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Textbook

Calculus I: A Guided Inquiry

ISBN: 978-1-118-87748-7
246 pages
July 2014, ©2013
Calculus I: A Guided Inquiry (1118877489) cover image

Description

Students learn when they are activity engaged and thinking in class. The activities in this book are the primary classroom materials for teaching Calculus 1, using the POGIL method. Each activity leads students to discovery of the key concepts by having them analyze data and make inferences.  The result is an "I can do this" attitude, increased retention, and a feeling of ownership over the material.

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Table of Contents

Functions

F1: Review of Functions
F2: Characteristics of Functions
F3: Compositions of Functions

Limits

L1: Limit of a Function
L2: Limit Laws
L3: Precise Definition of a Limit
L4: Continuity

Derivatives

D1: Velocity, Introduction to Derivatives
D2: Derivative at a Point
D3: Derivative as a Function7
D4: Differentiability
D5: Second Derivative

Differentiation Techniques

DT1: Power, Constant Multiple, Sum and Difference Rules
DT2: Product and Quotient Rules
DT3: Derivatives of Exponential and Logarithm Functions
DT4 Pre-Activity: Review of Trigonometry (optional)
DT4: Derivatives of Trigonometric Functions
DT5 Pre-Activity: Review of Compositions (prerequisite for DT5)
DT5: The Chain Rule
DT6: Derivatives of Inverse Functions
DT7: Implicit Differentiation

Differentiation Applications

DA1: Related Rates
DA2: Linear Approximation
DA3: Mean Value Theorem
DA4: Maximum and Minimum Values
DA6: Optimization

Integration

I1: Area and Distance
I2: Riemann Sums
I3: Definite Integrals
I4: Fundamental Theorem of Calculus
I5: Antiderivatives and the Fundamental Theorem of Calculus
I6: Indefinite Integrals

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