needle
Random Walk
Chapter 8: Augmented Matrix
Manual Solution to Simultaneous Equations
Augmented Matrix Program
Twelve Simultaneous Equations
Chapter 9: File Access
First Program to Write a File
Writing a Large Data File
Medical Records File
Company Records File
Chapter 10: Differential Equations
Taylor and Maclaurin Series
Euler Method
Runge-Kutta Method
Second Order Differential Equations
Appendix A: Development Environment Reference
Visual Studio
Command Line
Appendix B: Syntax Reference
Mathematical Functions
Pointers
Standard Library Functions
Comparing Double, Float, and Integer
Appendix C: Answers to Problems
Index