Numerical C: Applied Computational Programming with Case Studies

Description

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. 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