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This book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package MATLAB. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with MATLAB, no starting knowledge of the package being assumed. The range of material is wide: matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations form the basic mathematics. This is applied to a large number of investigations and modelling 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.
• Based on class tested material
• No real competition
• Suitable for students in mathematics or engineering (or any other discipline where mathematical modelling is needed)
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 Miller's 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.
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