MATH 007A: Calculus for Life Sciences
Fall 2025

Instructor: Boris Tsvelikhovskiy    borist AT ucr.edu

Overview

This course provides a foundational understanding of calculus, with a focus on applications in life sciences. We begin by exploring the concepts of limits and continuity, followed by the behavior of functions at infinity. The formal definition of the derivative is introduced, along with its properties and basic rules of differentiation, such as the power rule and chain rule. We will also cover implicit differentiation, related rates, and higher derivatives, emphasizing their relevance in real-world biological scenarios. Key topics include monotonicity, concavity, extrema, and the Mean Value Theorem. Additionally, we will study the differentiation of trigonometric, exponential, logarithmic, and inverse functions. The course also includes L'Hopital's Rule and techniques for graphing functions and analyzing asymptotes, providing students with the tools necessary to apply calculus concepts effectively in the life sciences.

Texts

  • Calculus for Biology and Medicine (4th Edition) by C. Neuhauser and M. Roper (sections 3.1 through 5.6)

    • Lecture slides

    Bonus problems

    Exams