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First Semester Calculus by Sigurd B. Angenent

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First Semester Calculus written by Sigurd B. Angenent . This is an other great mathematics book cover the following topics.

  • Numbers and Functions
    What is a number?, Functions, Inverse functions and Implicit functions

  • Derivatives (1)
    The tangent to a curve, An example – tangent to a parabola, Instantaneous velocity, Rates of change, Examples of rates of change, Exercises

  • Limits and Continuous Functions
    Informal definition of limits, The formal, authoritative, definition of limit, Variations on the limit theme, Properties of the Limit, Examples of limit computations, When limits fail to exist, What’s in a name?, Limits and Inequalities, Continuity, Substitution in Limits, Two Limits in Trigonometry, Exercises

  • Derivatives (2)
    Derivatives Defined, Direct computation of derivatives, Differentiable implies Continuous, Some non-differentiable functions, The Differentiation Rules, Differentiating powers of functions, Higher Derivatives, Differentiating Trigonometric functions, The Chain Rule, Exercises, Implicit differentiation,

  • Graph Sketching and Max-Min Problems
    Tangent and Normal lines to a graph, The Intermediate Value Theorem, Finding sign changes of a function, Increasing and decreasing functions, Maxima and Minima, Must there always be a maximum?, Functions with and without maxima or minima, General method for sketching the graph of a function, Convexity, Concavity and the Second Derivative, Proofs of some of the theorems, Optimization Problems

  • Exponentials and Logarithms (naturally)
    Exponents, Logarithms, Properties of logarithms, Graphs of exponential functions and logarithms, The derivative of a x and the definition of e, Derivatives of Logarithms, Limits involving exponentials and logarithms, Exponential growth and decay

  • The Integral
    Area under a Graph, When f changes its sign, The Fundamental Theorem of Calculus, The indefinite integral, Properties of the Integral, The definite integral as a function of its integration bounds, Method of substitution, Exercises

  • Applications of the integral
    Areas between graphs, Cavalieri’s principle and volumes of solids, Examples of volumes of solids of revolution, Volumes by cylindrical shells, Distance from velocity, velocity from acceleration, The length of a curve, Examples of length computations, Work done by a force, Work done by an electric current

  • APPLICABILITY AND DEFINITIONS, VERBATIM COPYING, . COPYING IN QUANTITY, MODIFICATIONS, COMBINING DOCUMENTS, COLLECTIONS OF DOCUMENTS, AGGREGATION WITH INDEPENDENT WORKS, TRANSLATION, TERMINATION, FUTURE REVISIONS OF THIS LICENSE, RELICENS

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