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Functions, Graphs, and Limits | |
Functions | |
The Graph of a Function | |
Linear Functions | |
Functional Models | |
Limits | |
One-Sided Limits and Continuity | |
Differentiation: Basic Concepts | |
The Derivative | |
Techniques of Differentiation | |
Product and Quotient Rules; Higher-Order Derivatives | |
The Chain Rule | |
Marginal Analysis and Approximations Using Increments | |
Implicit Differentiation and Related Rates | |
Additional Applications of the Derivative | |
Increasing and Decreasing Functions; Relative Extrema | |
Concavity and Points of Inflection | |
Curve Sketching | |
Optimization; Elasticity of Demand | |
Additional Applied Optimization | |
Exponential and Logarithmic Functions | |
Exponential Functions: Continuous Compounding | |
Logarithmic Functions | |
Applications; Exponential Models | |
Integration | |
Antidifferentiation: The Indefinite Integral | |
Integration by Substitution | |
The Definite Integral and the Fundamental Theorem of Calculus | |
Applying Definite Integration: Area Between Curves and Average Value | |
Additional Applications to Business and Economics | |
Additional Applications to the Life and Social Sciences | |
Additional Topics in Integration | |
Integration by Parts; Integral Tables | |
Improper Integrals | |
Numerical Integration | |
Calculus of Several Variables | |
Functions of Several Variables | |
Partial Derivatives | |
Optimizing Functions of Two Variables | |
The Method of Least-Squares | |
Constrained Optimization: The Method of Lagrange Multipliers | |
Double Integrals | |
Differential Equations | |
Introduction to Differential Equations | |
First-Order Linear Differential Equations | |
Additional Applications of Differential Equations | |
Approximate Solutions of Differential Equations | |
Difference Equations; The Cobweb Model | |
Infinite Series and Taylor Series Approximations | |
Infinite Series; Geometric Series | |
Tests for Convergence | |
Functions as Power Series; Taylor Series | |
Probability and Calculus | |
Introduction to Probability; Discrete Random Variables | |
Continuous Random Variables | |
Expected Value and Variance of Continuous Random Variables | |
Normal and Poisson Probability Distributions | |
Trigonometric Functions | |
The Trigonometric Functions | |
Differentiation and Integration of Trigonometric Functions | |
Additional Applications Involving Trigonometric Function | |
Algebra Review | |
A Brief Review of Algebra | |
Factoring Polynomials and Solving Systems of Equations | |
Evaluating Limits with L’Hopital’s Rule | |
The Summation Notation | |
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