1. A Review of Limits, Derivatives, and Integrals

This chapter delves into the core concepts of calculus, focusing on limits, derivatives, and integrals, and demonstrates how MATLAB can be utilized to solve these problems effectively. It begins with a concise review of limits, explaining their significance and providing practical examples. The text then explores L’Hopital’s Rule for evaluating indeterminate forms, followed by a thorough examination of derivatives, including key differentiation rules and their applications. Partial derivatives are also discussed, highlighting their role in multivariable functions. The chapter further covers integrals, both definite and indefinite, and introduces tabular integration for complex integrals. Fractional integrals and polynomial division are also addressed. The practical application of these concepts is illustrated through various MATLAB examples, showcasing how to calculate limits, derivatives, and integrals using symbolic computation. The chapter concludes with exercises and examples that verify and reinforce the theoretical concepts, making it a comprehensive guide for professionals looking to enhance their calculus skills and apply them using MATLAB.