Course Description

Welcome to "Calculus Applied! Real world applications of calculus across various disciplines" offered by HarvardX. This intermediate-level course is designed to take you beyond the traditional calculus textbook and into the exciting world of practical applications. By collaborating with practitioners from social, life, and physical sciences, you'll gain a deep understanding of how calculus and mathematical models are utilized in real-world scenarios.

What Students Will Learn

• Authentic examples and case studies of calculus applications in various fields
• Analysis of mathematical models, including variables, constants, and parameters
• Appreciation for the complexities and assumptions involved in modeling real-world situations mathematically
• Hands-on experience with data analysis, graph interpretation, equation writing, and calculus computations
• Insight into how professionals use calculus in their respective fields

Pre-requisites

Students should have completed or be currently taking a single-variable calculus course at the high school (AP or IB) or college/university level. Familiarity with the following topics is essential:

• Basics of derivatives and integrals
• Fundamentals of differential equations
• Functions involving polynomials, exponentials, and logarithms

Course Content

• Standardized test question difficulty analysis using functions
• Economic modeling of price and demand interactions using rates of change
• Differences between X-rays and CT scans, and their relation to integrals
• Biological population modeling using differential equations
• The Lotka-Volterra predator-prey model and its origins
• Statistical modeling of data, such as income distributions
• Einstein's Energy Equation and its approximation to more complex equations

Target Audience

• Students who have recently completed an introductory Calculus course
• Teachers seeking authentic examples for their classrooms
• Anyone interested in exploring the practical applications of calculus across various disciplines

Real-World Application of Skills

The skills acquired in this course will enable learners to:

• Apply calculus concepts to solve real-world problems in various fields
• Understand and interpret mathematical models used in different industries
• Develop a more holistic approach to problem-solving by considering multiple variables and parameters
• Enhance critical thinking skills when analyzing complex systems and data
• Bridge the gap between theoretical calculus knowledge and practical applications
• Gain insights into potential career paths that utilize calculus in innovative ways

Course Benefits

This course offers a unique opportunity to expand your calculus knowledge beyond textbook examples and into the realm of real-world applications. By engaging with authentic case studies and working alongside practitioners, you'll develop a deeper appreciation for the power and versatility of calculus across multiple disciplines. Whether you're looking to enhance your academic understanding or explore potential career paths, this course will provide you with valuable insights and practical skills that can be applied in various professional settings.