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Applied Calculus with Python
  • Level Professional
  • Course by Johns Hopkins University
  • Offered by

About

This course is designed for the Python programmer who wants to develop the foundations of Calculus to help solve challenging problems as well as the student of mathematics looking to learn the theory and numerical techniques of applied calculus implemented in Python. By the end of this course, you will have learned how to apply essential calculus concepts to develop robust Python applications that solve a variety of real-world challenges. Video lectures, readings, worked examples, assessments, and Python code are all provided in the course. These are used to illustrate techniques to solve equations, work with functions, and compute and apply derivatives and integrals. If you are interested in starting to develop concepts in fields such as applied math, data science, cybersecurity, or artificial intelligence, or just need a refresher of calculus or coding in Python, then this course is right for you.

Modules

Introduction to Python and SymPy

    • 2 Videos
    • 4 Readings
    • 1 Assignment
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1 Assignment

  • Introduction to Python and SymPy

2 Videos

  • Introduction to Python
  • Working with SymPy

4 Readings

  • Options for Using Python
  • Data Types and Variables in Python
  • Operators and Expressions in Python
  • SymPy Basics

2.1 Introduction to Functions

    • 5 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • Introduction to Functions

5 Videos

  • Theory: Functions
  • Theory: More about Functions
  • Theory: Graphing and Composition
  • Python: Graphing Functions
  • Python: Interactive Quadratic Calculator

3 Readings

  • Functions and Linear Functions
  • Functions in Python
  • Sample Problems - Introduction to Functions

2.2 Exponential and Logarithmic Functions

    • 4 Videos
    • 4 Readings
    • 1 Assignment
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1 Assignment

  • Exponential and Logarithmic Functions

4 Videos

  • Theory: Exponential Functions
  • Theory: Logarithmic Functions
  • Theory: The Natural Logarithm
  • Python: Exponentials and Logarithms

4 Readings

  • Exponential and Logarithmic Functions
  • Exponents and Logarithms in SymPy
  • Solving Equations in SymPy
  • Sample Problems - Exponential and Logarithmic Functions

Module 2 Lab

    • 1 Lab
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1 Labs

  • Finding an Exponential Model

3.1 Limits and Rates of Change

    • 5 Videos
    • 4 Readings
    • 1 Assignment
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1 Assignment

  • Limits and Rates of Change

5 Videos

  • Theory: Introduction to Limits
  • Theory: Limits Involving Infinity
  • Theory: One-Sided Limits
  • Examples to Find Limits
  • Python: Finding Limits

4 Readings

  • Lists and Tuples in Python
  • Limits and Rates of Change
  • Limits and Rates of Change in SymPy
  • Sample Problems - Limits and Rates of Change

3.2 The Derivative

    • 6 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • The Derivative

6 Videos

  • Theory: Derivatives
  • Examples: Finding Derivatives using Limits
  • Theory: Using Limits to Find the Slope of the Tangent Line
  • Theory: Higher Derivatives
  • Theory: The Derivative as a Function
  • Python: Finding Derivatives using Sympy

3 Readings

  • The Derivative
  • Derivatives in SymPy
  • Sample Problems - The Derivative

Module 3 Lab

    • 1 Lab
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1 Labs

  • Graphing Tangent Lines

4.1 Derivative Rules

    • 5 Videos
    • 2 Readings
    • 1 Assignment
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1 Assignment

  • Derivative Rules

5 Videos

  • Theory: Derivatives of Polynomial Functions
  • Theory: Derivatives of Exponentials
  • Theory: The Quotient Rule
  • Theory: The Product Rule
  • Theory: Chain Rule

2 Readings

  • Derivative Rules
  • Sample Problems - Derivative Rules

4.2 Using the Derivative

    • 4 Videos
    • 4 Readings
    • 1 Assignment
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1 Assignment

  • Using the Derivative

4 Videos

  • Theory: Max and Min Values
  • Theory: How Derivatives Affect the Shape of a Graph
  • Python: Local Extrema Calculator
  • Optimization Examples

4 Readings

  • Maxima, Minima, Concavity, and Inflection Points
  • Optimization Word Problems
  • Using the Derivative with SymPy
  • Sample Problems - Using the Derivative

Module 4 Lab

    • 1 Lab
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1 Labs

  • Optimization

5.1 Distance, Accumulated Change, and the Definite Integral

    • 5 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • Distance, Accumulated Change, and the Definite Integral

5 Videos

  • Theory: Area under a Line
  • Theory: Area Under Curves
  • Theory: The Definite Integral
  • Theory: Properties of the Definite Integral
  • Python: Approximate and Exact Integration

3 Readings

  • Distance, Accumulated Change, and the Definite Integral
  • Riemann Sums and Definite Integrals in Python
  • Sample Problems - Distance, Accumulated Change, and the Definite Integral

5.2 The Fundamental Theorem of Calculus

    • 3 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • The Fundamental Theorem of Calculus

3 Videos

  • Theory: Antiderivatives
  • Theory: The Fundamental Theorem of Calc
  • Theory: Worked Examples

3 Readings

  • Antiderivatives and the Fundamental Theorem of Calculus
  • Indefinite Integrals in SymPy
  • Sample Problems - The Fundamental Theorem of Calculus

Module 5 Lab

    • 1 Lab
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1 Labs

  • Area Between Curves

Auto Summary

"Applied Calculus with Python" is an engaging and comprehensive course designed for both Python programmers and mathematics students. This professional-level course focuses on integrating essential calculus concepts with Python programming to solve real-world problems. Learners will explore the theory and numerical techniques of applied calculus, enhancing their ability to tackle challenges in various fields such as applied math, data science, cybersecurity, and artificial intelligence. Guided by video lectures, readings, worked examples, and hands-on Python code, participants will develop skills to solve equations, work with functions, and compute and apply derivatives and integrals effectively. The course is perfect for those seeking to build a foundation in these critical areas or needing a refresher in calculus or Python coding. Offered by Coursera, this course provides flexibility with a subscription option through the Starter plan. Whether you're a professional looking to expand your skill set or a student aiming to deepen your understanding, "Applied Calculus with Python" is an excellent choice to advance your knowledge and practical abilities in big data and analytics.

Joseph W. Cutrone, PhD
Instructor

Joseph W. Cutrone, PhD