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Über dieses Buch

This comprehensive and stimulating introduction to Matlab, a computer language now widely used for technical computing, is based on an introductory course held at Qian Weichang College, Shanghai University, in the fall of 2014.

Teaching and learning a substantial programming language aren’t always straightforward tasks. Accordingly, this textbook is not meant to cover the whole range of this high-performance technical programming environment, but to motivate first- and second-year undergraduate students in mathematics and computer science to learn Matlab by studying representative problems, developing algorithms and programming them in Matlab. While several topics are taken from the field of scientific computing, the main emphasis is on programming.

A wealth of examples are completely discussed and solved, allowing students to learn Matlab by doing: by solving problems, comparing approaches and assessing the proposed solutions.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Starting and Using Matlab

Abstract
It is shown how to get started with Matlab. The difference between Scripts and Functions is explained.
Walter Gander

Chapter 2. How a Computer Calculates

Abstract
This section is an excerpt of the material presented in Chap. 2 of [3]. It is important to realize that a computer cannot perform numerical computations exactly like one would expect them to be done in mathematics.
Walter Gander

Chapter 3. Plotting Functions and Curves

Abstract
In this section we learn how to define functions in Matlab and how functions and curves can be plotted.
Walter Gander

Chapter 4. Some Elementary Functions

Abstract
Standard functions are available in almost all programming languages. But how could we actually compute them by using only the 4 basic arithmetic operations \(\{+, -, \times , /\}\)? Algorithms for computing standard functions on computers were developed some 60 years ago.
Walter Gander

Chapter 5. Computing with Multiple Precision

Abstract
In this section we shall show how to perform some computations with more digits than given by the IEEE floating point arithmetic. The problems of this section will need integer operations and variables of integer data types. It is an opportunity to learn the corresponding Matlab features.
Walter Gander

Chapter 6. Solving Linear Equations

Abstract
In this chapter we shall develop a method to solve linear equations.
Walter Gander

Chapter 7. Recursion

Abstract
Recursion is a powerful concept in computer science. The basic idea is that the solution of a problem often can be reduced to solving some smaller instances of the same problem.
Walter Gander

Chapter 8. Iteration and Nonlinear Equations

Abstract
In this chapter we discuss some problems which lead to nonlinear equations. These equations are solved with bisection and with Newton’s method.
Walter Gander

Chapter 9. Simulation

Abstract
In this chapter we discuss some examples for discrete and continuous simulation: discrete events using random numbers, exhaustive search and differential equations.
Walter Gander

Chapter 10. Solutions of Problems

Abstract
This chapter contains the solutions of all exercises.
Walter Gander

Backmatter

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