Dr. Bryan Carrillo’s The Principles of Calculus Website

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This site contains the course content, demonstration questions, and the course schedule.

Each link in the Course Content section contains the slides, videos, knowledge checks and additional resources for that section.

Each link in the Demonstration Questions contains the questions for each demonstration assignment.

The Course Schedule section will tell you the weekly schedule.

To submit assignments, go to the Canvas page for the course.

To find the course syllabus, go to the Canvas page for the course and click syllabus.

About

This is where I describe what we will learn about in each chapter and section, what is available in each chapter and section, my recommendations on how to engage with the material.

• About this Course

Course Schedule

This is where you can find the class calendar.

• Spring 2025 Schedule for Math 2
• Spring 2025 Schedule for Math 3A

Course Content

This is where you can find links to the content for each chapter and section. In each link, you will find slides and videos, knowledge checks and links to other textbooks that you can read to get an additional perspective on the material.

Remember, you will submit your knowledge check answers and complete the knowledge check surveys in Canvas.

• Chapter 1.1: The Algebra of Sets
• Chapter 1.2: Intervals and Inequalities
• Chapter 1.3: Functions
• Chapter 1.4: Functions given by Simple Formulas
• Chapter 1.5: Manipulating Functions
• Chapter 1.6: Piecewise Functions
• Chapter 2.1: Vectors and Translation
• Chapter 2.2: Scaling Vectors and Subsets of the Plane
• Chapter 2.3: Movement along Lines
• Chapter 2.4: Orthogonality and Reflection
• Chapter 2.5: Inverse Functions
• Chapter 2.6: Describing Rotation in Cartesian Coordinates
• Chapter 2.7: Rotations
• Chapter 2.8: Involution
• Chapter 3.1: Polynomial Functions
• Chapter 3.2: Rational Functions
• Chapter 3.3: Solving Piecewise Rational Inequalities
• Chapter 3.4: Orders of Intersections
• Chapter 4.1: Introduction to Symmetry
• Chapter 4.2: Translational Symmetry
• Chapter 4.3: Symmetric Change
• Chapter 4.4: Symmetry of Tangential Intersections
• Chapter 4.5: Polar Coordinates
• Chapter 5.1: The Elementary Notion of Area
• Chapter 5.2: Sequences
• Chapter 5.3: Measurement of a Circle
• Chapter 5.4: Summation
• Chapter 5.5: Limits
• Chapter 5.6: Continuous Functions
• Chapter 5.7: Analysis of Error
• Chapter 5.8: Approximating Change
• Chapter 5.9: Approximating Area in the Plane
• Chapter 6.1: Approximation by the Tangent line
• Chapter 6.2: Differentiating Elementary Functions
• Chapter 6.3: Rigidity and the Local Linear Approximation
• Chapter 6.4: Shape and Change

Demonstration Questions

This is where you can find the questions you will need to answer so that you can do your Demonstration assignment. Remember, you will need to record yourself explaining how you did the problems and submit a video to Canvas.

• Demonstration Questions

Online Assignments and Discussion Boards

The instructions and prompts for the rest of the assignments, which are the online assignments and discussion boards, can be found in Canvas.

© Copyright 2025 by the POC Writing Team: Bryan Carrillo, Yat Sun Poon, and David Weisbart. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the POC Writing Team.