Calculus Concepts: An Informal Approach to the Mathematics of Change, Second Edition

Contents Note: The Brief Edition ends after Section 7.4. Each chapter includes a Summary, a Concept Check, and a Review Test. 1. Ingredients of Change: Functions and Linear Models 1.1 Models, Functions, and Graphs 1.2 Functions: Discrete and Continuous 1.3 Constructed Functions 1.4 Limits: Describing Function Behavior 1.5 Linear Functions and Models Project 1.1 Tuition Fees Project 1.2 Finding Data 2. Ingredients of Change: Nonlinear Models 2.1 Exponential and Logarithmic Functions and Models 2.2 Exponential Models in Action 2.3 Logistic Functions and Models 2.4 Polynomial Functions and Models 2.5 Shifting Data 2.6 Choosing a Model Project 2.1 Compulsory School Laws Project 2.2 Fund-Raising Campaign 3. Describing Change: Rates 3.1 Change, Percentage Change, and Average Rates of Change 3.2 Instantaneous Rates of Change 3.3 Derivatives 3.4 Drawing Rate-of-Change Graphs Project 3.1 Fee-Refund Schedules Project 3.2 Doubling Time 4. Determining Change: Derivatives 4.1 Numerically Finding Slopes 4.2 Algebraically Finding Slopes 4.3 Simple Rate-of-Change Formulas 4.4 More Simple Rate-of Change Formulas 4.5 The Chain Rule 4.6 The Product Rule Project 4.1 Fertility Rates Project 4.2 Superhighway 5. Analyzing Change: Applications of Derivatives 5.1 Approximating Change 5.2 Relative and Absolute Extreme Points 5.3 Derivatives in Action 5.4 Inflection Points 5.5 Interconnected Change: Related Rates Project 5.1 Hunting License Fees Project 5.2 Fund-Raising Campaign 6. Accumulating Change: Limits of Sums and the Definite Integral 6.1 Results of Change and Area Approximations 6.2 The Definite Integral as a Limit of Sums 6.3 Accumulation Functions 6.4 The Fundamental Theorem 6.5 The Definite Integral 6.6 Additional Definite Integral Topics Project 6.1 Acceleration, Velocity, and Distance Project 6.2 Estimating Growth 7. Analyzing Accumulated Change: Integrals in Action 7.1 Differences of Accumulated Changes 7.2 Streams in Business and Biology 7.3 Integrals in Economics 7.4 Average Value and Average Rate of Change 7.5 Probability Distributions and Density Functions Project 7.1 Arch Art 8. Repetitive Change: Cycles and Trigonometry 8.1 Functions of Angles: Sine and Cosine 8.2 Cyclic Functions as Models 8.3 Rates of Change and Derivatives 8.4 Extrema and Points of Inflection 8.5 Accumulation in Cycles Project 8.1 Seasonal Sales Project 8.2 Lake Tahoe Levels 9. Ingredients of Multivariable Change: Models, Graphs, Rates 9.1 Cross-Sectional Models and Multivariable Functions 9.2 Contour Graphs 9.3 Partial Rates of Change 9.4 Compensating for Change Project 9.1 Competitive and Complementary Products Project 9.2 Expert Witness 10. Analyzing Multivariable Change: Optimization 10.1 Multivariable Critical Points 10.2 Multivariable Optimization 10.3 Optimization Under Constraints 10.4 Least Squares Optimization Project 10.1 Snow Cover Project 10.2 Carbonated Beverage Packaging 11. Dynamics of Change: Differential Equations and Proportionality 11.1 Differential Equations and Slope Fields 11.2 Separable Differential Equations 11.3 Numerically Estimating Using Differential Equations; Euler's Method 11.4 Second-Order Differential EquationsLaurel L. Carpenter is the author of 'Calculus Concepts: An Informal Approach to the Mathematics of Change, Second Edition', published 2001 under ISBN 9780618121755 and ISBN 0618121757.