Calculus: A Comprehensive Course

Calculus is the mathematical exploration of continuous change. It comprises two primary divisions, namely, differential calculus and integral calculus. Differential calculus focuses on studying instantaneous rates of change and the slope of curves. Conversely, integral calculus addresses the accumulation of quantities and areas beneath and between curves. The fundamental theorem of calculus connects these branches, asserting that differentiation and integration are inverse operations. Calculus finds widespread application across fields where mathematical modeling and optimal problem-solving are pertinent. Thus, it is utilized across physical science, actuarial science, computer science, statistics, engineering, and numerous other disciplines. This book provides significant information on mathematics to help develop a good understanding of calculus and related fields. It unfolds the new aspects of this sphere which will be crucial for the holistic understanding of the subject matter. This textbook, with its detailed analyses and examples, will prove immensely beneficial to students involved in this area at various levels.