COMPREHENSIVE PRACTICE COLLECTION
Calculus
From functions and limits to multivariable calculus and differential equations.
28 chapters · 251 sections · 2,510 questions with worked solutions.
Table of Contents
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Chapter 1: Review
10 sections · p. 9Chapter 2: Limits
10 sections · p. 211Chapter 3: Derivatives
13 sections · p. 411- 3-1The Definition of the Derivative
- 3-2Interpretation of the Derivative
- 3-3Differentiation Formulas
- 3-4Product and Quotient Rule
- 3-5Derivatives of Trig Functions
- 3-6Derivatives of Exponential and Logarithm Functions
- 3-7Derivatives of Inverse Trig Functions
- 3-8Derivatives of Hyperbolic Functions
- 3-9Chain Rule
- 3-10Implicit Differentiation
- 3-11Related Rates
- 3-12Higher Order Derivatives
- 3-13Logarithmic Differentiation
Chapter 4: Application of Derivatives
14 sections · p. 675- 4-1Rates of Change
- 4-2Critical Points
- 4-3Minimum and Maximum Values
- 4-4Finding Absolute Extrema
- 4-5The Shape of a Graph, Part I
- 4-6The Shape of a Graph, Part II
- 4-7The Mean Value Theorem
- 4-8Optimization
- 4-9More Optimization
- 4-10L'Hospital's Rule and Indeterminate Forms
- 4-11Linear Approximations
- 4-12Differentials
- 4-13Newton's Method
- 4-14Business Applications
Chapter 5: Integrals
8 sections · p. 955Chapter 6: Application of Integrals
6 sections · p. 1121Chapter 7: Extras
9 sections · p. 1241Chapter 8: Integration Techniques
10 sections · p. 1421Chapter 9: Applications of Integrals
5 sections · p. 1621Chapter 10: Parametric Equations and Polar Coordinates
11 sections · p. 1721- 10-1Parametric Equations and Curves
- 10-2Tangents with Parametric Equations
- 10-3Area with Parametric Equations
- 10-4Arc Length with Parametric Equations
- 10-5Surface Area with Parametric Equations
- 10-6Polar Coordinates
- 10-7Tangents with Polar Coordinates
- 10-8Area with Polar Coordinates
- 10-9Arc Length with Polar Coordinates
- 10-10Surface Area with Polar Coordinates
- 10-11Arc Length and Surface Area Revisited
Chapter 11: Series and Sequences
18 sections · p. 1941- 11-1Sequences
- 11-2More on Sequences
- 11-3Series - The Basics
- 11-4Convergence and Divergence of Series
- 11-5Special Series
- 11-6Integral Test
- 11-7Comparison and Limit Comparison Tests
- 11-8Alternating Series Test
- 11-9Absolute Convergence and Divergence
- 11-10Ratio Test
- 11-11Root Test
- 11-12Strategy for Series
- 11-13Estimating the Value of a Series
- 11-14Power Series
- 11-15Power Series and Functions
- 11-16Taylor Series
- 11-17Applications of Series
- 11-18Binomial Series
Chapter 12: Vectors
4 sections · p. 2301Chapter 13: 3-Dimensional Space
13 sections · p. 2381- 13-1The 3-D Coordinate System
- 13-2Equations of Lines
- 13-3Equations of Planes
- 13-4Quadric Surfaces
- 13-5Functions of Several Variables
- 13-6Vector Functions
- 13-7Calculus with Vector Functions
- 13-8Tangent, Normal and Binormal Vectors
- 13-9Arc Length with Vector Functions
- 13-10Curvature
- 13-11Velocity and Acceleration
- 13-12Cylindrical Coordinates
- 13-13Spherical Coordinates
Chapter 14: 3-Dimensional Space
13 sections · p. 2641- 14-1The 3-D Coordinate System
- 14-2Equations of Lines
- 14-3Equations of Planes
- 14-4Quadric Surfaces
- 14-5Functions of Several Variables
- 14-6Vector Functions
- 14-7Calculus with Vector Functions
- 14-8Tangent, Normal and Binormal Vectors
- 14-9Arc Length with Vector Functions
- 14-10Curvature
- 14-11Velocity and Acceleration
- 14-12Cylindrical Coordinates
- 14-13Spherical Coordinates
Chapter 15: Partial Derivatives
7 sections · p. 2901Chapter 16: Applications of Partial Derivatives
5 sections · p. 3041Chapter 17: Multiple Integrals
10 sections · p. 3141- 17-1Double Integrals
- 17-2Iterated Integrals
- 17-3Double Integrals over General Regions
- 17-4Double Integrals in Polar Coordinates
- 17-5Triple Integrals
- 17-6Triple Integrals in Cylindrical Coordinates
- 17-7Triple Integrals in Spherical Coordinates
- 17-8Change of Variables
- 17-9Surface Area
- 17-10Area and Volume Revisited
Chapter 18: Line Integrals
7 sections · p. 3341Chapter 19: Surface Integrals
6 sections · p. 3481Chapter 20: Basic Concepts
3 sections · p. 3601Chapter 21: First Order Differential Equations
9 sections · p. 3661Chapter 22: Second Order Differential Equations
11 sections · p. 3841Chapter 23: Laplace Transforms
10 sections · p. 4061Chapter 24: Systems of Differential Equations
12 sections · p. 4261- 24-1Review : Systems of Equations
- 24-2Review : Matrices & Vectors
- 24-3Review : Eigenvalues & Eigenvectors
- 24-4Systems of Differential Equations
- 24-5Solutions to Systems
- 24-6Phase Plane
- 24-7Real Eigenvalues
- 24-8Complex Eigenvalues
- 24-9Repeated Eigenvalues
- 24-10Nonhomogeneous Systems
- 24-11Laplace Transforms
- 24-12Modeling