Applied Calculus with Python from Coursera

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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!

Functions

Functions arise whenever one quantity depends on another. Mathematically speaking, a function is a rule that assigns to each element x in a set D (called the domain) exactly one element, called f(x), in a set called the range. Because we continually make theories about dependencies between quantities in nature and society, functions are important tools in the construction of mathematical models. In this module, we will learn the theory of functions, see many examples and their graphs, as well as apply these functions. We will learn how to implement these functions in Python as well.

Rates of Change and the Derivative

Calculus is the science of measuring change. Early in its history, its tools were developed to solve problems involving the position, velocity, and acceleration of moving objects. Prior to the development of calculus, there was no way to express this change in a variable. In this section, we introduce the notion of limits to develop the derivative of a function. The derivative, commonly denoted as f'(x), will measure the instantaneous rate of change of a function at a certain point x = a. This number f'(a), when defined, will be graphically represented as the slope of the tangent line to a curve. We will see in this module how to find limits and derivatives both analytically and using Python.

Derivative Rules and Applications

The derivative is defined as a limit of the difference quotient. Computing this limit symbolically is very challenging for complicated functions. In this section, we develop rules that find the derivative without having to fall back on the limit definition each time. These rules are purely algebraic in nature and help us gain intuition into the behavior of a derivative function. More importantly, these rules help to demystify the Derivative() function and show the steps to produce the functions output. Understanding the process allows for mastery, adaptation, and more complicated applications of these concepts.

Accumulated Change and Integrals

One major topic in calculus is what is called "integral calculus," which involves finding areas or volumes of regions by adding up small slices. We start to think about areas or volumes as an accumulation of the smaller slices that make them and from that we can apply the theory of integral calculus to measure net change and total accumulations. Then, by the Fundamental Theorem of Calculus, this is then related back to where we started: derivatives. This module introduces some of the most beautiful and useful applications of calculus. Algebraic techniques will be shown alongside of numerical computations using Python.

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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

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

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Reinforce your understanding of calculus fundamentals through a comprehensive textbook.

View Algebra and Trigonometry on Amazon

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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

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Refresh your understanding of limits and continuity to strengthen your foundation for more advanced calculus concepts.

Browse courses on Limits

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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

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Enhance your Python coding skills by creating a program that can calculate the derivative of a function.

Browse courses on Derivatives

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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.

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Explore Tutorials on Integral Calculus Techniques

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Expand your knowledge of integral calculus techniques by exploring online tutorials.

Browse courses on Integral Calculus

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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

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Organize and share a collection of valuable resources for calculus learning.

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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

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Collaborate with peers to reinforce your understanding of calculus concepts.

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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

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Solidify your understanding of calculus concepts through targeted practice.

Browse courses on Calculus

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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

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Apply your calculus knowledge by contributing to an open-source project in the field.

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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

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 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

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

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

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

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

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.

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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

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.

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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

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

Applied Calculus with Python

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