alittlebitofcalculus-pdf-january2011-111112001007-phpapp01

S i n t 1 g t 2 2 yt 1 h1 t1 t t 2 t time even

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Unformatted text preview: 1 h1 t1 T T /2 t Time Even if the object is projected ver tically up (θ =π/2), this is what the graph of the VERTICAL POSITION will look like over the time inter val [0, T]. In y(t) = u . s i n θ . t -- 1 g t 2 when θ = π/2 when -- 2 1 g t 2, again a parabolic function. we get y(t) = u . t -- -2 The differentiation o peration allows us to find the VERTICAL SPEED from d ifferentiation the VERTICAL POSITION. And the integration o peration allows us to find i ntegration the CHANGE in the VERTICAL POSITION from the VERTICAL SPEED. The book is divided into 4 parts. On initial reading the student may skip part 3. iv CONTENTS 1 . INTRODUCTION Par t 1 : CONTINUITY 1 2. NUMBERS AND THE NUMBER LINE 8 4. TENDS TO and LIMIT 14 3. REALS, COMPLETE, CONTINUOUS 13 5. INFINITESIMALS 16 6. x and INSTANT 19 7. SINGLE VALUED FUNCTIONS 21 8. LIMIT of a Function 24 10. VALUE versus LIMIT 37 9. Analysis of Limits 34 11. CONTINUITY of a Function Par t 2 : DIFFERENTIATION 12. INSTANTANEOUS RATE OF CHANGE of 13. INSTANTANEOUS RATE OF CHANGE of 14. INSTANTANEOUS RATE OF CHANGE of 15. Differentiation from FIRST PRINCIPLES 16. Tables and Rules 17. Units of Measure 39 y(t) 57 xn 65 f(x) 61 71 79 84 18. DIFFERENTIABILITY 86 v Par t 3 : ANALYTICAL GEOMETRY 19. FIRST DERIVATIVE = Slope of Tangent 98 20. Angle of Intersection 104 22. Decreasing, MINIM UM , Increasing 113 21. Increasing, MA XIM UM , Decreasing 23. MA XIMA and M INIM A 24. Points of INFLEXIO N Par t 4 : INTEGRATION 108 116 121 25. F(x) = ANTIDERIVATIVE {f(x)} 129 27. F(x) = ANTIDERIVATIVE {f(x)} = f(x)dx 136 26. F(x) = area under f(x) = f(x)dx b 131 28. f(x)dx = CHANGE in F(x) 138 29. Direction of Integrationand CHANGE in F(x) 140 31. Constant of Integration 163 a 30. Area under f(x) and Plotting FC ( x) 32. INDEFINITE and DEFINITE INTEGRAL 33. INTEGRABLE 34. Applications of Integration vi 157 167 170 178 1. INTRODUCTION Microbiologists work with small things called cells that form the basic unit of matter they are dealing with. Physicists and chemists work with molecules representative of a compound or atoms representative of...
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This note was uploaded on 11/29/2012 for the course PHYSICS 105 taught by Professor Tamerdoğan during the Fall '09 term at Middle East Technical University.

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