Programming Mathematics Using MATLAB

A Practical Bridge Between Mathematics and MATLAB

Programming Mathematics Using MATLAB is a classroom-tested guide for readers who want to use MATLAB as a tool for mathematical exploration, not just as a syntax reference. Lisa A. Oberbroeckling, of the Department of Mathematics and Statistics at Loyola University Maryland, builds the book around a clear progression: first the programming habits and commands that make MATLAB work, then a series of mathematical topics where those skills turn into visual, computational results.

What the Book Covers

Part 1 introduces the MATLAB environment and the core skills needed to write useful scripts. Chapters move through basic mathematics, variables, diaries and script files, vectors and matrices, array addressing, component-wise calculations, random numbers, 2D and 3D plotting, functions, control flow, and miscellaneous commands. Later chapters in this part look at code improvement techniques such as vectorization and preallocation.

• Vectors, matrices, and array addressing
• 2D and 3D plots, surfaces, level curves, and coordinate systems
• Functions, if statements, switch/case, for loops, and while loops
• Formatting output, saving and loading, timing, symbolic commands, and polynomials

Mathematics Through Computation

Part 2 applies MATLAB to mathematical subjects that benefit from experiment and visualization. Readers work with linear and affine transformations, fern fractals, complex numbers, the Chaos Game, line-replacement fractals, geometric series, power series, Taylor polynomials and Taylor series, numerical integration through Riemann sums and Simpson’s rule, and vector spaces leading to orthonormal vectors and the Gram–Schmidt process.

Projects and Appendices

The appendices cover publishing and Live Scripts, including sections, text formatting, HTML links, images, and LaTeX equations. A set of final projects gives readers open-ended problems such as ciphers, the Game of Pig, linearization and Newton’s method, the disk and shell methods, and Powerball data. Linear algebra projects extend the work with matrix calculations, linear systems, the Hill cipher, and least-squares solutions.

Who This Book Is For

Undergraduate students in mathematics, engineering, or data-focused courses will find a structured introduction to computational mathematics. Instructors can use the examples and exercises to support MATLAB-based classes, while independent learners can work through the material at their own pace. The book is not only a MATLAB manual; it shows how programming can make abstract mathematical ideas visible, testable, and easier to explore.

Why It Works

By pairing exercises with visual outputs and mathematical projects, the text encourages experimentation. A matrix operation, a loop, or a plotting command becomes part of solving a larger problem, and readers see how each piece connects. The result is a resource that supports both a first course in computational mathematics and self-directed practice with MATLAB.