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MATLAB Essentials: Symbolic and Numeric Problem-Solving in Engineering

  • 2025
  • Book
Author
Lester W. Schmerr, Jr.
Publisher
Springer Nature Switzerland
Part of
Springer Professional "Business + Economics & Engineering + Technology"
Springer Professional "Engineering + Technology"
Springer Professional "Business + Economics"
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About this book

This book introduces MATLAB as a direct problem-solving tool, where the many built-in functions and commands of MATLAB can be used to perform even complex tasks. In this mode MATLAB acts as a very advanced scientific calculator. The primary purpose of this book is to teach the reader how to use the functions and commands of this calculator and, when necessary, how to save the problem-solving steps so that the solution obtained can be re-used or re-evaluated under different conditions. The book also introduces symbolic calculations extensively in addition to the traditional numerical methods found in other texts. MATLAB was initially introduced as a numerical tool for linear algebra problems and over the years has extended those numerical capabilities significantly to many areas of science and engineering. Consequently, it is not surprising that most books retain a strong emphasis on numerical solutions and treat symbolic calculations only briefly, if at all. A key point is that while symbolic algebra can be used to solve problems symbolically, it can also be used to make the formulation of problems much simpler, even if the ultimate solution is found numerically. Recognizing and demonstrating this important property of symbolic calculations is unique to this book.

Examines symbolic and numeric MATLAB tools with engineering examples of linear and nonlinear equations, eigenvalue problems, and differential equations

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
This chapter describes how to use MATLAB. Short sections will outline some major tools and capabilities that are essential for productively using MATLAB in the Command Window as a sophisticated engineering calculator. A reader new to MATLAB can treat these sections as a tutorial for acquiring the background needed to start using MATLAB. Users with some or with extensive MATLAB experience can treat these sections instead as a convenient reference guide for locating specific MATLAB capabilities directly from the section listings for this chapter in the table of contents.
Lester W. Schmerr, Jr.
Chapter 2. Vectors and Vector Operations
Abstract
This chapter describes the use of numerical and symbolic vectors in MATLAB. Physical vectors are expressed in terms of a magnitude and an arrow that represents the vector's direction. In MATLAB vectors are described either by a scalar magnitude and a unit vector to represent the vector direction, or by their components. Both the vector dot product and vector cross product, which appear frequently in vector applications, are discussed. Engineering examples of vectors and vector operations are given.
Lester W. Schmerr, Jr.
Chapter 3. Matrices and Matrix Operations
Abstract
This chapter describes the use of numerical and symbolic matrices in MATLAB. Matrix operations and the MATLAB functions that implement those operations are discussed. Two important examples of matrices that appear in engineering – the direction cosine matrix and the mass moment of inertia matrix – are defined and used as part of solving matrix eigenvalue problems.
Lester W. Schmerr, Jr.
Chapter 4. Linear Equations
Abstract
This chapter describes the numerical and symbolic solution of systems of linear equations. Systems where the number of unknowns is equal to the number of equations are considered as well as systems where there are more equations than unknowns (overdetermined systems) or fewer equations than unknowns (underdetermined systems). In all cases simple examples and graphical interpretations of the results are given. A unique way to solve the underdetermined systems found in statically indeterminate problems is discussed.
Lester W. Schmerr, Jr.
Chapter 5. Ordinary Differential Equations
Abstract
This chapter describes the numerical and symbolic solution of systems of ordinary differential equations (ODEs). In numerical solutions it is necessary to control the errors, a topic that will be covered with examples using the popular numerical MATLAB solver ode45. For symbolic solutions we will use the MATLAB dsolve function. We will also show how to use symbolic algebra to define the function needed by ode45 to obtain a numerical solution. The ODEs that govern engineering dynamics problems are often best described through animation and movie functions. A particular example, the spring-pendulum, will be thoroughly solved and animated to illustrate the types of unexpected motions and behavior that can occur in even simple dynamic systems.
Lester W. Schmerr, Jr.
Chapter 6. Nonlinear Problems
Abstract
 This chapter describes the numerical and symbolic solution of nonlinear equations. The numerical solutions are typically obtained with iterative procedures. Symbolic algebra will also be used to solve nonlinear problems. Another important use of symbolic algebra is to formulate a problem which is then solved numerically. Engineering problems will illustrate the use of the MATLAB tools available for nonlinear problems.
Lester W. Schmerr, Jr.
Chapter 7. Advanced Plotting
Abstract
This chapter significantly extends the discussion of plots in chapter 1, covering the two-dimensional plots described there in more depth. Other plots, including multiple plots, subplots, specialized plots, and three-dimensional plots are described. Symbolic plots in both two- and three-dimensions are also covered.
Lester W. Schmerr, Jr.
Backmatter
Title
MATLAB Essentials: Symbolic and Numeric Problem-Solving in Engineering
Author
Lester W. Schmerr, Jr.
Copyright Year
2025
Electronic ISBN
978-3-031-99308-4
Print ISBN
978-3-031-99307-7
DOI
https://doi.org/10.1007/978-3-031-99308-4

PDF files of this book have been created in accordance with the PDF/UA-1 standard to enhance accessibility, including screen reader support, described non-text content (images, graphs), bookmarks for easy navigation, keyboard-friendly links and forms and searchable, selectable text. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com.

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