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What is included with this book?
A Library Of Functions | |
Functions and Change | |
Exponential Functions | |
New Functions from Old | |
Logarithmic Functions | |
Trigonometric Functions | |
Powers, Polynomials, and Rational Functions | |
Introduction to Continuity | |
Limits | |
Review Problems | |
Check Your Understanding | |
Projects: Matching Functions to Data, Which Way Is the Wind Blowing? | |
Key Concept: The Derivative | |
How Do We Measure Speed? | |
The Derivative at a Point | |
The Derivative Function | |
Interpretations of the Derivative | |
The Second Derivative | |
Differentiability | |
Review Problems | |
Check Your Understanding | |
Projects: Hours of Daylight as a Function of Latitude, US Population | |
Short-Cuts To Differentiation | |
Powers and Polynomials | |
The Exponential Function | |
The Product and Quotient Rules | |
The Chain Rule | |
The Trigonometric Functions | |
The Chain Rule and Inverse Functions | |
Implicit Functions | |
Hyperbolic Functions | |
Linear Approximation and the Derivative | |
Theorems about Differentiable Functions | |
Review Problems | |
Check Your Understanding | |
Projects: Rule of 70, Newtonâ s Method | |
Using The Derivative | |
Using First and Second Derivatives | |
Optimization | |
Families of Functions | |
Optimization, Geometry, and Modeling | |
Applications to Marginality | |
Rates and Related Rates | |
Lâ hopitalâ s Rule, Growth, and Dominance | |
Parametric Equations | |
Review Problems | |
Check Your Understanding | |
Projects: Building a Greenhouse, Fitting a Line to Data, Firebreaks | |
Key Concept: The Definite Integral | |
How Do We Measure Distance Traveled? | |
The Definite Integral | |
The Fundamental Theorem and Interpretations | |
Theorems about Definite Integrals | |
Review Problems | |
Check Your Understanding | |
Projects: The Car and the Truck, An Orbiting Satellite | |
Constructing Antiderivatives | |
Antiderivatives Graphically and Numerically | |
Constructing Antiderivatives Analytically | |
Differential Equations | |
Second Fundamental Theorem of Calculus | |
The Equations of Motion | |
Review Problems | |
Check Your Understanding | |
Projects: Distribution of Resources, Yield from an Apple Orchard, Slope Fields | |
Integration | |
Integration by Substitution | |
Integration by Parts | |
Tables of Integrals | |
Algebraic Identities and Trigonometric Substitutions | |
Approximating Definite Integrals | |
Approximation Errors and Simpsonâ s Rule | |
Improper Integrals | |
Comparison of Improper Integrals | |
Review Problems | |
Check Your Understanding | |
Projects: Taylor Polynomial Inequalities | |
Using The Definite Integral | |
Areas and Volumes | |
Applications to Geometry | |
Area and Arc Length in Polar Coordinates | |
Density and Center of Mass | |
Applications to Physics | |
Applications to Economics | |
Distribution Functions | |
Probability, Mean, and Median | |
Review Problems | |
Check Your Understanding | |
Projects: Volume Enclosed by Two Cylinders, Length of a Hanging Cable, Surface Area of an Unpaintable Can of Paint, Maxwellâ s Distribution of Molecular Velocities | |
Sequences And Series | |
Sequences | |
Geometric Series | |
Convergence of Series | |
Tests for Convergence | |
Power Series and Interval of Convergence | |
Review Problems | |
Check Your Understanding | |
Projects: A Definition of e, Probability of Winning in Sports, Prednisone | |
Approximating Functions Using Series | |
Taylor Polynomials | |
Taylor Series | |
Finding and Using Taylor Series | |
The Error in Taylor Polynomial Approximations | |
Fourier Series | |
Review Problems | |
Check Your Understanding | |
Projects: Shape of Planets, Machinâ s Formula and the Value of pi, Approximation the Derivative | |
Differential Equations | |
What Is a Differential Equation? | |
Slope Fields | |
Eulerâ s Method | |
Separation of Variables | |
Growth and Decay | |
Applications and Modeling | |
The Logistic Model | |
Systems of Differential Equations | |
Analyzing the Phase Plane | |
Second-Order Differential Equations: Oscillations | |
Linear Second-Order Differential Equations | |
Review Problems | |
Check Your Understanding | |
Projects: SARS Predictions for Hong Kong, A S-I-R Model for SARS, Paretoâ s Law, Vibrations in a Molecule | |
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