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Preliminaries | |
The Real Numbers and the Cartesian Plane | |
Lines and Functions | |
Graphing Calculators and Computer Algebra Systems | |
Solving Equations | |
Trigonometric Functions | |
Exponential and Logarithmic Functions | |
Transformations of Functions | |
Preview of Calculus | |
Limits and Continuity | |
The Concept of Limit | |
Computation of Limits | |
Continuity and its Consequences | |
Limits Involving Infinity | |
Formal Definition of the Limit | |
Limits and Loss-of-Significance Errors | |
Differentiation | |
Tangent Lines and Velocity | |
The Derivative | |
Computation of Derivatives: The Power Rule | |
The Product and Quotient Rules | |
Derivatives of Trigonometric Functions | |
Derivatives of Exponential and Logarithmic Functions | |
The Chain Rule | |
Implicit Differentiation and Related Rates | |
The Mean Value Theorem | |
Applications of Differentiation | |
Linear Approximations adn L'Hopital's Rule | |
Newton's Method | |
Maximum and Minimum Values | |
Increasing and Decreasing Functions | |
Concavity | |
Overview of Curve Sketching | |
Optimization | |
Rates of Change in Applications | |
Integration | |
Antiderivatives | |
Sums and Sigma Notation | |
Area | |
The Definite Integral | |
The Fundamental Theorem of Calculus | |
Integration by Substitution | |
Numerical Integration | |
Applications of the Definite Integral | |
Area Between Curves | |
Volume | |
Volumes by Cylindrical Shells | |
Arc Length and Surface Area | |
Projectile Motion | |
Work, Moments, and Hydrostatic Force | |
Probability | |
Exponentials, Logarithms, and Other Transcendental Functions | |
The Natural Logarithm Revisited | |
Inverse Functions | |
The Exponential Function Revisited | |
Growth and Decay Problems | |
Separable Differential Equations | |
Euler's Method | |
The Inverse Trigonometric Functions | |
The Calculus of the Inverse Trigonometric Functions | |
The Hyperbolic Functions | |
Integration Techniques | |
Review of Formulas and Techniques | |
Integration by Parts | |
Trigonometric Techniques of Integration | |
Integration of Rational Functions using Partial Fractions | |
Integration Tables and Computer Algebra Systems | |
Indeterminate Forms and L'Hopital's Rule | |
Improper Integrals | |
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 | |
Fourier Series | |
Parametric Equations and Polar Coordinates | |
Plane Curves and Parametric Equations | |
Calculus and Parametric Equations | |
Arc Length and Surface Area in Parametric Equations | |
Polar Coordinates | |
Calculus and Polar Coordinates | |
Conic Sections | |
Conic Sections in Polar Coordinates | |
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 | |
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 Integ | |
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