HarvardX: Calculus Applied! course Syllabus

Overview: This course provides a rigorous introduction to applied calculus, emphasizing real-world problem solving in STEM, economics, and engineering. Over approximately 12–16 weeks, learners engage with core concepts through modeling, graphical analysis, and analytical reasoning. Each module combines theory with practical applications, requiring 6–8 hours per week. The course concludes with a final project integrating key skills in quantitative modeling.

Module 1: Derivatives and Real-World Rates of Change

Estimated time: 24 hours

• Understand limits and foundational concepts
• Apply derivative rules to motion problems
• Solve optimization and maximum/minimum scenarios
• Interpret slope and tangent lines graphically

Module 2: Modeling Growth and Decay

Estimated time: 24 hours

• Explore exponential and logarithmic functions
• Model population growth and radioactive decay
• Apply calculus to economic and financial systems
• Analyze real-life predictive scenarios

Module 3: Integrals and Accumulation

Estimated time: 24 hours

• Understand definite and indefinite integrals
• Calculate area under curves
• Apply accumulation functions to physical systems
• Model change over time

Module 4: Applied Problem Solving and Analysis

Estimated time: 24 hours

• Develop mathematical models from practical situations
• Interpret graphical and numerical outputs
• Solve multi-step applied calculus problems
• Strengthen analytical and quantitative reasoning

Module 5: Graphical Interpretation and Analytical Reasoning

Estimated time: 12 hours

• Connect derivatives to real-world rates of change
• Analyze functions using graphical methods
• Integrate analytical reasoning with visual models
• Strengthen conceptual understanding of calculus behavior

Module 6: Final Project

Estimated time: 20 hours

• Design a quantitative model using derivatives and integrals
• Analyze a real-world system involving growth, decay, or motion
• Present findings with graphical and analytical support

Prerequisites

• Strong foundation in algebra
• Proficiency in pre-calculus topics
• Familiarity with basic mathematical functions and graphing

What You'll Be Able to Do After

• Apply derivatives to model motion, growth, and optimization
• Use integrals to calculate accumulation and area in real contexts
• Model exponential and logarithmic systems in science and economics
• Interpret and solve complex problems using graphical and analytical tools
• Build a foundation for advanced STEM and quantitative coursework