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R. Algebra Reference | |
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Polynomials | |
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Factoring | |
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Rational Expressions | |
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Equations | |
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Inequalities | |
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Exponents | |
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Radicals | |
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Functions | |
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Lines and Linear Functions | |
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The Least Squares Line | |
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Properties of Functions | |
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Quadratic Functions; Translation and Reflection | |
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Polynomial and Rational Functions | |
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Exponential, Logarithmic, and Trigonometric Functions | |
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Exponential Functions | |
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Logarithmic Functions | |
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Applications: Growth and Decay | |
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Trigonometric Functions | |
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The Derivative | |
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Limits | |
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Continuity | |
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Rates of Change | |
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Definition of the Derivative | |
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Graphical Differentiation | |
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Calculating the Derivative | |
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Techniques for Finding Derivatives | |
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Derivatives of Products and Quotients | |
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The Chain Rule | |
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Derivatives of Exponential Functions | |
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Derivatives of Logarithmic Functions | |
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Derivatives of Trigonometric Functions | |
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Graphs and the Derivative | |
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Increasing and Decreasing Functions | |
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Relative Extrema | |
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Higher Derivatives, Concavity, and the Second Derivative Test | |
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Curve Sketching | |
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Applications of the Derivative | |
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Absolute Extrema | |
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Applications of Extrema | |
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Implicit Differentiation | |
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Related Rates | |
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Differentials: Linear Approximation | |
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Integration | |
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Antiderivatives | |
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Substitution | |
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Area and the Definite Integral | |
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The Fundamental Theorem of Calculus | |
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Integrals of Trigonometric Functions | |
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The Area Between Two Curves | |
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Further Techniques and Applications of Integration | |
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Numerical Integration | |
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Integration by Parts | |
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Volume and Average Value | |
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Improper Integrals | |
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Multivariable Calculus | |
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Functions of Several Variables | |
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Partial Derivatives | |
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Maxima and Minima | |
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Total Differentials and Approximations | |
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Double Integrals | |
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Linear Algebra | |
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Solution of Linear Systems | |
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Addition and Subtraction of Matrices | |
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Multiplication of Matrices | |
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Matrix Inverses | |
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Eigenvalues and Eigenvectors | |
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Differential Equations | |
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Solutions of Elementary and Separable Differential Equations | |
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Linear First-Order Differential Equations | |
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Euler's Method | |
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Linear Systems of Differential Equations | |
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Nonlinear Systems of Differential Equations | |
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Applications of Differential Equations | |
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Probability | |
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Sets | |
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Introduction to Probability | |
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Conditional Probability; Independent Events; Bayes' Theorem | |
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Discrete Random Variables; Applications to Decision Making | |
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Probability and Calculus | |
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Continuous Probability Models | |
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Expected Value and Variance of Continuous Random Variables | |
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Special Probability Density Functions | |