MATHEMATICAL EXPLORATIONS WITH MATLAB
暫譯: 使用 MATLAB 的數學探索

Description:

Mathematical Explorations with MATLAB examines the mathematics most frequently encountered in first-year university courses. A key feature of the book is its use of MATLAB, a popular and powerful software package. The book's emphasis is on understanding and investigating the mathematics by putting the mathematical tools into practice in a wide variety of modeling situations. Even readers who have no prior experience with MATLAB will gain fluency. The book covers a wide range of material: matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations from the basic mathematics. These lessons are applied to a rich variety of investigations and modeling problems, from sequences of real numbers to cafeteria queues, from card shuffling to models of fish growth. All extras to the standard MATLAB package are supplied on the World Wide Web.

Table of Contents:

Part I. Foundations: 1. Introduction
2. Matrices and complex numbers
3. Whole numbers
4. Graphs and curves
5. Representation of data
6. Probability and random numbers
7. Differential and difference equations
Part II. Investigations: 8. Magic squares
9. GCDs, pseudoprimes and Millers test
10. Graphics: curves and envelopes
11. Zigzags and fast curves
12. Sequences of real numbers
13. Newton-Raphson iteration and fractals
14. Permutations
15. Iterations for nonlinear equations
16. Matrices and solutions of linear systems
17. Functional interpolations and approximation
18. Ordinary differential equations
Part III. Modelling: 19. Checkout queues: long or short
20. Fish farming
21. Epidemics
22. Dynamics of snowboating
23. Tides.