Calculus for Business and Social Science Angela Allen & Patrick Orchand

Calculus for Business and Social Sciences by Angela J. Allen and Patrick J. Orchard is an applied calculus textbook designed for students in business, economics, and the social sciences who need a practical and conceptual understanding of calculus without the heavy theoretical emphasis found in traditional mathematics texts. The book emphasizes real-world applications, intuitive explanations, and skill development that directly support decision-making, modeling, and analysis in applied fields.

The text begins with a thorough exploration of limits and continuity, establishing the foundation for all subsequent topics. Limits are introduced graphically, numerically, and algebraically, allowing students to build intuition about how functions behave near specific points and at infinity. Continuity is then framed from a calculus perspective, clarifying when functions behave smoothly and how this relates to practical modeling situations.

Building on this foundation, the book introduces derivatives as rates of change and slopes of tangent lines, with strong connections to average and instantaneous change. Derivative rules, including the product rule, quotient rule, and chain rule, are developed gradually, with consistent attention to marginal analysis—an essential concept in business and economics. Applications such as cost, revenue, profit, and elasticity highlight how derivatives describe how quantities respond to changes in inputs.

The text then moves into curve sketching and optimization, showing students how derivatives can be used to analyze increasing and decreasing behavior, identify extrema, determine concavity, and solve optimization problems. These topics are directly connected to real-world scenarios such as maximizing profit, minimizing cost, and identifying points of diminishing returns.

Integration is introduced through antidifferentiation and the definite integral, with a focus on understanding accumulation, area under curves, and net change. The Fundamental Theorem of Calculus links derivatives and integrals, reinforcing the unity of the subject. Applications include total cost and revenue, consumer and producer surplus, and average value of a function.

Pedagogically, the book emphasizes learning objectives, clear definitions, worked examples, and frequent “Try-It” exercises that encourage active engagement. Practice problems are organized into Basic Skills, Intermediate Skills, Mastery, and Communication categories, supporting students at different stages of learning. Overall, the text provides a coherent, accessible, and application-driven introduction to calculus tailored to the needs of business and social science students.