## Introduction to Computational Science and MathematicsAn Introduction to Computational Science and Mathematics will help introductory computer science, math, science, and engineering students develop computational intuition and introductory programming skills. The interactions between mathematics, physical experimentation, and computer simulation are crucial to the scientific enterprise. Students need to be comfortable with these dimensions early in their studies to maximize their ability to solve problems in many disciplines. The text assumes a first-semester calculus background and ease with trigonometry. Programming exercises use Think Pascal, though the concepts are developed without dependence on syntax. |

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### Contents

From Formula to Program | 1 |

2t Numerical Exploration | 25 |

O Elementary Graphics | 49 |

Sequences | 75 |

O Random Simulations | 89 |

O Fast Faster Fastest | 103 |

Exponential Growth | 115 |

Patterns | 137 |

Tables | 287 |

16 | 317 |

17 | 331 |

Polygons | 359 |

Special Arithmetics | 385 |

2i U Polynomials | 405 |

Permutations | 423 |

2i2i Optimization | 449 |

### Common terms and phrases

0uterA AnotherEg approximate arithmetic assignment begin ShowDrawing begin ShowText benchmarking binomial coefficient boolean boolean-valued function bubble sort centroid ChaplSCodes ClearScreen coefficients Complete the following computational science const declared defined digit displayed distance divisors Draw ellipse end end Fibonacci FIGURE floating point following function following procedure fragment function function grid implementation initialized InnerA insertion sort integer interval involves k-th k:integer length line segment longint loop main program merge sort n-gon obtain p_scale parameters perfect shuffle pixels per xy plot polygon polynomial Post Post:Draws Post:The Powerbook 170 PROBLEM program Example program that prints r:real radius rand(r random number real number RealList RealPoint rectangle recursive representation root Sample output scientific notation screen location sequence simulation sort square StartTime StopTime string substring Swap TickCount tile triangle unit DDCodes upper left corner variable Write a program writeln writeln('Enter x,y:RealList xval xy unit