Description

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Table of Content

Chapter 0: Preparation for Calculus
0.1: Graphs and Models
0.2: Linear Models and Rates of Change
0.3: Functions and Their Graphs
0.4: Fitting Models to Data

Chapter 1: Limits and Their Properties
1.1: A Preview of Calculus
1.2: Finding Limits Graphicalls and Numerically
1.3: Evaluating Limits Analytically
1.4: Continuity and One-Sided Limits
1.5: Infinite Limits

Chapter 2: Differentiation
2.1: The Derivative and the Tangent Line Problem
2.2: Basic Differentiation Rules and Rates of Change
2.3: Product and Quotient Rules and Higher-Order Derivatives2
2.4: The Chain Rule
2.5: Implicit Differentiation
2.6: Related Rates

Chapter 3: Applications of Differentiation
3.1: Extrema on an Interval
3.2: Rolle's Theorem and the Mean Value Theorem
3.3: Increasing and Decreasing Functions and the First Derivative Test
3.4: Concavity and the Second Derivative Test
3.5: Limits at Infinity
3.6: A summary of Curve Sketching
3.7: Optimization Problems
3.8: Newton's Method
3.9: Differentials

Chapter 4: Integration
4.1: Antiderivatives and Indefinite Integration
4.2: Area
4.3: Riemann Sums and Definite Integrals
4.4: The Fundamental Theorem of Calculus
4.5: Integration by Substitution
4.6: Numerical Integration

Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
5.1: The Natural Logarithmic Function: Differentiation
5.2: The Natural Logarithmic Function: Integration
5.3: Inverse Functions
5.4: Exponential Functions: Differentiation and Integration
5.5: Exponential Functions: Differentiation and Integration
5.6: Inverse Trigonometric Functions: Differentiation
5.7: Inverse Trigonometric Functions: Integration
5.8: Hyperbolic Functions

Chapter 6: Differential Equations
6.1: Slope Fields and Euler's Method
6.2: Differential Equations: Growth and Decay
6.3: Separation of Variables and the Logistic Equation
6.4: First-Order Linear Differential Equations

Chapter 7: Applications of Integration
7.1: Area of a Region Between Two Curves
7.2: Volume: The Disk Method
7.3: Volume: The Shell Method
7.4: Arc Length and Surfaces of Revolution
7.5: Work
7.6: Moments, Centers of Mass, and Centroids
7.7: Fluid Pressure and Fluid Force

Chapter 8: Integration Techniques, L'Hopital's Rule, and Improper Integrals
8.1: Basic Integration Rules
8.2: Integration by Parts
8.3: Trigonometric Integrals
8.4: Trigonometric Substitution
8.5: Partial Fractions
8.6: Integration by Tables and Other Integration Techniques
8.7: Indeterminate Forms and L'Hopital's Rule
8.8: Improper Integrals

Chapter 9: Infinite Series
9.1: Sequences
9.2: Series and Convergence
9.3: The Integral Test and p-Series
9.4: Comparisons of Series
9.5: Alternating Series
9.6: The Ratio and Root Tests
9.7: Taylor Polynomials and Approximations
9.8: Power Series
9.9: Representation of Functions by Power Series
9.10: Taylor and Maclaurin Series

Chapter 10: Conics, Parametric Equations, and Polar Coordinates
10.1: Conics and Calculus
10.2: Plane Curves and Parametric Equations
10.3: Parametric Equations and Calculus
10.4: Polar Coordinates and Polar Graphs
10.5: Area and Arc Length in Polar Coordinates
10.6: Polar Equations of Conics and Kepler's Laws

Chapter 11: Vectors and the Geometry of Space
11.1: Vectors in the Plane
11.2: Space Coordinates and Vectors in Space
11.3: The Dot Product of Two Vectors
11.4: The Cross Product of Two Vectors in Space
11.5: Lines and Planes in Space
11.6: Surfaces in Space
11.7: Cylindrical and Spherical Coordinates

Chapter 12: Vector-Valued Functions
12.1: Vector-Valued Functions
12.2: Differentiation and Integration of Vector-Valued Functions
12.3: Velocity and Acceleration
12.4: Tangent Vectors and Normal Vectors
12.5: Arc Length and Curvature

Chapter 13: Functions of Several Variables
13.1: Introduction to Functions of Several Variables
13.2: Limits and Continuity
13.3: Partial Derivatives
13.4: Differentials
13.5: Chain Rules for Functions of Several Variables
13.7: Tangent Planes and Normal Lines
13.8: Extrema of Functions of Two Variables
13.9: Applications of Extrema of Functions of Two Variables
13.10: Lagrange Multipliers

Chapter 14: Multiple Integration
14.1: Iterated Integrals and Area in the Plane
14.2: Double Integrals and Volume
14.3: Change of Variables: Polar Coordinates
14.4: Center of Mass and Moments of Inertia
14.5: Surface Area
14.6: Triple Integrals and Applications
14.7: Triple Integrals in Cylindrical and Spherical Coordinates
14.8: Change of Variables: Jacobians

Chapter 15: Vector Analysis
15.1: Vector Fields
15.2: Line Integrals
15.3: Conservative Vector Fields and Independence of Path
15.4: Green's Theorem
15.5: Parametric Surfaces
15.6: Surface Integrals
15.7: Divergence Theorem
15.8: Stokes's Theorem

Chapter 16: Additional Topics in Differential Equations
16.1: Exact First-Order Equations
16.2: Second-Order Homogeneous Linear Equations
16.3: Second-Order Nonhomogeneous Linear Equations
16.4: Series Solutions of Differential Equations

Chapter QP: Quick Prep Topics