![]() Introduction: Some Advice on Problem Solvingġ.2 Substitution, or Making Things “Easy on the Eyes”Ģ.6 Roberval, Conic Sections, and the Dynamic ApproachĢ.7 Snell’s Law and the Limitations of Adequalityģ. The text also incorporates curated activities from the TRansforming Instruction in Undergraduate Mathematics Instruction via Primary Historical Sources (TRIUMPHS) project to provide students with ample opportunities to develop relevant competencies.ĭifferential Calculus: From Practice to TheoryĠ.2 Some (Possibly Startling) Choices We’ve MadeĠ.5 Rantings From the Cranky Old Guys in the Back of the Roomġ. This approach is more historically accurate than the usual development of calculus and, more importantly, it is pedagogically sound. At that point, the foundational ideas (limits, continuity) are developed to replace infinitesimals, first intuitively then rigorously. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus.
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