Название: Mathematics for Business AnalysisАвтор: Paul Turner, Justine Wood
Издательство: Mercury Learning and Information
Год: 2024
Страниц: 377
Язык: английский
Формат: pdf (true)
Размер: 16.0 MB
Designed for students, faculty, and professionals, this book describes the role of mathematics in the world of economics and business. Beginning with the fundamental nature of numbers and progressing into more complex realms like hyperreal numbers and the intricacies of set theory, this book constructs a strong foundational understanding of mathematical concepts. The book uses Python code throughout the text to illustrate problems numerically. As readers advance, the text seamlessly integrates essential topics such as linear simultaneous equations, which are pivotal in analyzing market equilibrium, and covers the mechanics of matrices for solving larger equation systems. Furthermore, chapters dedicated to calculus, especially its applications in economics and the innovative use of infinitesimal methods, equip learners with tools to tackle profit maximization challenges, factor optimization, and beyond. Later chapters unfold the world of differential and difference equations, revealing their significance in analyzing dynamic systems. All these concepts are illuminated through practical examples and numerous images from economics and business, ensuring relevance and clarity.
Our approach is as follows: first, in Chapter 1, we develop the very basics of mathematics in terms of the nature of numbers, starting with the natural numbers and progressing to the integers, real numbers and finally, introducing more exotic concepts such as complex numbers and the hyperreals. This naturally allows us to develop the idea of sets which act as a basic organizing structure in mathematics. Chapter 2 then builds on this to develop the idea of mathematical functions as a ‘mapping’ from one set to another. Much of this initial material is designed to allow students to become comfortable with the language of mathematics and to enable them to express familiar concepts in a more formal manner.
The basic material of Chapters 1 and 2 is then followed by applications which make use of mathematical functions to address topics of interest for students of economics and business. In Chapter 3, we look at the solution of systems of simultaneous equations. This has obvious applications in the analysis of interactions between economic agents and the determination of market equilibrium. We consider methods for the solution of systems of equations and show how these can be applied to both linear and non-linear systems. Our initial treatment of this topic is limited to small systems containing only two or three equations, but this is later extended in Chapter 8 when we introduce the method of matrices as a way of extending our solution methods to larger systems.
Features:
Integrates computational understanding with chapters dedicated to PYTHON code examples that illuminate mathematical concepts
Covers infinitesimal methods, a distinct approach that emphasizes intuition and comprehensive technique development
Includes differential and difference equations, vital for understanding how variables evolve over time in response to external influences
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