Overview1. FUNCTIONS AND MODELS. 1.1 Functions 1.2 Linear Functions 1.3 Quadratic Functions 1.4 Polynomial and Rational Functions 1.5 Exponential Functions and Logarithms 1.6 Function Modeling and Combining Functions. 2. THE DERIVATIVE. 2.1 Average Rate of Change 2.2 Limits and Instantaneous Rates of Change 2.3 The Derivative as a Slope: Graphical Methods 2.4 The Derivative as a Function: Algebraic Method 2.5 Interpreting the Derivative 3. DIFFERENTIATION TECHNIQUES. 3.1 Basic Derivative Rules 3.2 The Product and Quotient Rules 3.3 The Chain Rule 3.4 Exponential and Logarithmic Rules 3.5 Implicit Differentiation 4. DERIVATIVE APPLICATIONS. 4.1 Maxima and Minima 4.2 Applications of Maxima and Minima 4.3 Concavity and the Second Derivative 4.4 Related Rates. 5. THE INTEGRAL. 5.1 Indefinite Integrals 5.2 Integration by Substitution 5.3 Using Sums to Approximate Area 5.4 The Definite Integral 5.5 The Fundamental Theorem of Calculus. 6. ADVANCED INTEGRATION TECHNIQUES AND APPLICATIONS. 6.1 Integration by Parts 6.2 Area Between Two Curves 6.3 Differential Equations and Applications 6.4 Differential Equations: Limited Growth and Logistic Growth Models. 7. MULTIVARIABLE FUNCTIONS AND PARTIAL DERIVATIVES. 7.1 Multivariable Functions 7.2 Partial Derivatives 7.3 Multivariable Maxima and Minima 7.4 Constrained Maxima and Minima and Applications.
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