From Theory to Practice
Explore a curated collection of project-based learning assignments for Applied Calculus. This interactive resource bridges the gap between abstract concepts and real-world applications in business, engineering, and science. Click on any project to discover its objectives, tasks, and underlying principles.
Derivatives & Optimization
This section focuses on the cornerstone of applied calculus: understanding rates of change and finding optimal solutions. These projects use derivatives to model physical phenomena, make business decisions, and solve complex engineering challenges.
Rate of Change Labs
Investigate rates of change with physical intuition, focusing on concavity and graphical analysis.
Chapters 1 & 2 • Physics/GeneralThe Zipline Challenge
An engineering-themed project on optimization and linear approximation.
Chapters 1 & 2 • EngineeringProfit Maximization
A business case study using marginal analysis to find maximum profit.
Chapter 2 • Business/EconomicsRelated Rates Scenarios
Use implicit differentiation to solve dynamic problems like the classic lighthouse or conical tank scenarios.
Chapter 3 • Physics/GeometryGrowth, Decay & Finance
Explore the power of exponential and logarithmic functions. These projects cover fundamental models for phenomena across science and finance, from disease modeling and radioactive decay to the principles of compound interest.
Epidemiology: The S-I-R Model
Analyze the spread of a disease using a system of rate equations without needing to solve them.
Chapters 4 & 5 • BiologyPharmacokinetics & Decay
Model radioactive decay and drug concentration in the bloodstream using half-life.
Chapters 4 & 5 • PharmacologyThe Power of Compound Interest
Explore the transition from discrete to continuous compounding in finance.
Chapters 4 & 5 • FinanceAdvanced Applications
This final section presents capstone-style projects that utilize integral calculus and multivariable functions. These assignments demonstrate the power of calculus to solve sophisticated problems in economics and resource management.
Economic Welfare Analysis
Use definite integrals to calculate consumer and producer surplus in a market.
Chapter 6 • EconomicsResource Consumption Models
Frame the definite integral as the total accumulation of a quantity when its rate of change is known.
Chapter 6 • Environmental ScienceConstrained Optimization
A capstone project using Lagrange multipliers to maximize consumer utility subject to a budget.
Chapter 7 • Economics