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Integral Calculus and Numerical Analysis for Data Science
James Bird
and
Jane Wall
James Bird
and
Jane Wall
Are you interested in Data Science but lack the math background for it? Has math always been a tough subject that you tend to avoid? This course will provide an intuitive understanding of foundational integral calculus, including integration by parts, area under a curve, and integral computation. It will also cover root-finding methods, matrix decomposition, and partial derivatives.
Read more
Are you interested in Data Science but lack the math background for it? Has math always been a tough subject that you tend to avoid? This course will provide an intuitive understanding of foundational integral calculus, including integration by parts, area under a curve, and integral computation. It will also cover root-finding methods, matrix decomposition, and partial derivatives.
Read more
Are you interested in Data Science but lack the math background for it? Has math always been a tough subject that you tend to avoid? This course will provide an intuitive understanding of foundational integral calculus, including integration by parts, area under a curve, and integral computation. It will also cover root-finding methods, matrix decomposition, and partial derivatives.
This course is designed to prepare learners to successfully complete Statistical Modeling for Data Science Application, which is part of CU Boulder's Master of Science in Data Science (MS-DS) program.
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Register for this course and see more details by visiting:
OpenCourser.com/course/ox4by2/integral
What's inside
Syllabus
Area Under The Curve
Explore the notion of area under a curve, how that relates to the integral and compute basic integrals.
Numerical Analysis Intro
Read more
Syllabus
Area Under The Curve
Explore the notion of area under a curve, how that relates to the integral and compute basic integrals.
Numerical Analysis Intro
Read more
Introduction to Numerical Analysis using 2 root-finding methods.
Diagonalization & SVD
Explore general matrix decomposition, as well as a specialized and useful version called Singular Value Decomposition.
Partial Derivatives & Steepest Descent
We will learn a core calculus concept called partial derivatives, as well as delving into directional derivatives and their usefulness in higher level statistics.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Teaches integral calculus concepts that are fundamental for data science, including integration by parts, area under a curve, and integral computation
Provides a solid foundation for the Statistical Modeling for Data Science Application course of CU Boulder's Master of Science in Data Science program
Covers essential math concepts like root-finding methods, matrix decomposition, and partial derivatives, which are crucial for data science
Assumes no prior math background, making it accessible to learners with diverse backgrounds
Course instructors, Jane Wall and James Bird, are experienced professionals in data science
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Save Integral Calculus and Numerical Analysis for Data Science to your list so you can find it easily later:
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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 Integral Calculus and Numerical Analysis for Data Science with these
activities:
Organize your notes, assignments, quizzes, and exams
Show steps
Organizing your materials will help you prepare for the final exam review.
Show steps
-
Gather all of your notes, assignments, quizzes, and exams.
-
Organize your materials by topic.
-
Create a study schedule.
-
Review your materials regularly.
Revisit the concept of area under a curve
Show steps
Practice the concept of area to better follow along with the concept of integration which heavily builds upon the idea of area.
Show steps
-
Find 2 or 3 online videos on finding area under a curve and watch them.
-
Try a few example problems without the aid of a calculator and check your work.
Practice root finding by hand
Show steps
Building intuition for finding the roots of polynomials by hand can be a helpful way to understand the ideas of using computational methods like Newton's method.
Show steps
-
Find examples of a few cubic polynomials with real solutions and try to find their roots by hand.
-
Continue with a few quartic polynomials, and optionally go on to a quintic polynomial.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Watch video on diagonalization and SVD
Show steps
Diagonalization and SVD are very powerful linear transformations. Watching a video on these concepts can be very insightful.
Show steps
-
Find a 3Blue1Brown video on diagonalization or SVD and watch it.
-
Optionally, find videos from other sources on these topics.
Write an intuitive explanation of partial derivatives
Show steps
Writing an explanation of partial derivatives in your own words can help you to more deeply understand the concept.
Show steps
-
Write out the definition of partial derivatives.
-
Explain how partial derivatives are used to find the slope of a surface.
-
Give an example of how partial derivatives are used in a real-world application.
Practice solving partial differential equations
Show steps
Solving partial differential equations is a key skill in data science. This activity will give you practice with this important technique.
Show steps
-
Find a set of practice problems on partial differential equations.
-
Solve the problems using the method of separation of variables.
-
Check your answers using a computer algebra system.
Contribute to a data science open source library
Show steps
Contribute to help advance the field of knowledge with a concrete deliverable.
Show steps
-
Find an open-source data science library that you are interested in contributing to.
-
Read the library's documentation and familiarize yourself with the codebase.
-
Identify a bug or feature that you would like to fix or implement.
-
Submit a pull request with your changes.
-
Respond to feedback from the library's maintainers and make changes as necessary.
Organize your notes, assignments, quizzes, and exams
Show steps
Organizing your materials will help you prepare for the final exam review.
Show steps
Show steps
Show steps
- Gather all of your notes, assignments, quizzes, and exams.
- Organize your materials by topic.
- Create a study schedule.
- Review your materials regularly.
Revisit the concept of area under a curve
Show steps
Practice the concept of area to better follow along with the concept of integration which heavily builds upon the idea of area.
Show steps
Show steps
Show steps
- Find 2 or 3 online videos on finding area under a curve and watch them.
- Try a few example problems without the aid of a calculator and check your work.
Practice root finding by hand
Show steps
Building intuition for finding the roots of polynomials by hand can be a helpful way to understand the ideas of using computational methods like Newton's method.
Show steps
Show steps
Show steps
- Find examples of a few cubic polynomials with real solutions and try to find their roots by hand.
- Continue with a few quartic polynomials, and optionally go on to a quintic polynomial.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Watch video on diagonalization and SVD
Show steps
Diagonalization and SVD are very powerful linear transformations. Watching a video on these concepts can be very insightful.
Show steps
Show steps
Show steps
- Find a 3Blue1Brown video on diagonalization or SVD and watch it.
- Optionally, find videos from other sources on these topics.
Write an intuitive explanation of partial derivatives
Show steps
Writing an explanation of partial derivatives in your own words can help you to more deeply understand the concept.
Show steps
Show steps
Show steps
- Write out the definition of partial derivatives.
- Explain how partial derivatives are used to find the slope of a surface.
- Give an example of how partial derivatives are used in a real-world application.
Practice solving partial differential equations
Show steps
Solving partial differential equations is a key skill in data science. This activity will give you practice with this important technique.
Show steps
Show steps
Show steps
- Find a set of practice problems on partial differential equations.
- Solve the problems using the method of separation of variables.
- Check your answers using a computer algebra system.
Contribute to a data science open source library
Show steps
Contribute to help advance the field of knowledge with a concrete deliverable.
Show steps
Show steps
Show steps
- Find an open-source data science library that you are interested in contributing to.
- Read the library's documentation and familiarize yourself with the codebase.
- Identify a bug or feature that you would like to fix or implement.
- Submit a pull request with your changes.
- Respond to feedback from the library's maintainers and make changes as necessary.
Career center
Learners who complete Integral Calculus and Numerical Analysis for Data Science will develop knowledge and skills
that may be useful to these careers:
Quantitative Analyst
Quantitative Analyst
A Quantitative Analyst develops and implements mathematical and statistical models to analyze financial data. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives, which can help you develop models to predict financial outcomes.
Data Analyst
Data Analyst
A Data Analyst collects, analyzes, and interprets data to help businesses make informed decisions. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. This course can help you build a foundation in the mathematical concepts and techniques that are essential for data analysis.
Data Scientist
Data Scientist
A Data Scientist collects, analyzes, and interprets data to extract meaningful insights and knowledge. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. This course can help you build a foundation in the mathematical concepts and techniques that are essential for data science.
Machine Learning Engineer
Machine Learning Engineer
A Machine Learning Engineer designs, develops, and maintains machine learning models. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives.This course can help you build a foundation in the mathematical concepts and techniques that are essential for machine learning.
Statistician
Statistician
A Statistician collects, analyzes, and interprets data to help businesses and organizations make informed decisions. This course will provide you with the necessary foundation to be successful as a Statistician, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. These concepts will form the basis of the statistical models that you will use in your work.
Financial Analyst
Financial Analyst
A Financial Analyst analyzes financial data to make recommendations and inform investment decisions. This course will provide you with the foundational skills in integral calculus, numerical analysis, root finding methods, matrix decomposition, and partial derivatives. Using these concepts you will be better equipped to understand the financial markets and make sound investment decisions.
Business Analyst
Business Analyst
A Business Analyst analyzes data and identifies opportunities to improve business processes. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. These concepts are used to analyze data and develop insights to improve business outcomes.
Operations Research Analyst
Operations Research Analyst
An Operations Research Analyst uses mathematical and analytical methods to improve the efficiency of business processes. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. These concepts are used to model and analyze business processes to make them more efficient.
Consultant
Consultant
A Consultant provides advice and guidance to businesses on how to improve their operations. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. These concepts are used to analyze data and develop recommendations to improve business outcomes.
Actuary
Actuary
An Actuary analyzes and evaluates risk in order to develop insurance policies and financial plans. This course will provide you with the necessary foundation to be successful as an Actuary. Integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives are core concepts in actuarial science, and are essential for understanding and quantifying risk.
Software Engineer
Software Engineer
A Software Engineer designs, develops, and maintains software applications. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. These concepts are used to develop efficient algorithms and optimize software performance.
Physicist
Physicist
A Physicist conducts research in physics and applies physics principles to solve problems in a variety of fields. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. These concepts are essential for developing and applying physical theories and models.
Mathematician
Mathematician
A Mathematician conducts research in mathematics and applies mathematical principles to solve problems in various fields. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. These concepts are essential for developing and applying mathematical theories and models.
Economist
Economist
An Economist analyzes economic data and develops economic models to explain economic phenomena and make predictions. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. These concepts are used to develop economic models and analyze economic data to understand how economies work.
Data Engineer
Data Engineer
A Data Engineer designs, builds, and maintains data pipelines and databases. This course will provide you with the foundational skills necessary for success in this role, including integral calculus, numerical analysis, root-finding methods, matrix decomposition, and partial derivatives. These concepts are used to design and optimize data pipelines and databases, as well as to analyze data to improve data quality.
For more career information including salaries, visit:
OpenCourser.com/course/ox4by2/integral
Reading list
We've selected ten 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
Integral Calculus and Numerical Analysis for Data Science.
This textbook is an introduction to linear algebra for students in the data sciences. It covers a wide range of topics, including matrix operations, eigenvalues and eigenvectors, and singular value decomposition.
This textbook is an introduction to convex optimization for students in the data sciences. It covers a wide range of topics, including linear programming, nonlinear programming, and semidefinite programming.
Acts as a comprehensive guide to understanding and approaching partial differential equations and is useful as a supplemental reference guide to the course.
Acts as a comprehensive guide to matrix analysis and applied linear algebra and is useful as a supplemental reference guide to the course.
Acts as a comprehensive introduction to numerical methods and is useful as background knowledge for this course.
Save
Acts as a comprehensive introduction to numerical analysis and is useful as background knowledge for this course.
Comprehensive introduction to calculus and is useful as background knowledge for this course.
Save
Comprehensive introduction to calculus and is useful as background knowledge for this course.
Classic reference on numerical methods and is useful as a supplemental reference guide to the course.
Is an introduction to partial differential equations with MATLAB and is useful as a supplemental reference guide to the course.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/ox4by2/integral
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Effort
4 weeks of study
Level
Intermediate
Via
Coursera
Institution
University of Colorado Boulder
Instructors
James Bird
Jane Wall
Language
English
Transcripts
Español
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Português
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中文
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This course belongs to a
collection
called
Expressway to Data Science: Essential Math. It's comprised of three courses:
- Integral Calculus and Numerical Analysis for Data Science (viewing)
- Algebra and Differential Calculus for Data Science
- Essential Linear Algebra for Data Science
Good to know
Teaches integral calculus concepts that are fundamental for data science, including integration by parts, area under a curve, and integral computation
Provides a solid foundation for the Statistical Modeling for Data Science Application course of CU Boulder's Master of Science in Data Science program
Covers essential math concepts like root-finding methods, matrix decomposition, and partial derivatives, which are crucial for data science
Assumes no prior math background, making it accessible to learners with diverse backgrounds
Course instructors, Jane Wall and James Bird, are experienced professionals in data science
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