This first course in calculus and analytic geometry covers limits and continuity, the definition of the derivative, rate of change, and slope, derivatives of polynomial, rational, trigonometric, exponential, and logarithmic functions, the chain rule, implicit differentiation, approximation by differentials, L'Hopital's Rule, higher order derivatives, Rolle's Theorem, the Mean Value Theorem, applications of derivatives, an introduction to antiderivatives and definite integrals, areas and the Fundamental Theorem of Calculus. Prereq: C or better in MTH111 and 112; or C or better in MTH129 and MTH130; or C or better in MTH130 and required placement score; or placement by assessment. IntroductionAs you probably know, geometry is the study of shapes and algebra is the study of relationships. Calculus is the mathematical study of change.Calculus has two major branches: **Differential calculus**(concerning rates of change and slopes of curves)**Integral calculus**(concerning accumulation of quantities and the areas under and between curves)
fundamental theorem of calculus. Both branches make use of the fundamental notions of limits which is basically what separates algebra from calculus.Today, calculus has widespread uses in science, engineering and economics and can help solve many problems that elementary algebra alone cannot. |