This book continues the journey of discovering mathematics that started with the college-level book Discovering Mathematics with Excel (DME), in which the fundamentals of many areas of mathematics, including geometry, algebra, trigonometry, probability, logic, algorithms, number theory, vectors, calculus, and differential equations were uncovered. In this second book, these topics are explored more deeply, moving from one-dimensional functions to functions of two or more variables. Chapter 1 will review essential topics from Chapter 1 in DME, including finding slopes and areas of functions, the meaning of e, the base of natural logarithms, the fundamental theorem of calculus, and the complex plane. You will learn how to use MATLAB to produce the same results found in Chapter 1 of DME using Excel.
You will go on to use MATLAB to discover the fundamentals of functions of more than one variable. In Chapter 2, you will discover partial derivatives and the meaning of gradient, divergence and curl. While exploring multiple integrals in Chapter 3, you will discover how to use MATLAB to plot functions of more than one variable. In Chapter 4, you will discover many important topics from linear algebra, including matrices, solving linear equations, eigenvalues and eigenvectors, and solving systems of ordinary differential equations. You will explore vector fields in Chapter 5, derive Kepler’s Laws of orbital motion, and learn about electric and magnetic fields, resulting in the discovery of Maxwell’s equations. In Chapter 6, you will discover how to solve partial differential equations using MATLAB. In the final chapter on transforms, you will discover how the Fourier Transform, Fourier Series, the Discrete-Time Fourier Transform, the Discrete Fourier Transform, the Laplace Transform, and the Z-Transform are related.
Once you complete these two Discovering Mathematics books, you will be well on your way to mastering the mathematics you need to be successful in any science or engineering major. Let’s get started!
Richard E. Haskell
Darrin M. Hanna
