MATLAB Essentials: Symbolic and Numeric Problem-Solving in Engineering

Inhaltsverzeichnis

1. Frontmatter

2. Chapter 1. Introduction

   Lester W. Schmerr, Jr.

   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.

3. Chapter 2. Vectors and Vector Operations

   Lester W. Schmerr, Jr.

   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.

4. Chapter 3. Matrices and Matrix Operations

   Lester W. Schmerr, Jr.

   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.

5. Chapter 4. Linear Equations

   Lester W. Schmerr, Jr.

   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.

6. Chapter 5. Ordinary Differential Equations

   Lester W. Schmerr, Jr.

   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.

7. Chapter 6. Nonlinear Problems

   Lester W. Schmerr, Jr.

   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.

8. Chapter 7. Advanced Plotting

   Lester W. Schmerr, Jr.

   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.

9. Backmatter