Preliminaries | |
Polynomial and Rational Functions | |
Graphing Calculators and Computer Algebra Systems | |
Inverse Functions | |
Trigonometric and Inverse Trigonometric Functions | |
Exponential and Logarithmic Functions | |
Transformations of Functions | |
Parametric Equations and Polar Coordinates | |
Limits and Continuity | |
A Brief Preview of Calculus | |
The Concept of Limit | |
Computation of Limits | |
Continuity and its Consequences | |
Limits Involving Infinity | |
Limits and Loss-of-Significance Errors | |
Differentiation | |
Tangent Lines and Velocity | |
The Derivative | |
Computation of Derivatives: The Power Rule | |
The Product and Quotient Rules | |
The Chain Rule | |
Derivatives of Trigonometric and Inverse Trigonometric Functions | |
Derivatives of Exponential and Logarithmic Functions | |
Implicit Differentiation | |
The Mean Value Theorem | |
Applications of Differentiation | |
Linear Approximations and Newton's Method | |
Indeterminate Forms and L'Hopital's Rule | |
Maximum and Minimum Values | |
Increasing and Decreasing Functions | |
Concavity and Overview of Curve Sketching | |
Optimization | |
Rates of Change in Economics and the Sciences | |
Related Rates and Parametric Equations | |
Integration | |
Area Under a Curve | |
The Definite Integral | |
Antiderivatives | |
The Fundamental Theorem of Calculus | |
Integration by Substitution | |
Integration by Parts | |
Other Techniques of Integration | |
Integration Tables and Computer Algebra Systems | |
Numerical Integration | |
Improper Integrals | |
Applications of the Definite Integral | |
Area Between Curves | |
Volume | |
Arc Length and Surface Area | |
Projectile Motion | |
Applications of Integration to Physics and Engineering | |
Probability | |
Differential Equations | |
Growth and Decay Problems | |
Separable Differential Equations | |
Euler's Method | |
Second Order Equations with Constant Coefficients | |
Nonhomogeneous Equations: Undetermined Coefficients | |
Infinite Series | |
Sequences of Real Numbers | |
Infinite Series | |
The Integral Test and Comparison Tests | |
Alternating Series | |
Absolute Convergence and the Ratio Test | |
Power Series | |
Taylor Series | |
Applications of Taylor Series | |
Fourier Series | |
Power Series Solutions of Differential Equations | |
Vectors and the Geometry of Space | |
Vectors in the Plane | |
Vectors in Space | |
The Dot Product | |
The Cross Product | |
Lines and Planes in Space | |
Surfaces in Space | |
Vector-Valued Functions | |
Vector-Valued Functions | |
Parametric Surfaces | |
The Calculus of Vector-Valued Functions | |
Motion in Space | |
Curvature | |
Tangent and Normal Vectors | |
Functions of Several Variables and Differentiation | |
Functions of Several Variables | |
Limits and Continuity | |
Partial Derivatives | |
Tangent Planes and Linear Approximations | |
The Chain Rule | |
The Gradient and Directional Derivatives | |
Extrema of Functions of Several Variables | |
Constrained Optimization and Lagrange Multipliers | |
Multiple Integrals | |
Double Integrals | |
Area, Volume and Center of Mass | |
Double Integrals in Polar Coordinates | |
Surface Area | |
Triple Integrals | |
Cylindrical Coordinates | |
Spherical Coordinates | |
Change of Variables in Multiple Integrals | |
Vector Calculus | |
Vector Fields | |
Curl and Divergence | |
Line Integrals | |
Independence of Path and Conservative Vector Fields | |
Green's Theorem | |
Surface Integrals | |
The Divergence Theorem | |
Stokes' Theorem | |
Applications of Vector Calculus | |
Graphs of Additional Polar Equations | |
Formal Definition of Limit | |
Comple | |
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