Calculus Applied! Course from Harvard

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Product is rated as #2 in category Mathematics
Learning Experience9.4
Content Rating9.2

Calculus applied: Go beyond the calculus textbook, with practitioners to understand how calculus and mathematical models play a role in their work.

Last updated on July 22, 2021 2:26 pm

Introduction

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

Prerequisites

Single-variable Calculus (derivatives, integrals, and basics of differential equations); College or AP/IB High School Level

Syllabus for the Course on ‘Calculus Applied’:

Section 0:

  • Introduction and Course Orientation

Section 1

  • What Makes a Good Test Question? Mathematical Models to Measure Knowledge and Improve Learning,

Section 2

  • Economic Applications of Calculus: Elasticity and A Tale of Two Cities

Section 3

  • From X-rays to CT scans: Mathematics and Medical Imaging

Section 4

  • What is Middle Income? Thinking about Income Distributions with Statistics and Calculus

Section 5

  • Population Dynamics Part I: the Evolution of Population Models

Section 6

  • Population Dynamics II: A Biological Puzzle OR How Fishing Affects a Predator-Prey System

Section 7

  • Bifurcation Part I: Extinction, Chaos and other Bifurcation Behavior

Optional Sections (CHOOSE 1 of 3)

Section 8

  • Bifurcation Part II: Outbreak! Budworm Populations and Bifurcations (OPTIONAL)

Section 9

  • Bifurcation Part III: Species in Competition: Coexistence or Exclusion (OPTIONAL)

Section 10:

  • E = mc²: Taylor Approximation and the Energy Equation (OPTIONAL)

Section 11

  • Final Assessment

Final Assessment Part II

  • Option I: Physics: Pondering a Pendulum (CHOOSE ONE)

Final Assessment Part II

  • Option II: Climate (CHOOSE ONE)

Section 12

  • Course Wrap Up

Note: Your review matters 

If you have already done this course, kindly drop your review in our reviews section. It would help others to get useful information and better insight into the course offered.

FAQ

Free Course
Verified Certificate at

$139.00

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  • EDX
  • Harvard University
  • Online Course
  • Self-paced
  • Intermediate
  • 1-3 Months
  • Free Course (Affordable Certificate)
  • English
  • Calculus Maths
Learning Experience
9.4
Content Rating
9.2
PROS: In-depth, well-structured course content. Step-by-step and very keen explanations by instructors. Quizzes allows us to key in any expressions and even sketch graphs. Authentic examples and case studies.
CONS: One should be familiar with college or AP/IB High School Level mathematics. Need to improve course material bugs.

Description

Introduction

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

Prerequisites

Single-variable Calculus (derivatives, integrals, and basics of differential equations); College or AP/IB High School Level

Syllabus for the Course on ‘Calculus Applied’:

Section 0:

  • Introduction and Course Orientation

Section 1

  • What Makes a Good Test Question? Mathematical Models to Measure Knowledge and Improve Learning,

Section 2

  • Economic Applications of Calculus: Elasticity and A Tale of Two Cities

Section 3

  • From X-rays to CT scans: Mathematics and Medical Imaging

Section 4

  • What is Middle Income? Thinking about Income Distributions with Statistics and Calculus

Section 5

  • Population Dynamics Part I: the Evolution of Population Models

Section 6

  • Population Dynamics II: A Biological Puzzle OR How Fishing Affects a Predator-Prey System

Section 7

  • Bifurcation Part I: Extinction, Chaos and other Bifurcation Behavior

Optional Sections (CHOOSE 1 of 3)

Section 8

  • Bifurcation Part II: Outbreak! Budworm Populations and Bifurcations (OPTIONAL)

Section 9

  • Bifurcation Part III: Species in Competition: Coexistence or Exclusion (OPTIONAL)

Section 10:

  • E = mc²: Taylor Approximation and the Energy Equation (OPTIONAL)

Section 11

  • Final Assessment

Final Assessment Part II

  • Option I: Physics: Pondering a Pendulum (CHOOSE ONE)

Final Assessment Part II

  • Option II: Climate (CHOOSE ONE)

Section 12

  • Course Wrap Up

Note: Your review matters 

If you have already done this course, kindly drop your review in our reviews section. It would help others to get useful information and better insight into the course offered.

FAQ

Specification:

  • EDX
  • Harvard University
  • Online Course
  • Self-paced
  • Intermediate
  • 1-3 Months
  • Free Course (Affordable Certificate)
  • English
  • Calculus Maths

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Calculus Applied! Course from Harvard
Calculus Applied! Course from Harvard

$139.00

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