# MTH131: Calculus With Analytic Geometry I

## Syllabus

### 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