MTH131: Calculus With Analytic Geometry I

Course Description

  • This first course in calculus presents analytic geometry and the calculus of algebraic and transcendental functions including the study of limits, derivatives, differentials and an introduction to integration.

  • The techniques of calculus will be used to analyze functions and their graphs, solve real-world applications, develop computational and numerical methods, and analyze the relationship between differentiation and integration using the Fundamental Theorem of Calculus.

Course Objectives

  • Throughout this course, the student will learn to:

    • Quiz 1

  1. evaluate limits of functions

  2. state and use the epsilon-delta definition of the limit

  3. apply the concept of continuity, including the Intermediate Value Theorem

  4. locate asymptotes of graphs of functions

  • Quiz 2

  1. use the definition of the derivative and interpret the derivative as both an instantaneous rate of change and as the slope of the tangent line to a function at a point

  2. differentiate functions using the rules for differentiation: power, product, quotient, and chain rules

  3. differentiate exponential, logarithmic, and trigonometric functions

  • Quiz 3

  1. locate extreme values and points of inflection of graphs of functions

  2. find and apply higher-order derivatives and understand how they relate to the graph of a function

  3. apply Newton's Method

  4. apply Rolle's Theorem and the Mean Value Theorem

  • Quiz 4

  1. solve applied optimization problems

  • Quiz 5

  1. use implicit differentiation and solve related rates problems

  • Quiz 6

  1. state and use the Fundamental Theorem of Calculus