Before Calculus | |
Functions | |
New Functions from Old | |
Families of Functions | |
Inverse Functions; Inverse Trigonometric Functions | |
Exponential and Logarithmic Functions | |
Limits and Continuity | |
Limits (An Intuitive Approach) | |
Computing Limits | |
Limits at Infinity; End Behavior of a Function | |
Limits (Discussed More Rigorously) | |
Continuity | |
Continuity of Trigonometric, Exponential, and Inverse Functions | |
The Derivative | |
Tangent Lines and Rates of Change | |
The Derivative Function | |
Introduction to Techniques of Differentiation | |
The Product and Quotient Rules | |
Derivatives of Trigonometric Functions | |
The Chain Rule | |
Topics in Differentiation | |
Implicit Differentiation | |
Derivatives of Logarithmic Functions | |
Derivatives of Exponential and Inverse Trigonometric Functions | |
Related Rates | |
Local Linear Approximation; Differentials | |
L'Hôpital's Rule; Indeterminate Forms | |
The Derivative in Graphing and Applications | |
Analysis of Functions I: Increase, Decrease, and Concavity | |
Analysis of Functions II: Relative Extrema; Graphing Polynomials | |
Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents | |
Absolute Maxima and Minima | |
Applied Maximum and Minimum Problems | |
Rectilinear Motion | |
Newton's Method | |
Rolle's Theorem; Mean-Value Theorem | |
Integration | |
An Overview of the Area Problem | |
The Indefinite Integral | |
Integration by Substitution | |
The Definition of Area as a Limit; Sigma Notation | |
The Definite Integral | |
The Fundamental Theorem of Calculus | |
Rectilinear Motion Revisited Using Integration | |
Average Value of a Function and its Applications | |
Evaluating Definite Integrals by Substitution | |
Logarithmic and Other Functions Defined by Integrals | |
Applications of the Definite Integral in Geometry, Science, and Engineering | |
Area Between Two Curves | |
Volumes by Slicing; Disks and Washers | |
Volumes by Cylindrical Shells | |
Length of a Plane Curve | |
Area of a Surface of Revolution | |
Work | |
Moments, Centers of Gravity, and Centroids | |
Fluid Pressure and Force | |
Hyperbolic Functions and Hanging Cables | |
Principles of Integral Evaluation | |
An Overview of Integration Methods | |
Integration by Parts | |
Integrating Trigonometric Functions | |
Trigonometric Substitutions | |
Integrating Rational Functions by Partial Fractions | |
Using Computer Algebra Systems and Tables of Integrals | |
Numerical Integration; Simpson's Rule | |
Improper Integrals | |
Mathematical Modeling with Differential Equations | |
Modeling with Differential Equations | |
Separation of Variables | |
Slope Fields; Euler's Method | |
First-Order Differential Equations and Applications | |
Infinite Series | |
Sequences | |
Monotone Sequences | |
Infinite Series | |
Convergence Tests | |
The Comparison, Ratio, and Root Tests | |
Alternating Series; Absolute and Conditional Convergence | |
Maclaurin and Taylor Polynomials | |
Maclaurin and Taylor Series; Power Series | |
Convergence of Taylor Series | |
Differentiating and Integrating Power Series; Modeling with Taylor Series | |
Parametric and Polar Curves; Conic Sections | |
Parametric Equations; Tangent Lines and Arc Length for Parametric Curves | |
Polar Coordinates | |
Tangent Lines, Arc Length, and Area for Polar Curves | |
Conic Sections | |
Rotation of Axes; Second-Degree Equations | |
Conic Sections in Polar Coordinates | |
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