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Quick Facts

Medium Of InstructionsMode Of LearningMode Of Delivery
EnglishSelf StudyVideo and Text Based

Course Overview

This certificate course on Calculus Applied!  offered by HarvardX is created to apply the tools in single variable calculus theory for creating and analyzing mathematical models used in real-life sciences as well as physical and social sciences. The course goes beyond the scope of textbook knowledge and calculus where it works with the practitioners in all the required sciences for understanding how mathematical and calculus models work in those areas. The course is instructed by real practitioners who will help the candidate explore the concepts in a very hands-on manner. 

The Calculus Applied certification course acts as a unique addition to the area of calculus training mentoring concepts of integrals, derivatives, differential equations, and mathematical models with their applications and provides inferences. The course requires the candidate to be familiar with calculus concepts and learn about their applications rather than the theory. The Calculus Applied course offered has a three-person faculty preparation for the curriculum. The course in the audit mode is self-paced but only provides a limited period of access whereas the candidates during the verified mode will be able to learn the course in an unlimited time frame.

The Highlights

  • Program is self-paced
  • Certificate of completion granted by edX
  • Audit option for the course
  • English mode of instruction
  • Harvard University faculty course instructors.
  • 10 weeks of course duration
  • 100% e-learning course

Programme Offerings

  • Video transcripts
  • assignments
  • Self-assessment
  • quizzes
  • Final Assessment
  • Case Studies

Courses and Certificate Fees

Certificate AvailabilityCertificate Providing Authority
yesHarvard University, Cambridge

Eligibility Criteria


The candidate needs to have a college degree or a minimum high school degree (AP/IB) with prerequisite coursework on single-variable calculus involving integrals, derivatives and basics of differential equations.

Certification qualifying details

In the verified track program, the candidates who pay the specified program fee and pass the several assignments, assessments, quizzes which carry A grade and successfully pass through the final exam assessment will be given the verified certificate of completion.

What you will learn

Mathematical skill

This course on Calculus Applied! trains the candidates for the following fields:

  • The candidates will learn to apply calculus for problems in other associated fields. 
  • The candidates will learn how to analyze mathematical models including constants, parameters and variables. 
  • The candidates will learn to make proper application assumptions for mathematical modeling of real-world situations. 
  • The candidates will learn how functions help in standardized test difficulties.
  • The candidates will learn how pricing is worked by models in economics.
  • The candidate will learn how integrals are used to differentiate scans.
  • The candidates will learn how biologists predict population changes such as explosion or extinction using differential models.
  • The candidates will learn how to solve biological puzzles using the Lotka-Volterra predator-prey method.
  • The candidates will learn to use statistics for income distribution and statistics associated with middle income. 
  • The candidates will be exposed to the Einstein energy equation as a complicated equation along with Taylor’s approximation.

Who it is for

This coursework on Calculus Applied! will be benefiting the following people: 

  • Science graduates who are interested in learning to apply the concept of Calculus in several science disciplines. 
  • Graduates or students in math who wish to work in the area of calculus.

Admission Details

The step-by-step directions for receiving admission offer into the course are simple to follow and the candidate is expected to follow these steps to become a participant in the Calculus Applied program.

The admission for the Calculus Applied!  course is: 

Step 1: The candidate visits the given link to create an account with all details that are required.

Step 2: Post-registration, the candidates are able to enroll using the "Enroll" option for the desired course. 

Step 3: You must opt for the "Verified" option for the applicant obtaining the credential. 

Step 4: With the declared fee, the candidate will make the payment for the course here with the link 

Step 5: "Place Order" may be selected by the individual and any online method of payment such as Paypal etc. 

The Syllabus

  • What is an x-ray?   
  • Help forum
  • Medical imaging in a real patient's case   
  • Ct scans: what they can reveal in a real patient's case
  • A mathematical model for an x-ray   
  • Quiz part 2   
  • Exploratory quiz   
  • X-rays through a non-uniform material   
  • Finding the attenuation function from many views   
  • Additional resources
  • Summary quiz: from X-rays to CT-scans

  • Price and demand   
  • Elasticity and maximizing revenue   
  • A tale of two cities: public transit fares in new york and Boston   
  • Help forum 
  • Summary quiz - a little more about math and economics from Kiran gajwani 
  • Price elasticity of demand: a calculus viewpoint   
  • Measuring what matters: price elasticity of demand   
  • A tale of two cities revisited
  • Price and demand part 2  

  • Summary quiz: how the parameters of the item response model relate to difficulty, discrimination and guessing
  • What makes a good question? Introduction
  • The item response model and its parameters
  • Modeling a test question 
  • A dynamic model for improving learning in education
  • Creating and using item response curves
  • Help forum
  • Item response curves

  • Welcome to the course
  • Pre-course survey
  • Help forum
  • Exploratory quiz
  • Goals, prerequisites and getting started
  • Course policies
  • Grading, assignments and schedule
  • Course community
  • Introduce yourself!

  • Limits on growth: Verhulst's model   
  • Summary quiz: population models   
  • Introduction to population models   
  • How populations change in a predator-prey system   
  • Help forum
  • Volterra's model in action: marlin and sardines   
  • Species interact: D'ancona puzzle and Volterra's predator-prey model   

  • Modeling fish populations
  • Survival or extinction: the effect of harvesting on fish population   
  • What is a bifurcation? Introduction   
  • Summary quiz: bifurcations and fishing   
  • Help forum
  • Mathematics and biology: a symbiotic relationship

  • From histogram of data to continuous model: probability density functions   
  • What is middle income? Looking at income distributions   
  • Optional video: a little more from Nina about statistics in her work
  • Summary quiz
  • What is middle income? Mean and median for the continuous model
  • Help forum
  • Looking at income distributions: frequency and relative frequency histograms   
  • What is middle income? Mean, median and beyond   
  • Using integration to estimate households in the middle income range

  • The average value of populations in a predator-prey system   
  • Introduction to the biological puzzle
  • Help forum 
  • D'Ancona puzzle again and implications for fishing regulations
  • The effect of fishing on the predator-prey system   
  • Summary quiz 
  • Making a good model: issues and limitations (optional)

E = mc²: taylor approximation and the energy equation (optional)
  • Taylor approximation for the energy-mass equation   
  • Making sense of the first few terms of the approximation   
  • Help forum 
  • Higher terms and faster speeds 
  • String theory, the energy equation and a physicist's dream
  • Summary quiz: e = mc²: Taylor approximation and the energy equation   
  • Introducing the energy-mass equation 
  • Additional resources
  • Acknowledgments and special thanks
Bifurcation part II: outbreak! budworm populations and bifurcations (optional)
  • Modifying the budworm model to include predation   
  • Help forum
  • Introduction to the budworm model   
  • Summary
  • Increasing the carrying capacity further   
  • Equilibrium points and carrying capacity   
  • Summary quiz: budworm population outbreaks  
Final assessment
  • Help forum for final assessments
  • Final assessment instructions and part i
  • Video: in closing... And final assessment
  • Final assessment part II: self-review practice and instructions
Bifurcation part III: species In competition: coexistence or exclusion (optional)
  • How weak competition affects the system   
  • Help forum
  • A model of species in competition   
  • Summary quiz: species in competition and bifurcation values
  • The bifurcation value and competition in economic systems
  • How strong competition affects the system  
Final assessment part II; option I: physics: pondering a pendulum
  • Model of pendulum motion   
  • Introduction and intuition
  • A first approach: solving a simplified pendulum model   
  • Summary quiz   
  • How does gravity or pendulum weight and length affect the period?   
  • Another approach: a qualitative analysis of the original model  
Course wrap up
  • End of course survey and feedback forum
Final assessment part II; option II: climate (choose one)
  • Modeling temperature change
  • What is the effect of albedo on the temperature in the long run? - 5.0 making a more realistic model: the temperature-albedo interaction   
  • Introduction and intuition
  • Quiz: making sense of the model   
  • Exploratory quiz   
  • Making a more realistic model: the temperature-albedo interaction
  • Summary quiz: part II self-assessment
  • Summary quiz: part I  


Harvard University, Cambridge Frequently Asked Questions (FAQ's)

1: Is this a course for beginners in calculus?

No, this Calculus Applied course is not introductory by nature and does require certain eligibility for the student to pursue.

2: What are the different areas covered in this program?

This Calculus Applied program covers applications of Calculus in subjects such as Physics, Biology, Economics and Statistics, etc.

3: Will it be possible for the applicant to audit this program?

Yeah, the participants can use the audit option provided they do not seek any certificates or assessments.

4: Is there any information about the faculty instructor associated with this course?

John Wesley Cain, Juliana Belding and Peter M. Garfield are the three instructors who have designed the curriculum and planned instruction of coursework for the candidates. 

5: What are some important program offerings made available for students?

This program offers some important requirements for learning such as

  • Self-assessment
  • Case studies
  • Quizzes
  • Final assessment
6: How much time will the student give towards completing this certificate?

Candidates need to spend around 3 to 6 hours a week for finishing this coursework. 

7: How is the student graded for all activities provided in this course?

By requirements of this program, the candidate needs to attend several requirements such as assessments, quizzes, and case studies to receive a certificate of completion.

8: How can the student plan to study this course?

The student can enroll in this Calculus Applied course and have a self-paced mode of study without being instructor-led at all times. 


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