This course module is designed to accompany the first semester of an introductory honours calculus course. The course is intended primarily for students who need or expect to pursue further studies in mathematics, physics, chemistry, engineering and computer science. Topics include: trigonometry including the compound angle formulas; inequalities and absolute values; limits and continuity using rigorous definitions, the derivative and various applications (extreme, related rates, graph sketching); Rolle's Theorem and the Mean Value Theorem for derivatives; the differential and anti-differentiation; the definite integral with application to area problems; the Fundamental Theorem of Calculus; logarithmic and exponential functions; the Mean Value Theorem for Integrals.
This material has been used at the University of Guelph for the last three years, and was used by approximately 500 students each time. This updated version incorporates some improvements and minor corrections found during the first two years of use. The course module consists of 11 test banks and 11 assignments, designed to be used weekly. Almost all questions are algorithmic. About half are Maple graded. Many are created using a multi-part format which provides online questions where students produce all the steps they would produce in a full written solution on a midterm or final.
For more information about how this material is structured, and for some sample tests, view the preview document.
