MATH 1910 - Calculus I

4 sem hrs cr

This course is a study of limits and continuity of functions; derivatives of algebraic and trigonometric expressions and their applications to graphing, maxima and minima, and related rates; integration of algebraic and trigonometric expressions and area under curves. Prerequisite: At least four high school credits in college preparatory mathematics including Algebra I, Algebra II, Geometry and Trigonometry (or a Pre-Calculus course containing Trigonometry) and a minimum ACT Mathematics Subject Score of 25 or MATH 1710  and MATH 1720  or MATH 1730  and exemption from or completion of ENGL 0810  and READ 0810  

In rare and unusual circumstances, a course prerequisite can be overridden with the permission of the Department Lead for the discipline.

This course may include proctored exams which must be completed on campus or at an instructor approved proctoring center which may require additional costs to the student. Please consult your instructor for additional details.

  Formerly/Same As (Formerly MAT 2510)

Transfer (UT) or Non-Transfer Course (UN): UT

By the end of the course, students will be able to…

• fulfill the mathematics requirement for those students required to take only MATH 1910 as well as to prepare those students who are required to take MATH 1920.
• use technology in a manner that will promote better understanding of concepts introduced throughout the course.
• introduce and demonstrate the concepts of continuity and limit of a function intuitively.
• teach methods of differentiation of algebraic and trigonometric functions.
• use the derivative in sketching the graphs of algebraic and trigonometric functions and relations.
• apply the derivative to specific modeling problems involving, for example, motion, maxima and minima, and related rates.
• introduce the concept of integration, show its application to area under curves, and practice integration of algebraic and trigonometric expressions.

Student Objectives

Throughout the course, students will have the opportunity to…

• understand basic ideas about what calculus is.
• examine and determine by tables and graphs whether or not the limit of a function exists at a given value of x and if so, find that limit.
• discuss the formal epsilon and delta definition of a limit (optional).
• discuss analytic properties of the limits of algebraic and trigonometric functions; examine techniques and strategies such as substitution, cancellation, rationalizing, reduction of complex fractions, and trig identities for evaluating limits.
• indicate whether a given function is continuous or discontinuous at a given value of x or on an interval containing x and examine removable and nonremovable discontinuities.
• evaluate one-sided limits and discuss their relationship to the ideas of continuity.
• graph and investigate the greatest integer function and piece-wise functions in relation to limits and continuity. (Greatest integer function is optional.)
• evaluate infinite limits by graphic and algebraic processes and discuss their relationship to vertical asymptotes.
• find the slope of a curve at point P by use of the slope of a secant line through P and another point on the curve near P.
• find the derivative of a function by use of the definition and discuss the relationship between differentiability and continuity.
• write the equation of the line tangent to a given curve at a given point.
• differentiate functions using constant, power, constant multiple, sum, and trigonometric rules and apply to simple motion problems.
• differentiate algebraic and trigonometric functions using product, quotient, chain and general power rules and evaluate at given values of x.
• find the derivate of a function using implicit differentiation.
• find the higher order derivatives of functions by both explicit and implicit differentiation and apply to equations of motion.
• apply differentiation processes to related rates problems.
• find critical numbers and locate extrema of a function, including endpoints on an interval (endpoints optional).
• state and verify Rolle’s theorem and the mean value theorem for given functions (optional).
• determine intervals over which a curve is increasing or decreasing and determine relative maximum and minimum values of given functions by use of the first derivative.
• determine intervals of concavity, find points of inflection, and test for maxima and minima by use of the second derivative. (Maxima and minima test is optional.)
• evaluate limits at infinity graphically and algebraically and discuss their relationship to horizontal asymptotes.
• sketch the graphs of given functions by use of intercepts, asymptotes, and information obtained by use of the first and second derivatives.
• apply derivatives to solve optimization (maximum/minimum) problems.
• use Newton’s method to find zeros of functions (optional).
• understand and find differentials of functions and apply to determining error. (Error is optional.)
• define anti-differentiation; find the anti-derivate of given polynomial, power, ration, and trigonometric functions; and apply to initial value problems.
• use anti-derivatives to find the equation of motion when given acceleration or velocity of a particle at a given time (optional).
• perform operations with sigma notation and use it to find the area under the graphs of certain polynomial functions by using the definition of definite integral and rectangular subdivisions.
• study geometric and analytic properties of the definite and indefinite integral.
• study the Fundamental Theorem of Calculus and use it to evaluate definite integrals of polynomial and other algebraic relations and trigonometric functions, and apply to finding the area under curves.
• evaluate indefinite and definite integrals of algebraic and trigonometric expressions by the general power rule for integration and by u-substitution procedures.
• derive and apply the Trapezoid Rule and Simpson’s Rule to the approximation of definite integrals and analyze error of results (optional).