In the Calculus Applied course, you will apply tools of single-variable calculus to create and analyze mathematical models used by real practitioners in social, life, and physical sciences.
About this course on ‘Calculus Applied’
In this course, we go beyond the calculus textbook, working with practitioners in social, life, and physical sciences to understand how calculus and mathematical models play a role in their work.
Through a series of case studies in the Calculus Applied course, you’ll learn:
- How standardized test makers use functions to analyze the difficulty of test questions;
- How economists model the interaction of price and demand using rates of change, in a historical case of subway ridership;
- We’ll see how an x-ray is different from a CT-scan, and what this has to do with integrals;
- Know how biologists use differential equation models to predict when populations will experience dramatic changes, such as extinction or outbreaks;
- Learn how the Lotka-Volterra predator-prey model was created to answer a biological puzzle;
- How statisticians use functions to model data, like income distributions, and how integrals measure chance;
- See how Einstein’s Energy Equation, E=mc2 is an approximation to a more complicated equation.
With real practitioners as your guide, you’ll explore these situations in a hands-on way: looking at data and graphs, writing equations, doing calculus computations, and making educated guesses and predictions.
This course provides a unique supplement to a course in single-variable calculus. Key topics include the application of derivatives, integrals and differential equations, mathematical models, and parameters.
This course is for anyone who has completed or is currently taking a single-variable calculus course (differential and integral), at the high school (AP or IB) or college/university level. You will need to be familiar with the basics of derivatives, integrals, and differential equations, as well as functions involving polynomials, exponentials, and logarithms.
Learn applications of calculus to other fields, and NOT a course to learn the basics of calculus. Whether you’re a student who has just finished an introductory Calculus course or a teacher looking for more authentic examples for your classroom, there is something for you to learn here, and we hope you’ll join us!
What you will learn from the ‘Calculus Applied’ Course?
- Authentic examples and case studies of how calculus is applied to problems in other fields
- How to analyze mathematical models, including variables, constants, and parameters
- Appreciation for the assumptions and complications that go into modeling real-world situations with mathematics
Single-variable Calculus (derivatives, integrals, and basics of differential equations); College or AP/IB High School Level
Syllabus for the Course on ‘Calculus Applied’:
- Introduction and Course Orientation
- What Makes a Good Test Question? Mathematical Models to Measure Knowledge and Improve Learning,
- Economic Applications of Calculus: Elasticity and A Tale of Two Cities
- From X-rays to CT scans: Mathematics and Medical Imaging
- What is Middle Income? Thinking about Income Distributions with Statistics and Calculus
- Population Dynamics Part I: the Evolution of Population Models
- Population Dynamics II: A Biological Puzzle OR How Fishing Affects a Predator-Prey System
- Bifurcation Part I: Extinction, Chaos and other Bifurcation Behavior
Optional Sections (CHOOSE 1 of 3)
- Bifurcation Part II: Outbreak! Budworm Populations and Bifurcations (OPTIONAL)
- Bifurcation Part III: Species in Competition: Coexistence or Exclusion (OPTIONAL)
- E = mc²: Taylor Approximation and the Energy Equation (OPTIONAL)
- Final Assessment
Final Assessment Part II
- Option I: Physics: Pondering a Pendulum (CHOOSE ONE)
Final Assessment Part II
- Option II: Climate (CHOOSE ONE)
- Course Wrap Up
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- Harvard University
- Online Course
- 1-3 Months
- Free Course (Affordable Certificate)
- Calculus Maths