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Sách: Calculus

CalculusPublisher: Wikibooks 2011Number of pages: 456Description:This wikibook aims to be a quality calculus textbook through which users may master the discipline. Standard topics such as limits, differentiation and integration are covered as well as sequences and series, multivariable and differential calculus. | 1 CALCULUS Book 1 by Peter J. Ponzo 2 TABLE OF CONTENTS EXAMPLE PROBLEMS.5 ASSORTED PROBLEMS.5 LECTURE 0.8 SOME BASICS.8 NUMBERS . and INFINITY.8 EQ f 5 0 . 8 5 is NOT a number.8 INEQUALITIES. 8 FUNCTIONS.9 vertical line test .9 functions and their domain.10 ABSOLUTE VALUES.10 To plot y f x .11 SOME TRIG IdEnTiTIeS.11 the RADIAN measure of an angle.11 SOME TRIG GRAPHS. 12 SOME GEOMETRY. 13 LOGARITHMS and EXPONENTIALS. 13 exponential functions.13 logarithmic function. 13 ODDS n Ends.14 geometric series.14 Sigma notation.15 MAPLE.15 LECTURE 1.15 LIMITS.15 LIMIT RULES.17 ONE SIDED LIMITS.19 LECTURE 2.20 INFINITE LIMITS. 20 ASYMPTOTES. 21 CONTINUOUS FUNCTIONS.22 LECTURE 3. .24 TECHNIQUES FOR EVALUATING LIMITS WHEN THE .24 The form EQ f . 24 The form TO - rc .24 The form EQ f 0 0 . 24 Reduce the given limit to one you know.24 to make tea.24 the SQUEEZE THEOREM.26 the graph of y f x sin x.27 LECTURE 4. 28 the DERIVATIVE.28 the DIFFERENTIAL.30 more on DERIVATIVES.31 DIFFERENTIATION RULES. 31 the CHAIN RULE. 32 HIGHER DERIVATIVES.32 concave up. 33 concave down. 33 the Logistic Equation.34 3 velocity.34 acceleration.34 LECTURE 5.34 IMPLICIT DIFFERENTIATION TRANSCENDENTAL FUNCTIONS.34 IMPLICIT DIFFERENTIATION. .34 the slope at a point x y .35 greatest integer function.37 trig exponential and log functions.37 weird limits.37 the TRIG FUNCTIONS and their derivatives.38 the EXPONENTIAL and LOG functions.38 ln x.38 LECTURE 6.39 INVERSE fUncTiONS. 39 horizontal line test.40 TESTING TO SEE IF A FUNCTION HAS AN iNVeRsE.40 Examples of Inverses.41 the Derivative of an Exponential Function.41 LOGARITHMIC DIFfErENTIATION. .42 About Exponential Growth.43 About the number e.43 ODDS n ENDS ON CURVE SKETCHING.45 Even and Odd Functions.45 Quick Dirty Curve Sketching.46 LECTURE 7. 47 MORE ON INVERSE FUNCTIONS.47 the INVERSE TANGENT.49 the INVERSE SINE.49 restricting the domain.52 Check the dimensions.52 the limit of EQ f sin A A .54 y sin x with x in DEGREES.54 LECTURE 8. .55 ABSOLUTE .