Functions And Linear Models | |

Functions | |

Function Notation | |

Graphs of Functions | |

Domain and Range | |

Exercises | |

Linear Functions | |

Intercepts | |

Linear Equations | |

Finding the Equation of a Line | |

Other Forms of Linear Equations | |

Graphing Linear Functions | |

Exercises | |

Nonlinear Models | |

Quadratic Function Models | |

Exercises | |

Exponential Function Models | |

Exponential Function Graphs | |

Properties of Exponents | |

Finding an Exponential Function from a Table | |

Using Exponential Regression to Model Data | |

Finding an Exponential Function from a Verbal Description | |

Exercises | |

The Derivative | |

Average Rate of Change | |

Graphical Interpretation of the Difference Quotient | |

Exercises | |

Limits and Instantaneous Rates of Change | |

Limits | |

Exercises | |

The Derivative as a Slope: Graphical Methods | |

Tangent-Line Approximations | |

Numerical Derivatives | |

Exercises | |

The Derivative as a Function: Algebraic Method | |

Estimating Derivatives | |

Exercises | |

Interpreting the Derivative | |

Exercises | |

Differentiation Techniques | |

Basic Derivative Rules | |

Derivative Notation | |

The Constant Rule | |

The Power Rule | |

Constant Multiple Rule | |

Sum and Difference Rule | |

Exercises | |

The Product and Quotient Rules | |

Exercises | |

The Chain Rule | |

Composition of Functions | |

The Chain Rule | |

Chain Rule: Alternative Form | |

Exercises | |

Exponential and Logarithmic Rules | |

Exponential Rule | |

Logarithmic Rule | |

Exercises | |

Implicit Differentiation | |

Exercises | |

Derivative Applications | |

Maxima and Minima | |

Continuity | |

Relative and Absolute Extrema | |

Critical Values | |

The First Derivative TeSt. Exercises | |

Applications of Maxima and Minima | |

Revenue, Cost, and Profit | |

Area and Volume | |

Exercises | |

Concavity and the Second Derivative | |

Concavity | |

The Second Derivative TeSt. Point of Diminishing Returns | |

Position, Velocity, and Acceleration | |

Curve Sketching | |

Exercises | |

Related Rates | |

Exercises | |

The Integral | |

Indefinite Integrals | |

Basic Integration Rules | |

Indefinite Integral Applications | |

Exercises | |

Integration by Substitution | |

Differentials | |

Integration by Substitution | |

Exercises | |

Using Sums to Approximate Area | |

Exercises | |

The Definite Integral | |

Summation Notation | |

The Definite Integral | |

Definite Integral Properties | |

Exercises | |

The Fundamental Theorem of Calculus | |

Changing Limits of Integration | |

Exercises | |

Advanced Integration Techniques And Applications | |

Integration by Parts | |

Exercises | |

Area Between Two Curves | |

Difference of Accumulated Changes | |

Exercises | |

Differential Equations and Applications | |

Newton's Law of Heating and Cooling | |

Exercises | |

Differential Equations: Limited Growth and Logistic Growth Models | |

Limited Growth Model | |

Logistic Growth Model | |

Exercises | |

Multivariable Functions And Partial Derivatives | |

Multivariable Functions | |

Exercises | |

Partial Derivatives | |

Cross Sections of a Surface | |

Second-Order Partial Derivatives | |

Exercises | |

Multivariable Maxima and Minima | |

Exercises | |

Constrained Maxima and Minima and Applications | |

Graphical Interpretation of Constrained Optimization Problems | |

Exercises | |

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