- Pikes Peak Library District
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- Topic Guides - Math and Science
- Pre-Calc and Calculus

This how-to guide helps students and parents navigate resources connected to Math and Science topics.

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Specific key words or phrases are necessary to find information in databases or the library catalog. We recommend:

- Limit
- Derivative
- Velocity / Acceleration
- Chain Rule
- Logarithm
- Logarithmic differentiation
- Slope field
- Integral
- Theorem

- You can use these search terms to find books in the library catalog and eBooks or eAudiobooks in the eLibrary.
- To narrow your search, type two terms into a search bar in this format: "Term 1" AND "Term 2". This search will only provide resources that include both terms. Combine any two search terms from the box into a database search bar to see what you find.
- Find more database search tips on the Debate Issues & Paper Topics guide, in the Database Search Tops box.

This guide is connected to the following Colorado Academic Standards

- Math Practice MP1. Make sense of problems and persevere in solving them.
- Math Practice MP2. Reason abstractly and quantitatively.
- Math Practice MP3. Construct viable arguments and critique the reasoning of others.
- Math Practice MP5. Use appropriate tools strategically.

This guide will support students by building further knowledge in:

- Different library resources – what they are and how they are useful for studying pre-calculus and calculus.
- How to effectively find information in these sources using search terms.

Databases are subject-specific search engines that provide access to journal articles and other reliable resources. The following PPLD databases are recommended for students studying pre-calc and calculus:

- Academic Search Premier This link opens in a new windowSearches almost 3500 full text academic and scholarly journals.
- Explora for Public Libraries This link opens in a new windowFind articles and facts from the worldâ€™s leading magazines and reference books in one search.
- Gale Virtual Reference Library This link opens in a new windowSearches our entire collection of Gale eBooks on a variety of subjects, including history, science, government, business and more.
- HelpNow (Brainfuse) This link opens in a new windowLive homework help and skills building from expert tutors in math, science, social studies and English plus writing and reading assistance. Designed for grades K - Adults. Tutors available online Monday - Sunday from 2 - 11 p.m. MDT.

Reference materials are things like encyclopedias and handbooks that provide quick facts and summaries of different subjects. The following encyclopedias and dictionaries in the PPLD catalog support the study of pre-calc and calculus:

- The Britannica Guide to Analysis and Calculus by Erik Gregersen (Editor); Britannica Educational Publishing StaffISBN: 9781615302208Publication Date: 2010-08-30The dynamism of the natural world means that it is constantly changing, sometimes rapidly, sometimes gradually. By mathematically interpreting the continuous change that characterizes so many natural processes, analysis and calculus have become indispensable to bridging the divide between mathematics and the sciences. This comprehensive volume examines the key concepts of calculus, providing students with a robust understanding of integration and differentiation.

Reference materials are things like encyclopedias and handbooks that provide quick facts and summaries of different subjects. The following books in the PPLD catalog support the study of pre-calc and calculus:

- E-Z Calculus by Douglas DowningISBN: 9780764144615Publication Date: 2009-08-01The author of this imaginative self-teaching book tells an entertaining story about travels in the fictional land of Carmorra. In the process he introduces a series of problems and solves them by applying principles of calculus. Readers are introduced to derivatives, natural logarithms, exponential functions, differential equations, and much more. Skill-building exercises are presented at the end of every chapter.
- The Manga Guide to Calculus by Hiroyuki Kojima; Shin Togami; Becom Co. Ltd.ISBN: 9781593271947Publication Date: 2009-08-01In The Manga Guide to Calculus, you'll follow along with Noriko as she learns that calculus is more than just a class designed to weed out would-be science majors. You'll see that calculus is a useful way to understand the patterns in physics, economics, and the world around us, with help from real-world examples like probability, supply and demand curves, the economics of pollution, and the density of Shochu (a Japanese liquor).

You can use trusted, online sources to find information. For more information on reliable, online sources, please visit PPLD’s Debate Issues & Paper Topics guide. PPLD recommends:

- LinkedIn Learning - CalculusLinkedIn Learning - Calculus. You will need to login to LinkedIn Learning using your library card number and pin to access expert-led courses across a variety of online class topics.
- Khan Academy - PrecalculusThis Khan Academy course covers topics including composite and inverse functions, trigonometry, complex numbers, rational functions, matrices, and limits and continuity.
- Khan Academy - Differential CalculusHow would you like to follow in the footsteps of Euclid and Archimedes? Would you like to be able to determine precisely how fast Usain Bolt is accelerating exactly 2 seconds after the starting gun? Differential calculus deals with the study of the rates at which quantities change. It is one of the two principal areas of calculus (integration being the other).
- Khan Academy - Integral CalculusHow do you find the area under a curve? What about the length of any curve? Is there a way to make sense out of the idea of adding infinitely many infinitely small things? Integral calculus gives us the tools to answer these questions and many more. Surprisingly, these questions are related to the derivative, and in some sense, the answer to each one is the opposite of the derivative.

Use these multimedia sources to watch or listen to information on this topic.

- The Joy of Integral CalculusGeometry and trigonometry are used to determine the areas of simple figures such as triangles and circles. But how are more complex shapes measured? Calculus comes to the rescue with a technique called integration, which adds the simple areas of many tiny quantities. This video is accessible through Kanopy in the PPLD eLibrary.

- Last Updated: Aug 29, 2023 11:20 AM
- URL: https://research.ppld.org/topic-guides-math-science
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