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.

Chapter 1: Decomposition

• 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: Transformation

• 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: Rigidity

• 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: Symmetry

• 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: Finite Approximation

• 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: Local Linear Approximation

• 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

© 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.