MAT 1095 - SURVEY OF CALCULUS

credits: 4.0
Survey of Calculus is an introduction to calculus for students who do not need the rigor or depth of the traditional Calculus sequence. Calculus is the study of functions and how those functions change. An understanding of limits and continuity will provide the foundation. From there, derivatives and integrals will be developed and methods for calculating each will be studied, as will be the Fundamental Theorem of Calculus which links these two processes. Applications of derivatives and integrals will be emphasized with special attention given to applications in business, the natural sciences, and the social sciences; this focuses our attention on algebraic, exponential, and logarithmic functions. An ALEKS score of at least 46, or equivalent coursework, is required. Objectives: A) Calculate the limits of algebraic, exponential, and logarithmic functions; B) Use the definition of continuity and determine if a function is continuous at a point, continuous on an interval, or continuous; C) Calculate derivatives of algebraic, exponential, and logarithmic functions by using the definition of the derivative and by applying derivative rules such as the product or chain rules; D) Sketch curves using the derivative and second derivative; E) Apply derivatives appropriately to real-world problems such as optimizing functions, and finding instantaneous rates of change, marginal costs and profits, and relative rates of change; F) Calculate integrals of algebraic, exponential, and logarithmic functions by using the definition of the integral and by applying methods such as u-substitution or integration by parts; G) Be able to apply the Fundamental Theorem of Calculus; H) Apply integrals appropriately to real-world problems such as finding the areas under and between curves, the average value of a function, and the net change of a function; I) Approximate derivatives and integrals given a table or a graph. Find derivatives and integrals using formulas or technology. Method of Instruction: Discussion of readings, lectures, small group work, and in-class activities. Method of Evaluation: A final grading system has not yet been established; however, a possible grading system is given below. Meets *MQR Distribution Requirement.

Prerequisite(s): An ALEKS score of at least 46, or equivalent coursework (successful completion of MAT 1030 College Algebra, MAT 1060 Modeling the Real World with Mathematics, or MAT 1090 Precalculus).