Full Frontal Calculus An Infinitesimal Approach

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Front Matter
	Cover
	Title Page
	Copyright Page
	Table of Contents
	Acknowledgements
	Preface for Teachers
	Changes in the 2nd Edition
	Preface for Students
Part I: Differential Calculus
	Chapter 1: The Basic Ideas
		Calculus: From A to The
		Resurrection
		The World of Calculus: An Overview
		Differential Calculus: The Key Geometric Idea
		Rates of Change
		The Derivative of a Function
		A Gift from Leibniz: d-Notation
		An Infinitesimal Bit of an Infinitesimal Bit
		The Derivative of y=x^2
		Derivatives of Polynomials
		One Last Example
	Chapter 2: The Differential Calculus Proper
		The Derivatives of Sine and Cosine
		The Product Rule
		The Quotient Rule
		Derivatives of Exponential Functions
		The Chain Rule
	Chapter 3: Applications - Contrived and Genuine
		Concavity and the Second Derivative
		Optimization
		Light on Light: Optics and Optimization
		Implicit Differentiation
		Related Rates
	Chapter Pi: Limits
		A Different Dialect: Limits
		Zero Over Zero (and Other Indeterminate Forms)
Part II: Integral Calculus
	Chapter 4: The Basic Ideas
		Integrals: Intuition and Notation
		Positives and Negatives
		Preparation for the FTC: The Antiderivative Lemma
		Preparation for the FTC: Accumulation Functions
		The Fundamental Theorem of Calculus (Stage 1: The Acorn)
		The Fundamental Theorem of Calculus (Stage 2: The Oak)
	Chapter 5: The Integral Calculus Proper
		Antiderivatives
		Substitution
		Interlude with Elementary Functions
		Algebraic Trickery (Rational Functions)
		Trigonometric Trickery (Part 1)
		Trigonometric Trickery (Part 2)
		Integration by Parts
	Chapter 6: Odds and Ends
		Arclength
		Surface Area
		Improper Integrals
		Riemann Sums
		Escape From Flatland
Part III: Special Topics
	Chapter 7: Taylor Polynomials and Series
		Taylor Polynomials
		The Errror in a Taylor Approximation
		Taylor Series
		Infinite Series in General, Geometric Series in Particular
		The Divergence Test and the Harmonic Series
		Comparison Tests and P-Series
		Absolute Series, Absolute Convergence
		The Ratio Test
		Power Series
		(Five Terms in) A Series of Stories of Series
	Chapter 8: Polar Coordinates and Parametric Equations
		Polar Coordinates
		Polar Equations and their Graphs
		Conversions
		Areas in Polar Coordinates
		Slopes in Polar Coordinates
		Parametric Equations
		Calculus and Parametric Equations
Selected Answers to Exercises
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter Pi
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 8
Back Matter
	Index
	About the Author