# 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**

evaluate

**limits**of functionsstate and use the

**epsilon-delta definition of the limit**apply the concept of continuity, including the

**Intermediate Value Theorem**locate

**asymptotes**of graphs of functions

**Quiz 2**

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**differentiate**functions using the rules for differentiation:**power, product, quotient, and chain rules****differentiate**exponential, logarithmic, and trigonometric functions

**Quiz 3**

locate

**extreme values**and**points of inflection**of graphs of functionsfind and apply

**higher-order derivatives**and understand how they relate to the graph of a functionapply

**Newton's Method**apply

**Rolle's Theorem and the Mean Value Theorem**

**Quiz 4**

solve applied

**optimization**problems

**Quiz 5**

use

**implicit differentiation**and solve**related rates**problems

**Quiz 6**

state and use the

**Fundamental Theorem of Calculus**