VII. Higher Order Approximation

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VII.1. Sequences and Series of Functions

Linguistic Mapping VII.1

Peer Engagement VII.1

VII.1.1. Sequences of Functions

VII.1.2. Series of Functions and their Convergence

VII.1.3. Polynomial Approximation of Continuous Functions

VII.1.4. Power Series and the Radius of Convergence

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VII.2. Approximation by Power Series

Linguistic Mapping VII.2

Peer Engagement VII.2.1

Peer Engagement VII.2.2

VII.2.1. Taylor Polynomials and Taylor’s Theorem

VII.2.2. Taylor Series

VII.2.3. Rigidity of Analytic Functions

Knowledge Check VII.2.1

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VII.3. Differentiating Series

Linguistic Mapping VII.3

Peer Engagement VII.3

VII.3.1. Term-by-term Differentiation

VII.3.2. Application of Series

Knowledge Check VII.3.1

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VII.4. The Geometry of Particle Motion Revisited

Linguistic Mapping VII.4

Peer Engagement VII.4

VII.4.1. Acceleration and Force

VII.4.2. Parameterizing Curves and Surfaces

VII.4.3. Constrained Motion

VII.4.4. Normal Forces

Knowledge Check VII.4.1

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Worksheets

Optional: For students and instructors looking for further exploration.

Worksheet VII.1: Title

Worksheet VII.2: Title

Worksheet VII.3: Title

Worksheet VII.4: Title

© Copyright 2023 by the POC Writing Team: Bryan Carrillo, Dylan Noack, project PI Yat Sun Poon, and lead author 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 David Weisbart and the POC Writing Team.

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