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Calculus I, II, and III: A Problem-Based Approach with Early Transcendentals:
W. Ted Mahavier < Allen, Browning, Daniel, So
1
Contents
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Contents
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Front Matter
To the Student
1
Functions, Limits, Velocity, and Tangents
Average Speed and Velocity
Limits and Continuity
Instantaneous Velocity and Growth Rate
Tangent Lines
Practice
Solutions
2
Derivatives
Derivatives of Polynomial, Root, and Rational Functions
Derivatives of the Trigonometric Functions
The Chain Rule
Derivatives of the Inverse Trigonometric Functions
Derivatives of the Exponential and Logarithmic Functions
Logarithmic and Implicit Differentiation
Practice
Solutions
3
Applications of Derivatives
Linear Approximations
Limits involving Infinity and Asymptotes
Graphing
The Theorems of Calculus
Maxima and Minima
Related Rates
Practice
Solutions
4
Integrals
Riemann Sums and Definite Integrals
Anti-differentiation and the Indefinite Integral
The Fundamental Theorem of Calculus
Applications
Practice
Solutions
5
Techniques of Integration
Change of Variable Method
Partial Fractions
Integration by Parts
Integrals of Trigonometric Functions
Integration by Trigonometric Substitution
The Hyperbolic Functions
Improper Integrals
Practice
Solutions
6
Sequences & Series
Sequences
Series with Positive Constant Terms
Alternating Series
Power Series
Practice
Solutions
7
Conic Sections, Parametric Equations, and Polar Coordinates
Conic Sections
Parametric Equations
Polar Coordinates
Practice
Solutions
8
Vectors and Lines
Practice
Solutions
9
Cross Product and Planes
Practice
Solutions
10
Limits and Derivatives
Practice
Solutions
11
Optimization and Lagrange Multipliers
Practice
Solutions
12
Integration
Practice
Solutions
13
Line Integrals, Flux, Divergence, Gauss' and Green's Theorem
Practice
Solutions
14
Appendices
Limit Definition
The Extended Reals
Exponential and Logarithmic Functions
Trigonometry
Summation Formulas
Authored in PreTeXt
Front Matter
1
Functions, Limits, Velocity, and Tangents
2
Derivatives
3
Applications of Derivatives
4
Integrals
5
Techniques of Integration
6
Sequences & Series
7
Conic Sections, Parametric Equations, and Polar Coordinates
8
Vectors and Lines
9
Cross Product and Planes
10
Limits and Derivatives
11
Optimization and Lagrange Multipliers
12
Integration
13
Line Integrals, Flux, Divergence, Gauss' and Green's Theorem
14
Appendices
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