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Essential Calculus with Applications, 3rd Edition
Essential Calculus with Applications, 3rd Edition
Chapter 0: Algebra Review
0.1
Real Numbers and Number Lines
0.2
Integer Exponents
0.3
Fractional Exponents and Radicals
0.4
Polynomials and Factoring
0.5
Lines and Their Graphs
0.6
Linear Equations in One Variable
0.7
Quadratic Equations in One Variable
0.8
Rational and Radical Equations
Chapter 1: Functions, Models, and Graphs
1.1
Introduction to Functions
1.2
Operations with Functions
1.3
Functions and Models
1.4
Functions and Their Graphs: A Calculator Section
Chapter 2: Limits and the Derivative
2.1
One-Sided Limits
2.2
Limits
2.3
More about Limits
2.4
Continuity
2.5
Average Rate of Change
2.6
Instantaneous Rate of Change
2.7
Definition of the Derivative and the Power Rule
2.8
Techniques for Finding Derivatives
2.9
Applications: Marginal Analysis
Chapter 3: More about the Derivative
3.1
The Product and Quotient Rules
3.2
The Chain Rule and the General Power Rule
3.3
Implicit Differentiation and Related Rates
3.4
Increasing and Decreasing Intervals
3.5
Critical Values and the First Derivative Test
3.6
Absolute Maximum and Minimum
Chapter 4: Applications of the Derivative
4.1
Concavity and Points of Inflection
4.2
The Second Derivative Test
4.3
Curve Sketching: Polynomial Functions
4.4
Curve Sketching: Rational Functions
4.5
Business Applications
4.6
Other Applications: Optimization, Distance, and Velocity
4.7
Differentials
Chapter 5: Exponential and Logarithmic Functions
5.1
Exponential Functions
5.2
The Natural Logarithm
5.3
Derivatives of Logarithmic Functions
5.4
Derivatives of Exponential Functions
5.5
Growth and Decay
5.6
Elasticity of Demand
Chapter 6: Integration with Applications
6.1
The Indefinite Integral
6.2
Integration by Substitution
6.3
Area and Riemann Sums
6.4
The Definite Integral and the Fundamental Theorem of Calculus
6.5
Area under a Curve (with Applications)
6.6
Area between Two Curves (with Applications)
6.7
Differential Equations
Chapter 7: Additional Integration Topics
7.1
Integration by Parts
7.2
Annuities and Income Streams
7.3
Tables of Integrals
7.4
Improper Integrals
7.5
Probability
7.6
Volume
Chapter 8: Multivariable Calculus
8.1
Functions of Several Variables
8.2
Partial Derivatives
8.3
Local Extrema for Functions of Two Variables
8.4
Lagrange Multipliers
8.5
The Method of Least Squares
8.6
Double Integrals
Chapter 9: Trigonometric Functions
9.1
Trigonometric Functions
9.2
Derivatives of Trigonometric Functions
9.3
Integration of Trigonometric Functions
9.4
Inverse Trigonometric Functions
Chapter 10: Sequences, Taylor Polynomials, and Power Series
10.1
Sequences and Series
10.2
Taylor Polynomials
10.3
Taylor Series, Power Series, and Their Applications