An Introduction to C++ and Numerical Methods

by Ortega, James M.; Grimshaw, Andrew S.

• ISBN13: 9780195117677
• ISBN10: 0195117670
• Format: Paperback
• Copyright: 1998-08-06
• Publisher: Oxford University Press

Summary

An Introduction to C++ and Numerical Methods provides a brief yet comprehensive introduction to programming and numerical methods for students in engineering, chemistry, physics, and applied mathematics. It is suitable for second semester or second year students who have had at least asemester of calculus. This text offers students both an introduction to programming in C++ and clear explanations of the basics of numerical methods, including numerical integration and the solution of ordinary differential equations, nonlinear equations, and systems of linear equations. It is unique among textbooksat this level in its extensive coverage of numerical methods used in scientific and engineering computation. An Introduction to C++ and Numerical Methods is designed to help students move quickly into writing interesting and sophisticated programs. The text begins with an introduction to scientific computing and the basic constructs of C++, including variables and assignment, typing, if statements, forand while loops, functions, one-dimensional arrays, and the cout and cin objects. After students have gained some experience with programming using these constructs, the topics are later revisited in greater detail, leading up to the important topic of classes and object-oriented programming.Throughout the text Ortega and Grimshaw emphasize the basic paradigms for constructing good programs and detecting errors.

Table of Contents

PREFACE	ix
PART I Basic Constructs	1	(114)
1 INTRODUCTION	3	(13)
1.1 Computers and Software	4	(2)
1.2 Binary Numbers and Memory	6	(3)
1.3 Rounding Errors	9	(2)
1.4 Programs	11	(5)
2 A FIRST C++ PROGRAM	16	(14)
2.1 Computation and Assignment	16	(2)
2.2 Variable Types	18	(2)
2.3 Input and Output	20	(2)
2.4 A Complete Program	22	(2)
2.5 Errors and Debugging	24	(6)
3 DECISIONS, DECISIONS	30	(14)
3.1 The if Statement	30	(4)
3.2 Logical Operators	34	(1)
3.3 Nested If and Switch Statements	35	(4)
3.4 Good Programming Practice	39	(5)
4 AROUND AND AROUND: ITERATION	44	(12)
4.1 The for Statement	44	(2)
4.2 The while Statement	46	(3)
4.3 An Approximation to e(x)	49	(1)
4.4 Advanced Loop Control	50	(6)
5 FUNCTIONS	56	(11)
5.1 Library Functions	57	(1)
5.2 User-Defined Functions	58	(3)
5.3 More General Functions	61	(2)
5.4 Local versus Global Variables	63	(4)
6 NUMERICAL INTEGRATION	67	(11)
6.1 Approximate Integration Formulas	67	(2)
6.2 Flow Charts	69	(1)
6.3 An Integration Program	70	(3)
6.4 Discretization Error	73	(5)
7 READING AND WRITING: INPUT/OUTPUT	78	(10)
7.1 Precision	78	(2)
7.2 Spacing	80	(2)
7.3 File Input/Output	82	(2)
7.4 The printf() Function	84	(4)
8 SOLUTION OF NONLINEAR EQUATIONS	88	(9)
8.1 The Bisection Method	89	(3)
8.2 Newton's Method	92	(2)
8.3 Errors and a Combined Method	94	(3)
9 LOTS OF VALUES: ARRAYS	97	(9)
9.1 Array Declarations	97	(3)
9.2 Arrays and Functions	100	(6)
10 DIFFERENTIAL EQUATIONS	106	(9)
10.1 The Initial Value Problem	106	(1)
10.2 Euler's Method	107	(3)
10.3 Systems of Equations	110	(5)
PART II Extensions of the Basic Constructs	115	(92)
11 MORE ON DATA TYPES AND OPERATIONS	117	(19)
11.1 Other Fundamental Data Types	117	(3)
11.2 Operations	120	(4)
11.3 Characters and Strings	124	(5)
11.4 User-Defined Data Types	129	(7)
12 LOTS MORE VALUES: TWO-DIMENSIONAL ARRAYS	136	(10)
12.1 Two-Dimensional Arrays	136	(3)
12.2 Arrays and Functions	139	(3)
12.3 Arrays of Strings	142	(4)
13 LINEAR EQUATIONS	146	(14)
13.1 Least-Squares Approximation	146	(2)
13.2 Gaussian Elimination	148	(4)
13.3 Errors	152	(5)
13.4 Efficiency	157	(3)
14 MORE ON FUNCTIONS	160	(16)
14.1 Reference versus Value	160	(3)
14.2 Recursive and Inline Functions	163	(3)
14.3 Function Miscellanea	166	(4)
14.4 Libraries of Functions	170	(6)
15 POINTERS	176	(14)
15.1 Pointer Variables	176	(3)
15.2 Pointers and Arrays	179	(2)
15.3 Pointers and Functions	181	(5)
15.4 Pointers and Strings	186	(4)
16 DYNAMIC MEMORY	190	(17)
16.1 Dynamic Memory Allocation	191	(5)
16.2 Matrices and Strings	196	(3)
16.3 Linked Lists	199	(8)
PART III Object-Oriented Programming	207	(54)
17 CLASSES AND OBJECTS	209	(22)
17.1 A Simple Class	209	(8)
17.2 Classes and Functions	217	(7)
17.3 Stream Classes	224	(7)
18 ARRAY CLASSES AND DYNAMIC MEMORY	231	(15)
18.1 A Vector Class	231	(1)
18.2 Dynamic Memory Allocation	232	(8)
18.3 A Matrix Class	240	(6)
19 INHERITANCE	246	(15)
19.1 Derived Classes	246	(4)
19.2 Polymorphism and Virtual Functions	250	(3)
19.3 Linear Equations	253	(8)
FURTHER READING	261	(2)
APPENDIX 1 ASCII CHARACTER CODES	263	(2)
APPENDIX 2 LIBRARY FUNCTIONS	265	(2)
INDEX	267