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Preface | |
Introduction | |
Functions | |
Functions and Their Graphs | |
Some Important Functions | |
The Algebra of Functions | |
Zeros of Functions-The Quadratic Formula and Factoring | |
Exponents and Power Functions | |
Functions and Graphs in Applications | |
The Derivative | |
The Slope of a Straight Line | |
The Slope of a Curve at a Point | |
The Derivative | |
Limits and the Derivative | |
Differentiability and Continuity | |
Some Rules for Differentiation | |
More About Derivatives | |
The Derivative as a Rate of Change | |
Applications of the Derivative | |
Describing Graphs of Functions | |
The First and Second Derivative Rules | |
The First and Second Derivative Tests and Curve Sketching | |
Curve Sketching (Conclusion) | |
Optimization Problems | |
Further Optimization Problems | |
Applications of Derivatives to Business and Economics | |
Techniques of Differentiation | |
The Product and Quotient Rules | |
The Chain Rule and the General Power Rule | |
Implicit Differentiation and Related Rates | |
Logarithm Functions | |
Exponential Functions | |
The Exponential Function ex | |
Differentiation of Exponential Functions | |
The Natural Logarithm Function | |
The Derivative of ln x | |
Properties of the Natural Logarithm Function | |
Applications of the Exponential and Natural Logarithm Functions | |
Exponential Growth and Decay | |
Compound Interest | |
Applications of the Natural Logarithm Function to Economics | |
Further Exponential Models | |
The Definite Integral | |
Antidifferentiation | |
Areas and Riemann Sums | |
Definite Integrals and the Fundamental Theorem | |
Areas in the xy-Plane | |
Applications of the Definite Integral | |
Functions of Several Variables | |
Examples of Functions of Several Variables | |
Partial Derivatives | |
Maxima and Minima of Functions of Several Variables | |
Lagrange Multipliers and Constrained Optimization | |
The Method of Least Squares | |
Double Integrals | |
The Trigonometric Functions | |
Radian Measure of Angles | |
The Sine and the Cosine | |
Differentiation and Integration of sin t and cos t | |
The Tangent and Other Trigonometric Functions | |
Techniques of Integration | |
Integration by Substitution | |
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