Precalculus Review | |
What is Calculus? | |
Review of Elementary Mathematics | |
Review of Inequalities | |
Coordinate Plane | |
Analytic Geometry | |
Functions | |
The Elementary Functions | |
Combinations of Functions | |
A Note on Mathematical Proof; Mathematical Induction | |
Limits and Continuity | |
The Limit Process (An Intuitive Introduction) | |
Definition of Limit | |
Some Limit Theorems | |
Continuity | |
The Pinching Theorem; Trigonometric Limits | |
Two Basic Theorems | |
The Derivative; The Process of Differentiation | |
The Derivative | |
Some Differentiation Formulas | |
Thed/dx Notation Derivatives of Higher Order | |
The Derivative as a Rate of Change | |
The Chain Rule | |
Differentiating the Trigonometric Functions | |
Implicit Differentiation Rational Powers | |
The Mean-Value Theorem; Applications of the First and Second Derivatives | |
The Mean-Value Theorem | |
Increasing and Decreasing Functions | |
Local Extreme Values | |
Endpoint Extreme Values; Absolute Extreme Values | |
Some Max-Min Problems | |
Concavity and Points of Inflection | |
Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps | |
Some Curve Sketching | |
Velocity and Acceleration; Speed | |
Related Rates of Change Per Unit Time | |
Differentials | |
Newton-Raphson Approximations | |
Integration | |
An Area Problem; A Speed-Distance Problem | |
The Definite Integral of a Continuous Function | |
The Function f(x) = Integral from a to x of f(t) dt | |
The Fundamental Theorem of Integral Calculus | |
Some Area Problems | |
Indefinite Integrals | |
Working Back from the Chain Rule; theu-Substitution | |
Additional Properties of the Definite Integral | |
Mean-Value Theorems for Integrals; Average Value of a Function | |
Some Applications of the Integral | |
More on Area | |
Volume by Parallel Cross-Sections; Discs and Washers | |
Volume by the Shell Method | |
The Centroid of a Region; PappusA?s Theorem on Volumes | |
The Notion of Work | |
Fluid Force | |
The Transcendental Functions | |
One-to-One Functions; Inverse Functions | |
The Logarithm Function, Part I | |
The Logarithm Function, Part II | |
The Exponential Function | |
Arbitrary Powers; Other Bases | |
Exponential Growth and Decay | |
The Inverse Trigonometric Functions | |
The Hyperbolic Sine and Cosine | |
The Other Hyperbolic Functions | |
Techniques of Integration | |
Integral Tables and Review | |
Integration by Parts | |
Powers and Products of Trigonometric Functions | |
Integrals Featuring Square Root of (a^2 - x^2), Square Root of (a^2 + x^2), and Square Root of (x^2 - a^2) | |
Rational Functions; Partial Functions | |
Some Rationalizing Substitutions | |
Numerical Integration | |
Differential Equations | |
First-Order Linear Equations | |
Integral Curves; Separable Equations | |
The Equationya??a?? +aya??+by = 0 | |
The Conic Sections; Polar Coordinates; Parametric Equations | |
Geometry of Parabola, Ellipse, Hyperbola | |
Polar Coordinates | |
Graphing in Polar Coordinates | |
Area in Polar Coordinates | |
Curves G | |
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