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Applied Calculus with Python

Joseph W. Cutrone, PhD

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.

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What's inside

Syllabus

Introduction to Python
Programming now has relevance well beyond just Computer Science. In this module and throughout this course, you will learn not only about programming using Python, but also how to use those skills to solve real, complex problems in future classes, at work, or elsewhere. To ensure this, copious amounts of examples are included, with explanations, throughout the course. You are strongly encouraged not only trace through them, but also experiment with (run, alter, break) them on your own. The assignments are linked to the respective module. Putting time in here will give you the opportunity to solve actual scientific problems and challenge you in a way that that’ll not only help you make use of the skills we’ll discuss in lecture, but also to leave you with that oh-so-satisfying feeling of having conquered the challenge when you’re done!
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Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Well-suited for Python programmers looking to develop Calculus foundations to solve challenging problems.
Also appropriate for mathematics students seeking to learn Calculus theory and numerical techniques with Python implementation
Provides a comprehensive study of essential Calculus concepts, including limits, derivatives, and integrals
Emphasizes the practical applications of Calculus to real-world challenges
Utilizes a blended learning approach with video lectures, readings, worked examples, and interactive materials for effective knowledge transfer

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Reviews summary

Applied calculus: python for real-world problems

According to learners, "Applied Calculus with Python" is a largely positive course that effectively integrates core calculus concepts with practical Python programming. Students particularly praise its real-world applications, especially for fields like data science and AI, and find the lectures clear and hands-on coding exercises invaluable for solidifying understanding. While the course provides a strong foundation, some learners suggest the pace can be fast or that prior Python knowledge is beneficial, potentially presenting a steep learning curve for absolute beginners. Its applied focus means less emphasis on theoretical proofs, appealing more to those seeking practical implementation.
Emphasizes practical application over deep theoretical proofs.
"It's definitely an applied course, so don't expect a deep dive into proofs."
"The mathematical rigor felt a bit light for someone wanting a pure calculus course."
"I felt some explanations were a bit too quick. Good for an introduction, but not comprehensive."
"For an 'applied' course, it met expectations; I wish there were more advanced topics."
Provides clear lectures and effective hands-on coding exercises.
"The lectures are clear, and the coding exercises truly solidify understanding."
"The instructor did a fantastic job breaking down complex topics."
"The hands-on approach is fantastic. Really enjoyed the derivative applications."
"The code examples were runnable and easy to follow, making learning effective."
Focuses on solving real-world challenges, especially in data science.
"I appreciated the real-world examples, especially for data science."
"Excellent course for data scientists! The practical applications of calculus using Python were exactly what I needed."
"Absolutely invaluable for anyone in data science or AI."
"Great for understanding how to use these concepts in ML or data science."
Seamlessly integrates calculus with practical Python coding.
"This course brilliantly bridges the gap between theoretical calculus and practical Python applications."
"The practical applications of calculus using Python were exactly what I needed."
"As a programmer, this course made calculus accessible and relevant by immediately showing how to implement concepts in Python."
"I learned a lot about applying calculus concepts numerically."
Pacing can be fast, potentially requiring prior Python or math background.
"The content is good, but the pace can be quite fast at times, especially in the later modules on integrals."
"Some parts assume a slightly stronger Python background than advertised, but overall, it's very beneficial."
"If you're a complete beginner to either calculus or Python, prepare for a steep learning curve."
"As someone with limited calculus background, I found it hard to keep up. More foundational math refreshers would have been helpful."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Applied Calculus with Python with these activities:
Read 'Calculus: Early Transcendentals' by James Stewart
Reinforce your understanding of calculus fundamentals through a comprehensive textbook.
View Algebra and Trigonometry on Amazon
Show steps
  • Read the assigned chapters and take notes on key concepts.
  • Work through the practice problems at the end of each chapter.
  • Review the chapter summaries and key takeaways.
Review Limits and Continuity
Refresh your understanding of limits and continuity to strengthen your foundation for more advanced calculus concepts.
Browse courses on Limits
Show steps
  • Review the definition of a limit.
  • Practice finding limits using algebraic techniques and graphical representations.
  • Understand the concept of continuity and apply it to functions.
Write a Python Program to Find the Derivative of a Function
Enhance your Python coding skills by creating a program that can calculate the derivative of a function.
Browse courses on Derivatives
Show steps
  • Choose a function to find the derivative for.
  • Implement the derivative formula using Python code.
  • Test your program with different functions and verify the results.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Explore Tutorials on Integral Calculus Techniques
Expand your knowledge of integral calculus techniques by exploring online tutorials.
Browse courses on Integral Calculus
Show steps
  • Identify specific integration techniques you need to strengthen.
  • Search for reputable online tutorials covering those techniques.
  • Follow the tutorials and practice the techniques provided.
Compile a Resource Guide for Calculus
Organize and share a collection of valuable resources for calculus learning.
Browse courses on Calculus
Show steps
  • Gather a list of relevant resources, including websites, tutorials, books, and videos.
  • Categorize the resources based on topic or purpose.
  • Create an online document or website to share the compiled resource guide with others.
Participate in a Study Group for Calculus
Collaborate with peers to reinforce your understanding of calculus concepts.
Show steps
  • Join or create a study group with other students taking the course.
  • Meet regularly to discuss course material, solve problems, and quiz each other.
Solve Calculus Practice Problems
Solidify your understanding of calculus concepts through targeted practice.
Browse courses on Calculus
Show steps
  • Find a collection of calculus practice problems.
  • Work through the problems, attempting to solve them without assistance.
  • Check your solutions against provided answer keys or online resources.
Contribute to an Open-Source Calculus Project
Apply your calculus knowledge by contributing to an open-source project in the field.
Show steps
  • Identify an open-source project related to calculus that aligns with your interests.
  • Review the project's documentation and codebase.
  • Propose and develop a contribution that adds value to the project.

Career center

Learners who complete Applied Calculus with Python will develop knowledge and skills that may be useful to these careers:
Applied Mathematician
Applied mathematicians use mathematical and statistical techniques to solve problems in various fields, such as engineering, finance, and biology. This course will help you develop the skills you need to analyze data, build models, and make recommendations that can solve complex problems in a variety of fields.
See salaries and explore the career path for Applied Mathematician
Data Analyst
Data analysts use their knowledge of mathematics and statistics to analyze data and extract meaningful insights. This course will help you develop the skills you need to clean, analyze, and interpret data, which are essential for success in data analysis.
See salaries and explore the career path for Data Analyst
Statistician
Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. With a strong foundation in calculus, you will be able to understand and analyze data, build statistical models, and make informed decisions. This course will help you build a strong foundation in calculus, which is essential for success in statistics.
See salaries and explore the career path for Statistician
Data Scientist
Data scientists use mathematical and statistical techniques to analyze data and extract meaningful insights. This course will help you develop the skills you need to clean, analyze, and interpret data, which are essential for success in data science.
See salaries and explore the career path for Data Scientist
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty. With a strong foundation in calculus, you will be able to understand and analyze actuarial data, build actuarial models, and make informed decisions about risk. This course will help you build a strong foundation in calculus, which is essential for success in actuarial science.
See salaries and explore the career path for Actuary
Quantitative Analyst
Quantitative analysts use mathematical and statistical techniques to analyze financial data and make investment decisions. With a strong foundation in calculus, you will be able to understand and analyze complex financial data, build quantitative models, and make informed investment decisions. This course will help you build a strong foundation in calculus, which is essential for success in quantitative analysis.
See salaries and explore the career path for Quantitative Analyst
Astronomer
Astronomers use mathematical and statistical techniques to understand the universe. With a strong foundation in calculus, you will be able to understand and analyze astronomical data, build astronomical models, and make informed predictions about the behavior of the universe. This course will help you build a strong foundation in calculus, which is essential for success in astronomy.
See salaries and explore the career path for Astronomer
Operations Research Analyst
Operations research analysts use mathematical and statistical techniques to solve complex problems in business and industry. This course will help you develop the skills you need to analyze data, build models, and make recommendations that can improve the efficiency and effectiveness of organizations.
See salaries and explore the career path for Operations Research Analyst
Biostatistician
Biostatisticians use mathematical and statistical techniques to analyze data in the field of medicine and public health. With a strong foundation in calculus, you will be able to understand and analyze medical data, build statistical models, and make informed decisions about public health policy. This course will help you build a strong foundation in calculus, which is essential for success in biostatistics.
See salaries and explore the career path for Biostatistician
Economist
Economists use mathematical and statistical techniques to analyze economic data and make policy recommendations. With a strong foundation in calculus, you will be able to understand and analyze economic data, build economic models, and make informed policy decisions. This course will help you build a strong foundation in calculus, which is essential for success in economics.
See salaries and explore the career path for Economist
Machine Learning Engineer
Machine learning engineers design and develop machine learning models. With a strong foundation in calculus, you will be able to understand the mathematical concepts underlying machine learning algorithms and data structures. This course will help you develop the skills you need to design and implement efficient machine learning models.
See salaries and explore the career path for Machine Learning Engineer
Financial Analyst
Financial analysts apply mathematical and statistical techniques to assess the performance of companies and make investment recommendations. With a strong foundation in calculus, you will be able to understand and analyze financial data, build financial models, and make informed investment decisions. This course will help you build a strong foundation in calculus, which is essential for success in financial analysis.
See salaries and explore the career path for Financial Analyst
Physicist
Physicists use mathematical and statistical techniques to understand the laws of nature. With a strong foundation in calculus, you will be able to understand and analyze physical data, build physical models, and make informed predictions about the behavior of the universe. This course will help you build a strong foundation in calculus, which is essential for success in physics.
See salaries and explore the career path for Physicist
Geoscientist
Geoscientists use mathematical and statistical techniques to understand the Earth's systems. With a strong foundation in calculus, you will be able to understand and analyze geological data, build geological models, and make informed predictions about the behavior of the Earth's systems. This course will help you build a strong foundation in calculus, which is essential for success in geoscience.
See salaries and explore the career path for Geoscientist
Software Engineer
Software engineers design, develop, and maintain software applications. With a strong foundation in calculus, you will be able to understand the mathematical concepts underlying software algorithms and data structures. This course will help you develop the skills you need to design and implement efficient software applications.
See salaries and explore the career path for Software Engineer

Reading list

We've selected 13 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Applied Calculus with Python.
Cover image
Mathematical Methods for Physics and Engineering
Save
Provides a solid foundation in mathematical methods commonly used in science, particularly in physics and engineering.
Mathematical Methods for Physics and Engineering: A...
Paperback
$$$
Mathematical Methods for Physics and Engineering: A...
Kindle Edition
$$$
Cover image
Python Programming and Numerical Methods
Save
Combines Python programming with numerical methods, providing practical examples of how to use Python to solve scientific and engineering problems.
Python Programming and Numerical Methods: A Guide...
Paperback
$$$
Python Programming and Numerical Methods: A Guide...
Kindle Edition
$$$
Cover image
Spreadsheet Problem Solving and Programming for...
Save
Covers various numerical methods with a focus on engineering and scientific applications. It provides clear explanations and practical examples using Python.
Spreadsheet Problem Solving and Programming for...
Paperback
Check
Spreadsheet Problem Solving and Programming for...
Kindle Edition
Check
Cover image
Introduction to Applied Linear Algebra
Save
Introduces linear algebra from an applied perspective, emphasizing its use in solving real-world problems. It includes extensive examples and exercises in Python.
Introduction to Applied Linear Algebra: Vectors,...
Hardcover
$$
Introduction to Applied Linear Algebra: Vectors,...
Kindle Edition
$$
Cover image
Numerical Python
Save
Practical guide to using NumPy, a Python library for scientific computing. It provides hands-on examples and covers various numerical methods.
Numerical Python
Paperback
Check
Numerical Python
Kindle Edition
Check
Cover image
Python for Data Analysis
Save
Comprehensive guide to data analysis with Python. It covers data manipulation, data visualization, and statistical modeling, providing a strong foundation for data analysis in Python.
Python for Data Analysis
Paperback
Check
Python for Data Analysis
Kindle Edition
Check
Cover image
Data Structures and Algorithms in Java, 6th Edition
Save
Provides a comprehensive introduction to data structures and algorithms in Python. It covers the fundamental concepts and techniques used in computer science and software development.
Data Structures and Algorithms in Java 6th Edition...
Paperback
$$$
Data Structures and Algorithms in Java, 6th Edition
Kindle Edition
$$$
Discrete Mathematics and Its Applications (Eighth...
Save
Comprehensive introduction to discrete mathematics, covering topics such as set theory, logic, counting, graph theory, and algorithms. It provides a solid foundation for computer science and mathematics.
(中文) Discrete Mathematics and Its Applications (in...
Paperback
$$
Machine Learning with Python for Everyone
Save
Gentle introduction to machine learning with Python. It covers the fundamental concepts and techniques without requiring prior knowledge in machine learning or artificial intelligence.
Machine Learning with Python for Everyone
Paperback
Check
Machine Learning with Python for Everyone
Kindle Edition
Check
Cover image
Deep Learning with Python, Second Edition
Save
Practical introduction to deep learning with Python. It covers the fundamental concepts and techniques used in deep learning, including neural networks, convolutional neural networks, and recurrent neural networks.
Deep Learning with Python, Second Edition
Paperback
$$
Deep Learning with Python, Second Edition
Kindle Edition
$$
Cover image
Artificial Intelligence with Python
Save
Comprehensive introduction to artificial intelligence with Python. It covers the fundamental concepts and techniques used in artificial intelligence, including machine learning, natural language processing, and computer vision.
Artificial Intelligence with Python
Paperback
Check
Artificial Intelligence with Python
Kindle Edition
Check
Cover image
Python Data Science Handbook
Save
Comprehensive guide to using Python for data science. It covers data manipulation, data analysis, machine learning, and deep learning, providing a solid foundation for data science in Python.
Python Data Science Handbook: Essential Tools for...
Paperback
$$$
Cover image
The Elements of Statistical Learning
Save
Classic reference for statistical learning and data mining. It covers a wide range of topics, including linear regression, logistic regression, decision trees, and support vector machines, providing a comprehensive overview of statistical learning techniques.
The Elements of Statistical Learning: Data Mining,...
Hardcover
$$$
The Elements of Statistical Learning: Data Mining,...
Hardcover
$$$
The Elements of Statistical Learning: Data Mining,...
Kindle Edition
$$$

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Intermediate
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Institution
Johns Hopkins University
Instructor
Joseph W. Cutrone, PhD
Language
English
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Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Well-suited for Python programmers looking to develop Calculus foundations to solve challenging problems.
Also appropriate for mathematics students seeking to learn Calculus theory and numerical techniques with Python implementation
Provides a comprehensive study of essential Calculus concepts, including limits, derivatives, and integrals
Emphasizes the practical applications of Calculus to real-world challenges
Utilizes a blended learning approach with video lectures, readings, worked examples, and interactive materials for effective knowledge transfer
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