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Welcome to MA005Calculus I
My name is Pamela Jones, I’m one of the professors that helped develop this course. Calculus can be thought of as the mathematics of change. Because everything in the world is changing, calculus helps us track those changes. Algebra, by contrast, can be thought of as dealing with a large set of numbers that are inherently constant. Solving an algebra problem, like \( y = 2x + 5 \), merely produces a pairing of two predetermined numbers, although an infinite set of pairs. Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate \( R \), such as \( Y = X_0+Rt \), where \( t \) is elapsed time and \( X_0 \) is the initial deposit. With compound interest, things get complicated for algebra, as the rate \( R \) is itself a function of time with \( Y = X_0 + R(t)t \). Now, we have a rate of change that itself is changing. Calculus came to the rescue, as Isaac Newton introduced the world to mathematics specifically designed to handle those things that change. Calculus is among the most important and useful developments of human thought. Even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful, beautiful, and useful set of ideas and techniques. You will see the fundamental ideas of this course over and over again in future courses in mathematics as well as in all of the sciences (like physics, biology, social sciences, economics, and engineering). However, calculus is an intellectual step up from your previous mathematics courses. Many of the ideas you will gain in this course are more carefully defined and have both a functional and a graphical meaning. Some of the algorithms are quite complicated, and in many cases, you will need to make a decision as to which appropriate algorithm to use. Calculus offers a huge variety of applications, and many of them will be saved for future courses.” This course is divided into five learning sections or units, plus a reference section or appendix. The course begins with a unit that provides a review of algebra specifically designed to help and prepare you for the study of calculus. The second unit discusses functions, graphs, limits, and continuity. Understanding limits could not be more important, as that topic really begins the study of calculus. The third unit introduces and explains derivatives. With derivatives, we are now ready to handle all of those changes mentioned above. The fourth unit makes visual sense of derivatives by discussing derivatives and graphs. The fifth unit introduces and explains antiderivatives and definite integrals. Finally, the reference section provides a large collection of reference facts, geometry, and trigonometry that will assist you in solving calculus problems long after the course is over. You can start by reviewing the course learning outcomes and the syllabus, you can find both on the left navigation panel Let’s get started!
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Source and License: This work is licensed by Saylor Academy under a Creative Commons Attribution-NonCommercial-Sharealike 4.0 International License (CC BY-NC-SA 4.0). This content was created using Genially and Synthesia. AI-generated avatars and voices in this video were created using Synthesia and remain subject to Synthesia’s Terms of Service; these elements are not covered by the Creative Commons license. Synthesia trademarks and services remain the property of Synthesia. All Genially proprietary elements such as templates, themes, built-in assets, stock media, and other “Genially Content” remain subject to Genially’s Terms of Service and are not covered by this Creative Commons license. These elements must remain embedded in the course and cannot be reused or redistributed independently.
Source and License: This work is licensed by Saylor Academy under a Creative Commons Attribution-NonCommercial-Sharealike 4.0 International License (CC BY-NC-SA 4.0). This content was created using Genially and Synthesia. AI-generated avatars and voices in this video were created using Synthesia and remain subject to Synthesia’s Terms of Service; these elements are not covered by the Creative Commons license. Synthesia trademarks and services remain the property of Synthesia. All Genially proprietary elements such as templates, themes, built-in assets, stock media, and other “Genially Content” remain subject to Genially’s Terms of Service and are not covered by this Creative Commons license. These elements must remain embedded in the course and cannot be reused or redistributed independently.
AI Summary
Calculus I introduces students to the mathematics of change and builds a foundation for advanced study in mathematics and the sciences. Here are some key takeaways:
- Understand how calculus extends algebra to model quantities that change over time.
- Learn the core concepts of limits, derivatives, and integrals and how they connect.
- Apply calculus concepts both graphically and analytically to real-world problems.
You can start by reviewing the course learning outcomes and the syllabus on the left navigation pan.
Course Introduction Video
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Created on February 11, 2026
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Experiencing playback issues or need translation options?
Welcome to MA005Calculus I
My name is Pamela Jones, I’m one of the professors that helped develop this course. Calculus can be thought of as the mathematics of change. Because everything in the world is changing, calculus helps us track those changes. Algebra, by contrast, can be thought of as dealing with a large set of numbers that are inherently constant. Solving an algebra problem, like \( y = 2x + 5 \), merely produces a pairing of two predetermined numbers, although an infinite set of pairs. Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate \( R \), such as \( Y = X_0+Rt \), where \( t \) is elapsed time and \( X_0 \) is the initial deposit. With compound interest, things get complicated for algebra, as the rate \( R \) is itself a function of time with \( Y = X_0 + R(t)t \). Now, we have a rate of change that itself is changing. Calculus came to the rescue, as Isaac Newton introduced the world to mathematics specifically designed to handle those things that change. Calculus is among the most important and useful developments of human thought. Even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful, beautiful, and useful set of ideas and techniques. You will see the fundamental ideas of this course over and over again in future courses in mathematics as well as in all of the sciences (like physics, biology, social sciences, economics, and engineering). However, calculus is an intellectual step up from your previous mathematics courses. Many of the ideas you will gain in this course are more carefully defined and have both a functional and a graphical meaning. Some of the algorithms are quite complicated, and in many cases, you will need to make a decision as to which appropriate algorithm to use. Calculus offers a huge variety of applications, and many of them will be saved for future courses.” This course is divided into five learning sections or units, plus a reference section or appendix. The course begins with a unit that provides a review of algebra specifically designed to help and prepare you for the study of calculus. The second unit discusses functions, graphs, limits, and continuity. Understanding limits could not be more important, as that topic really begins the study of calculus. The third unit introduces and explains derivatives. With derivatives, we are now ready to handle all of those changes mentioned above. The fourth unit makes visual sense of derivatives by discussing derivatives and graphs. The fifth unit introduces and explains antiderivatives and definite integrals. Finally, the reference section provides a large collection of reference facts, geometry, and trigonometry that will assist you in solving calculus problems long after the course is over. You can start by reviewing the course learning outcomes and the syllabus, you can find both on the left navigation panel Let’s get started!
AI Summary
Video Transcript
Source and License: This work is licensed by Saylor Academy under a Creative Commons Attribution-NonCommercial-Sharealike 4.0 International License (CC BY-NC-SA 4.0). This content was created using Genially and Synthesia. AI-generated avatars and voices in this video were created using Synthesia and remain subject to Synthesia’s Terms of Service; these elements are not covered by the Creative Commons license. Synthesia trademarks and services remain the property of Synthesia. All Genially proprietary elements such as templates, themes, built-in assets, stock media, and other “Genially Content” remain subject to Genially’s Terms of Service and are not covered by this Creative Commons license. These elements must remain embedded in the course and cannot be reused or redistributed independently.
Source and License: This work is licensed by Saylor Academy under a Creative Commons Attribution-NonCommercial-Sharealike 4.0 International License (CC BY-NC-SA 4.0). This content was created using Genially and Synthesia. AI-generated avatars and voices in this video were created using Synthesia and remain subject to Synthesia’s Terms of Service; these elements are not covered by the Creative Commons license. Synthesia trademarks and services remain the property of Synthesia. All Genially proprietary elements such as templates, themes, built-in assets, stock media, and other “Genially Content” remain subject to Genially’s Terms of Service and are not covered by this Creative Commons license. These elements must remain embedded in the course and cannot be reused or redistributed independently.
AI Summary
Calculus I introduces students to the mathematics of change and builds a foundation for advanced study in mathematics and the sciences. Here are some key takeaways:
- Understand how calculus extends algebra to model quantities that change over time.
- Learn the core concepts of limits, derivatives, and integrals and how they connect.
- Apply calculus concepts both graphically and analytically to real-world problems.
You can start by reviewing the course learning outcomes and the syllabus on the left navigation pan.