Calculus

Calculus by MILES MATHIS ii Contents I GENERALITIES 1 1 CENTRAL DISCOVERIES 3 2 DEATH BY MATHEMATICS 25 3 ELEVEN BIG QUESTIONS 35 4 A REVALUATION OF TIME 47 5 ANGULAR VELOCITY 57 6 UNIFIED FIELDS IN DISGUISE 65 7 THE KINETIC ENERGY EQUATION 71 8 THE EQUATION V = V + AT 770 iii iv CONTENTS II CALCULUS 85 9 A REDEFINITION OF THE DERIVATIVE 87 9.1 The Groundwork . . . . . . . . . . . . . . . . . . . . . . . . . 91 9.2 Historical Interlude . . . . . . . . . . . . . . . . . . . . . . . . 103 9.3 The Rest of the Groundwork . . . . . . . . . . . . . . . . . . . 111 9.4 The Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 9.5 The Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . 119 9.6 Application to Physics . . . . . . . . . . . . . . . . . . . . . . 123 9.7 The Second Derivative – Acceleration . . . . . . . . . . . . . . 126 10 THE CALCULUS IS CORRUPT 133 11 DERIVATIVE FOR POWERS 139 12 DERIVATIVE FOR EXPONENTIALS 151 13 DERIVATIVE FOR ln AND 1/x 179 14 DERIVATIVE FOR log 195 15 VARIABLE ACCELERATION 199 16 CALCULUS SIMPLIFIED 211 17 TRIG DERIVATIVES 233 CONTENTS v 18 ANOTHER FATAL FLAW 239 19 NEWTON’S LEMMAE 245 20 THE EQUATION a= v²=r 257 20.1 Newton’s Derivation . . . . . . . . . . . . . . . . . . . . . . . 259 20.2 The Current Solution . . . . . . . . . . . . . . . . . . . . . . . 264 20.3 Feynman’s Variation . . . . . . . . . . . . . . . . . . . . . . . 268 20.4 My Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 20.