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

5. 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

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

7. differentiate exponential, logarithmic, and trigonometric functions

• Quiz 3

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

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

10. apply Newton's Method

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

• Quiz 4

12. solve applied optimization problems

• Quiz 5

13. use implicit differentiation and solve related rates problems

• Quiz 6

14. state and use the Fundamental Theorem of Calculus

• Final Exam

  • The final exam is a cumulative exam involving all of the sections combined.

  • The REVIEW link above links to a previous final exam with a solution guide.