Towards improving the integration of undergraduate biology and mathematics education

Christopher Bergevin1

  • 1Department of Mathematics, University of Arizona, Tucson, AZ 85705.

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Fundamental Theorem of Calculus I01:23

Fundamental Theorem of Calculus I

Solving problems involving definite integrals requires a systematic approach that ensures clarity and efficiency. The first step is understanding the problem by identifying the calculated quantity, whether it involves accumulation, area, or a physical concept like force or probability. It is essential to recognize given conditions, such as the range of integration and any constraints that may affect the solution. Before computing, key properties of definite integrals should be analyzed to...
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
Applications of Molecular Taxonomy01:20

Applications of Molecular Taxonomy

Molecular taxonomy has revolutionized the understanding and classification of bacteria, providing precise insights into their diversity, evolutionary relationships, and ecological roles. By utilizing molecular techniques such as DNA sequencing and fingerprinting, researchers have made significant strides in various fields related to bacterial studies.Resolving Taxonomic AmbiguitiesMolecular taxonomy has been instrumental in distinguishing closely related bacterial species initially thought to...
Introduction to MATLAB01:24

Introduction to MATLAB

MATLAB stands for Matrix Laboratory. MathWorks developed MATLAB as a multi-paradigm numerical computing environment and proprietary programming language. It has evolved significantly over the years to become a tool utilized by engineers, scientists, and mathematicians for various tasks, including matrix calculations, developing algorithms, data analysis, and visualization. MATLAB's applications span various industries and disciplines. It's used in image and signal processing, communications,...
Fundamental Theorem of Calculus I: Problem Solving01:22

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In many engineering and environmental applications, accumulated quantities are determined from rates that vary over time. A common example arises in water management, where a supply system pumps water into a storage tank at a rate that changes with time. Accurately determining how much water has entered the tank over a given period is essential for maintaining proper pressure, scheduling operations, and ensuring system safety.The flow rate of water into the tank is described by a time-dependent...
Mathematical Induction01:29

Mathematical Induction

Mathematical induction is a structured method of proof used to confirm the truth of statements involving natural numbers. Consider the sum of the first n natural numbers:This formula describes a pattern that appears to hold true as more terms are added. To verify that it is valid for all natural numbers, mathematical induction proceeds in two essential steps. The first is the base case, where the formula is tested for the initial value, typically n = 1. Substituting into both sides confirms the...