Applied CALC (with Mathematics CourseMate with eBook Printed Access Card)
1. FUNCTIONS AND LINEAR MODELS. 1.1 Functions. Function Notation. Graphs of Functions. Domain and Range. Exercises. 1.2 Linear Functions. Intercepts. Linear Equations. Finding the Equation of a Line. Other Forms of Linear Equations. Graphing Linear Functions. Exercises. 2. NONLINEAR MODELS. 2.1 Quadratic Function Models. Exercises. 2.2 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. 3. THE DERIVATIVE. 3.1 Average Rate of Change. Graphical Interpretation of the Difference Quotient. Exercises. 3.2 Limits and Instantaneous Rates of Change. Limits. Exercises. 3.3 The Derivative as a Slope: Graphical Methods. Tangent-Line Approximations. Numerical Derivatives. Exercises. 3.4 The Derivative as a Function: Algebraic Method. Estimating Derivatives. Exercises. 3.5 Interpreting the Derivative. Exercises. 4. DIFFERENTIATION TECHNIQUES. 4.1 Basic Derivative Rules. Derivative Notation. The Constant Rule. The Power Rule. Constant Multiple Rule. Sum and Difference Rule. Exercises. 4.2 The Product and Quotient Rules. Exercises. 4.3 The Chain Rule. Composition of Functions. The Chain Rule. Chain Rule: Alternative Form. Exercises. 4.4 Exponential and Logarithmic Rules. Exponential Rule. Logarithmic Rule. Exercises. 4.5 Implicit Differentiation. Exercises. 5. DERIVATIVE APPLICATIONS. 5.1 Maxima and Minima. Continuity. Relative and Absolute Extrema. Critical Values. The First Derivative Test. Exercises. 5.2 Applications of Maxima and Minima. Revenue, Cost, and Profit. Area and Volume. Exercises. 5.3 Concavity and the Second Derivative. Concavity. The Second Derivative Test. Point of Diminishing Returns. Position, Velocity, and Acceleration. Curve Sketching. Exercises. 5.4 Related Rates. Exercises. 6. THE INTEGRAL. 6.1 Indefinite Integrals. Basic Integration Rules. Indefinite Integral Applications. Exercises. 6.2 Integration by Substitution. Differentials. Integration by Substitution. Exercises. 6.3 Using Sums to Approximate Area. Exercises. 6.4 The Definite Integral. Summation Notation. The Definite Integral. Definite Integral Properties. Exercises. 6.5 The Fundamental Theorem of Calculus. Changing Limits of Integration. Exercises. 7. ADVANCED INTEGRATION TECHNIQUES AND APPLICATIONS. 7.1 Integration by Parts. Exercises. 7.2 Area Between Two Curves. Difference of Accumulated Changes. Exercises. 7.3 Differential Equations and Applications. Newton's Law of Heating and Cooling. Exercises. 7.4 Differential Equations: Limited Growth and Logistic Growth Models. Limited Growth Model. Logistic Growth Model. Exercises. 8. MULTIVARIABLE FUNCTIONS AND PARTIAL DERIVATIVES. 8.1 Multivariable Functions. Exercises. 8.2 Partial Derivatives. Cross Sections of a Surface. Second-Order Partial Derivatives. Exercises. 8.3 Multivariable Maxima and Minima. Exercises. 8.4 Constrained Maxima and Minima and Applications. Graphical Interpretation of Constrained Optimization Problems. Exercises.