Calculus Concepts: An Informal Approach to the Mathematics of Change 5th edition

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• Chapter 1: Ingredients of Change: Functions an Limits
  • 1.1: Functions: Four Representations
  • 1.2: Function Behavior and End Behavior Limits
  • 1.3: Limits and Continuity
  • 1.4: Linear Functions and Models
  • 1.5: Exponential Functions and Models
  • 1.6: Models in Finance
  • 1.7: Constructed Functions
  • 1.8: Logarithmic Functions and Models
  • 1.9: Quadratic Functions and Models
  • 1.10: Logistic Functions and Models
  • 1.11: Cubic Functions and Models
  • 1.12: Cyclic Functions and Models
  • 1: Review Activities
  
  
• Chapter 2: Describing Change: Rates
  • 2.1: Measures of Change over an Interval
  • 2.2: Measures of Change at a Point—Graphical
  • 2.3: Rates of Change—Notation and Interpretation
  • 2.4: Rates of Change—Numerical Limits and Nonexistence
  • 2.5: Rates of Change Defined over Intervals
  • 2.6: Rate–of–Change Graphs
  • 2: Review Activities
  
  
• Chapter 3: Determining Change: Derivatives
  • 3.1: Simple Rate–of–Change Formulas
  • 3.2: Exponential, Logarithmic, and Cyclic Rate–of–Change Formulas
  • 3.3: Rates of Change for Functions That Can Be Composed
  • 3.4: Rates of Change of Composite Functions
  • 3.5: Rates of Change for Functions That Can Be Multiplied
  • 3.6: Rates of Change of Product Functions
  • 3.7: Limits of Quotients and L'Hôpital's Rule
  • 3: Review Activities
  
  
• Chapter 4: Analyzing Change: Applications of Derivatives
  • 4.1: Linearization and Estimates
  • 4.2: Relative Extreme Points
  • 4.3: Absolute Extreme Points
  • 4.4: Inflection Points and Second Derivatives
  • 4.5: Marginal Analysis
  • 4.6: Optimization of Constructed Functions
  • 4.7: Related Rates
  • 4: Review Activities
  
  
• Chapter 5: Accumulating Change: Limits of Sums and the Definite Integral
  • 5.1: An Introduction to Results of Change
  • 5.2: Limits of Sums and the Definite Integral
  • 5.3: Accumulation Functions
  • 5.4: The Fundamental Theorem
  • 5.5: Antiderivative Formulas for Exponential, Natural Log, and Sine Functions
  • 5.6: The Definite Integral—Algebraically
  • 5.7: Differences of Accumulated Change
  • 5.8: Average Value and Average Rate of Change
  • 5.9: Integration of Product or Composite Functions
  • 5: Review Activities
  
  
• Chapter 6: Analyzing Accumulated Change: Integrals in Action
  • 6.1: Perpetual Accumulation and Improper Integrals
  • 6.2: Streams in Business and Biology
  • 6.3: Calculus in Economics: Demand and Elasticity
  • 6.4: Calculus in Economics: Supply and Equilibrium
  • 6.5: Calculus in Probability (Part 1)
  • 6.6: Calculus in Probability (Part 2)
  • 6.7: Differential Equations: Slope Fields and Solutions
  • 6.8: Differential Equations: Proportionality and Common Forms
  • 6: Review Activities
  
  
• Chapter 7: Ingredients of Multivariable Change: Models, Graphs, Rates
  • 7.1: Multivariable Functions and Contour Graphs
  • 7.2: Cross–Sectional Models and Rates of Change
  • 7.3: Partial Rates of Change
  • 7.4: Compensating for Change
  • 7: Review Activities
  
  
• Chapter 8: Analyzing Multivariable Change: Optimization
  • 8.1: Extreme Points and Saddle Points
  • 8.2: Multivariable Optimization
  • 8.3: Optimization under Constraints
  • 8.4: Least-Squares Optimization
  • 8: Review Activities