MA 16010 - Spring 2020
Curve Sketching Classwork - PDF Free Download
Course Outline: If you draw the graph of a function and then pick a point on the graph, you should be able to draw the line tangent to the graph at that point. You can then estimate the slope of this tangent line by taking the quotient of the rise over the run. The beautiful notion is that for most functions given by a formula one can find another formula called the derivative which will enable you to find the exact value of the slope at any given point on the function. This may not seem to be such a big deal at first, but consider the fact that at points where a smooth function reaches a maximum or minimum value the slope of the tangent line must be 0. Thus, one can locate the exact maximum and minimum values achieved by a smooth function by using its derivative to locate the places where the function has a flat tangent line. One can probably imagine that this is an important idea. For example, an economist may wish to determine the number of units to produce in order to maximize profit.
calculus curve sketching
Fresco in the Library of El Escorial, Madrid. Part I includes functions, limits, continuity, differentiation of algebraic and trigonometric functions, mean value theorem, and various applications. Part II includes Riemann sums and integrals, techniques and applications of integration, improper integrals, transcendental functions logarithms, exponential functions, and inverse trigonometric functions , sequences, and series. Though not all results are derived rigorously, care is taken to distinguish intuitive arguments from rigorous proofs. Math and each fulfill the Formal Analysis requirement.
For students in Management. Limits, continuity, differentiation of algebraic and exponential functions. Applications, partial derivatives and applications.