Calculus Differential and Integral

This book is designed as an advanced guide to Calculus: limits of trigonometric functions, infinite limits, continuity, secant line and tangent line, derivative rules, trigonometric functions, chain rule, higher order derivatives, implicit derivation, rates of change, differentials,maximum and minimum, monotony and concavity, local extremes, graphing functions, mean value theorem, indefinite integrals, methods: decomposition, change of variable, integration by parts, trigonometric, rational functions and partial fractions, substitutions to rationalize, definite integral, area by inscribed and circumscribed polygons, Riemann sums, first and second fundamental theorem, area under the curve, area between two curves, symmetry and periodicity, volumes of revolution: discs, washers, cylindrical shells, arc length and lateral surface, indeterminate forms, infinite limits of integration,infinite integrands, functions: logarithmic, exponential, trigonometric,hyperbolic, inverse, introduction to differential equations, miscellaneous exercises. This is including the deduction of many formulas to clarify the concepts and meet all the needs of the students to reach the fundamentals of calculus.