9/17/2023 0 Comments Applied calculus textbook![]() ![]() This course provides a unique supplement to a course in single-variable calculus. With real practitioners as your guide, you’ll explore these situations in a hands-on way: looking at data and graphs, writing equations, doing calculus computations, and making educated guesses and predictions. How Einstein’s Energy Equation, E=mc2 is an approximation to a more complicated equation.How statisticians use functions to model data, like income distributions, and how integrals measure chance.How the Lotka-Volterra predator-prey model was created to answer a biological puzzle.How biologists use differential equation models to predict when populations will experience dramatic changes, such as extinction or outbreaks.How an x-ray is different from a CT-scan, and what this has to do with integrals.How economists model interaction of price and demand using rates of change, in a historical case of subway ridership. ![]() How standardized test makers use functions to analyze the difficulty of test questions. ![]() Through a series of case studies, you’ll learn: The course is part of the Ohio Transfer Module and is also named TMM005.In this course, we go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand how calculus and mathematical models play a role in their work. This work was completed and the course was posted in February 2019. The Calculus I course was developed through the Ohio Department of Higher Education OER Innovation Grant. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges the Saylor Foundation has modified some WSBCTC materials. This free course may be completed online at any time. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations find extreme values of modeling functions given by formulas or graphs predict, construct, and interpret the shapes of graphs solve equations using NewtonĺÎĺ_ĺĚĺ_s Method find linear approximations to functions using differentials festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results. ![]() Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals. The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. For a more traditional text designed for classroom use, see Fundamentals of Calculus (). This short text is designed more for self-study or review than for classroom use full solutions are given for nearly all the end-of-chapter problems. ![]()
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