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Understanding Basic Calculus by S.K.Chung

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Understanding Basic Calculus written by S.K.Chung cover the following topics.

  • Revision
    Exponents, Algebraic Identities and Algebraic Expressions, Solving Linear Equations, Solving Quadratic Equations, Remainder Theorem and Factor Theorem, Solving Linear Inequalities, Lines, Pythagoras Theorem, Distance Formula and Circles, Parabola, Systems of Equations

  • Sets, Real Numbers and Inequalities
    Sets (Introduction, Set Operations), Real Numbers (The Number Systems, Radicals), Solving Inequalities (Quadratic Inequalities, Polynomial Inequalities with degrees ≥ 3)

  • Functions and Graphs
    Functions, Domains and Ranges of Functions, Graphs of Equations, Graphs of Functions, Compositions of Functions, Inverse Functions, More on Solving Equations

  • Limits
    Introduction, Limits of Sequences, Limits of Functions at Infinity, One-sided Limits, Two-sided Limits, Continuous Functions

  • Differentiation
    Derivatives, Rules for Differentiation, Higher-Order Derivatives

  • Applications of Differentiation
    Curve Sketching (Increasing and Decreasing Functions, Relative Extrema, Convexity, Curve Sketching), Applied Extremum Problems (Absolute Extrema, Applied Maxima and Minima, Applications to Economics)

  • Integration
    Definite Integrals, Fundamental Theorem of Calculus, Indefinite Integrals, Application of Integration

  • Trigonometric Functions
    Angles, Trigonometric Functions, Differentiation of Trigonometric Functions

  • Exponential and Logarithmic Functions
    Exponential Functions, Logarithmic Functions, Differentiation of Exp and Log Functions

  • More Differentiation
    Chain rule, Implicit Differentiation, More Curve Sketching, More Extremum Problems

  • More Integration
    More Formulas, Substitution Method, Integration of Rational Functions, Integration by Parts, More Applications of Definite Integrals

  • A Answers

  • B Supplementary Notes
    Mathematical Induction, Binomial Theorem, Mean Value Theorem, Fundamental Theorem of Calculus

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