MUHAMMAD S AKHTAR, , El Paso Community College

Teaching Calculus with MATLAB

Introduction

Many engineering students start their education at a community college and then transfer to a four-year institution to complete their degree. During their time at community college, they take courses such as numerical analysis, image processing, and digital signal processing. In addition, many of their engineering professors assign projects that require a good knowledge of a high-level programming language.

Learning any programming language takes time and effort, and not every student has the knack for it. For this reason, most four-year colleges and universities allow students to use any programming language they know to complete their projects and assignments. However, they prefer that students have a good working knowledge of MATLAB because it offers many advantages for engineering students, including:

- Built-in mathematical functions and tools for solving linear and non-linear equations, numerical integration, optimization, and differential equations.

- Easy data import, manipulation, and analysis capabilities.

- Powerful plotting and graphing capabilities for creating 2D and 3D plots, charts, and graphs.

- Tools and libraries for deep learning and machine learning.

- Support for parallel computing.

- A comprehensive set of functions for signal processing applications and computer vision tasks.

- Widespread use in industry and research.

Teaching MATLAB in a Calculus Course

I teach college-level calculus and algebra courses, and my courses do not require knowledge of MATLAB. However, most of my students transfer to engineering programs in four-year colleges and universities where they are expected to have a working knowledge of MATLAB. With this in mind, I introduce MATLAB with examples in my calculus course using the following steps:

1. I explain to students how MATLAB can help them to visualize and solve complex mathematical problems to enhance their understanding of calculus concepts.

2. I introduce the MATLAB environment, command window, variables, and basic arithmetic operations.

3. I explain how MATLAB's symbolic math toolbox can be used to find derivatives, integrals, and solve equations.

4. I show students how they can use MATLAB to graph functions, find tangent lines, and find the area under curves.

5. I show students how to set up equations and use MATLAB to solve functions.

6. I provide practice problems that require students to apply MATLAB to solve calculus problems individually and in groups.

Summary

MATLAB is a powerful programming language that is widely used in engineering and research. It has many features that make it well-suited for solving calculus problems, such as built-in mathematical functions, tools for data analysis and visualization, and support for parallel computing.

I introduce MATLAB to my calculus students with the goal of preparing them for their future engineering studies. I focus on teaching them how to use MATLAB to solve calculus problems and visualize mathematical concepts.

Additional Thoughts

In addition to the steps outlined above, I also encourage my calculus students to use MATLAB to explore mathematical concepts on their own. For example, I might ask them to use MATLAB to graph a function and then use the graph to answer questions about the function's behavior, such as its extrema and intervals of increase/decrease. I might also ask them to use MATLAB to solve differential equations or to perform numerical integration.

I believe that using MATLAB in my calculus course helps my students to develop a deeper understanding of the material and to prepare them for the challenges they will face in their future engineering studies.

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