Applied Calculus Book

Note: Each chapter concludes with a Study Sheet, Review Exercises, and a Make It Real Project. 1. Functions and Linear Models 1.1 Functions 1.2 Linear Functions 1.3 Linear Models 2. Nonlinear Models 2.1 Quadratic Function Models 2.2 Higher Order Polynomial Function Models 2.3 Exponential Function Models 2.4 Logarithmic Function Models 2.5 Choosing a Mathematical Model 3. The Derivative 3.1 Average Rate of Change 3.2 Limits and Instantaneous Rates of Change 3.3 Limits and Continuity 3.4 The Derivative as a Slope: Graphical Method 3.5 The Derivative as a Function: Algebraic Method 3.6 Interpreting the Derivative 4. Differentiation Techniques 4.1 Basic Derivative Rules 4.2 Product Rule 4.3 Chain Rule 4.4 Exponential and Logarithmic Rules 4.5 Implicit Differentiation 5. Derivative Applications 5.1 Maxima and Minima 5.2 Applications of Maxima and Minima 5.3 Concavity and the Second Derivative 5.4 Related Rates 6. The Integral 6.1 The Indefinite Integral 6.2 Integration by Substitution 6.3 Using Sums to Approximate Area 6.4 The Definite Integral 6.5 The Fundamental Theorem of Calculus 7. Advanced Integration Techniques and Applications 7.1 Integration by Parts 7.2 Area Between Two Curves 7.3 Improper Integrals 8. Multivariable Functions and Partial Derivatives 8.1 Multivariable Functions 8.2 Partial Derivatives 8.3 Multivariable Maxima and Minima 8.4 Constrained Maxima and Minima and Applications 9. Trigonometric Functions 9.1 Trigonometric Function Equations and Graphs 9.2 Derivatives of Trigonometric Functions 9.3 Integrals of Trigonometric Functions 10. Differential Equations 10.1 Slope Fields 10.2 Euler's Method 10.3 Separable Differential Equations and Applications 10.4 Differential Equations: Limited Growth and Logistic Models 10.5 First-Order Linear Differential Equations 11. Sequences and Series 11.1 Sequences 11.2 Series and Convergence 11.3 Taylor Polynomials 11.4 Taylor Series 12. Probability and Calculus 12.1 Discrete Probability 12.2 Continuous Probability 12.3 Expected Value and Variance 12.4 Normal Distribution