May 19, 2019
MT 181 - Calculus and Analytic Geometry I
Credit Hours: 4
Intended for mathematics, science and engineering students, or anyone interested in seeing a rigorous approach to calculus. First in a four semester sequence. Topics from analytic geometry, limits, the derivative and its applications, continuity, integration and transcendental functions.
Fulfills SUNY General Education -- Mathematics.
Upon completion of this course, the student will be able to:
- understand the meaning of the limit of a function, and evaluate limits of algebraic and trigonometric functions, including one-sided limits, by using limit theorems and algebraic techniques;
- define, understand, and determine continuity of a function at a point and on an interval;
- define the limit of a function;
- define precisely the derivative of a function and compute derivatives from this definition;
- interpret the derivative as instantaneous velocity, slope of the tangent line, and instantaneous rate of change of the function;
- compute the derivatives of algebraic functions using differentiation rules;
- compute higher order derivatives and interpret the second derivative of a rectilinear motion function as instantaneous acceleration;
- differentiate expressions involving exponential and logarithmic functions;
- compute derivatives involving trigonometric functions;
- compute derivatives involving inverse trigonometric functions;
- compute derivatives of composite functions using the Chain Rule;
- perform implicit differentiation;
- solve related rate problems;
- define and compute and use the differentials dx and dy;
- state and use Rolle's Theorem and the Mean Value Theorem for derivatives;
- compute limits of indeterminate forms by using L'Hopital's Rule;
- make an accurate sketch of the graph of a function using information obtained from the calculus including critical numbers, the first and second derivatives tests for local extrema, test for increasing and decreasing functions, test for concavity, inflection points, and limits at infinity and infinite limits to determine horizontal and vertical asymptotes of a function;
- use a scientific graphics calculator and/or computer software package to reinforce and enhance topics involving limits, derivatives and anti-derivatives, integrals, and graphs;
- solve applied extreme value problems;
- define and compute anti-derivatives of elementary functions;
- find the area of a region bounded by a non-negative continuous function;
y = f(x), the x-axis, x = a, and x = b using the definition of area as a limit.
- define and understand a partition, norm of a partition, and Riemann sum, and use these concepts to define the definite integral of a function as a limit of sums;
- know and use the Fundamental Theorems of Calculus to evaluate definite integrals;
- evaluate definite and indefinite integrals by the method of substitution.
Prerequisites: MT 180 or equivalent and appropriate mathematics level code.*
F/S (C, N, S)
*Level code is determined by Mathematics Department placement test and/or successful completion of mathematics courses.