MATLAB Symbolic Algebra and Calculus Tools

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java.

MATLAB Symbolic Algebra and Calculus Tools introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic variables and functions, you will learn how to solve equations in MATLAB, both symbolically and numerically, and how to simplify the results. Extensive coverage of polynomial solutions, inequalities and systems of equations are covered in detail. You will see how MATLAB incorporates vector, matrix and character variables, and functions thereof. MATLAB is a powerful symbolic manipulator which enables you to factorize, expand and simplify complex algebraic expressions over all common fields (including over finite fields and algebraic field extensions of the rational numbers). With MATLAB you can also work with ease in matrix algebra, making use of commands which allow you to find eigenvalues, eigenvectors, determinants, norms and various matrix decompositions, among many other features. Lastly, you will see how you can use MATLAB to explore mathematical analysis, finding limits of sequences and functions, sums of series, integrals, derivatives and solving differential equation.

What you’ll learn

• How to use MATLAB to work with numeric and symbolic variables, including vector, matrix and character variables

• How to use MATLAB to handle polynomials and general algebraic expressions, factorizing, expanding and simplifying over a wide range of fields

• How to use MATLAB to work on matrix and vector functions, including all the standard matrix operations and decompositions

• How to solve equations and systems of equations using MATLAB

• How MATLAB can be used to explore mathematical analysis, by finding limits of sequences and functions, sums of series, integrals, derivatives, and solving differential equations

Who this book is for

This book is for anyone who wants to work in a practical, hands-on manner on symbolic algebra or calculus problems with MATLAB. You'll already have a core understanding of undergraduate level calculus, algebra and linear algebra, and have access to an installed version of MATLAB, but no previous experience of MATLAB is assumed.

Table of Contents

Chapter 1: Symbolic Variables and Functions

Chapter 2: Algebraic Expressions

Chapter 3: Polynomial Divisibility

Chapter 4: Symbolic Matrix Algebra

Chapter 5: Equations and Systems

Chapter 6: Series, Continuity, Integrals and Differential Equations

MATLAB是一種高階語言和環境，用於數值計算、可視化和編程。使用MATLAB，您可以分析數據、開發算法，並創建模型和應用程序。語言、工具和內置的數學函數使您能夠探索多種方法，並比使用電子表格或傳統編程語言（如C/C++或Java）更快地找到解決方案。

《MATLAB符號代數和微積分工具》通過實際的實踐指導和結果，介紹了MATLAB語言，讓您能夠快速實現目標。從符號變量和函數開始，您將學習如何在MATLAB中解方程，無論是符號還是數值，以及如何簡化結果。詳細介紹了多項式解、不等式和方程組。您將看到MATLAB如何結合向量、矩陣和字符變量及其函數。MATLAB是一個強大的符號操作器，可以在所有常見的領域（包括有限域和有理數的代數域擴展）上因式分解、展開和簡化複雜的代數表達式。使用MATLAB，您還可以輕鬆進行矩陣代數運算，利用命令找到特徵值、特徵向量、行列式、範數和各種矩陣分解等功能。最後，您將看到如何使用MATLAB探索數學分析，找到數列和函數的極限、級數的和、積分、導數和解微分方程。

本書的學習內容包括：
• 如何使用MATLAB處理數值和符號變量，包括向量、矩陣和字符變量
• 如何使用MATLAB處理多項式和一般代數表達式，在各種領域上進行因式分解、展開和簡化
• 如何使用MATLAB處理矩陣和向量函數，包括所有標準的矩陣運算和分解
• 如何使用MATLAB解方程和方程組
• 如何使用MATLAB進行數學分析，通過找到數列和函數的極限、級數的和、積分、導數和解微分方程

本書適合以下讀者：
• 任何希望以實際、實踐的方式使用MATLAB解決符號代數或微積分問題的人。您應該已經具備本科水平的微積分、代數和線性代數的核心理解，並且可以訪問已安裝的MATLAB版本，但不需要有MATLAB的先前經驗。

目錄：
第1章：符號變量和函數
第2章：代數表達式
第3章：多項式可除性
第4章：符號矩陣代數
第5章：方程和方程組
第6章：級數、連續性、積分和微分方程