# MAT 191 Calculus I

Instructor:
Office:
Office hours:
Phone:
Email:

### Course Description

Limits, continuity, derivatives, differentiation formulas, applications of derivatives, introduction to integration, fundamental theorem of calculus, inverse functions.

MAT 191 meets for five hours of lecture per week.

### Prerequisites

MAT 153 or equivalent with a grade of "C" or better.

### Objectives

After completing MAT 191 the student will be able to

• Demonstrate understanding of the four basic concepts of one-variable calculus; the limit, the concept of continuity, the derivative and the integral of a function of one variable
• Use the rules of differentiation to compute derivatives of algebraic and trigonometric functions
• Use derivatives to solve problems involving rates of change, tangent lines, velocity (speed), acceleration, optimization, and related rates.
• Investigate the graph of a function with the aid of its first and second derivatives: asymptotes, continuity, tangency, monotonicity, concavity, extrema, inflection points, etc.
• Demonstrate understanding of the meanings of the indefinite integral and the definite integral of a function of one variable, and their relationship to the derivative of a function via the Fundamental Theorem of Calculus
• Use rules of integration including the Substitution Rule to evaluate indefinite and definite integrals
• Differentiate Exponential, Logarithmic, and Inverse Trigonometric Functions
• Use l'Hospital's Rule

### Expected outcomes

Students should be able to demonstrate through written assignments, tests, and/or oral presentations, that they have achieved the objectives of MAT 191.

### Method of Evaluating Outcomes

Evaluations are based on homework, class participation, short tests and scheduled examinations covering students' understanding of topics covered in MAT 191.

### Text

Essential Calculus, by James Stewart, Brooks/Cole 2007. Covers MAT 191, MAT 193, and MAT 211.

#### Course Outline

MAT 191 covers the following topics from chapters 1-5 in the text.

1. FUNCTIONS AND LIMITS

• Functions and Their Representations
• A Catalog of Essential Functions
• The Limit of a Function
• Calculating Limits
• Continuity.
• Limits Involving Infinity

2. DERIVATIVES

• Derivatives and Rates of Change
• The Derivative as a Function
• Basic Differentiation Formulas
• The Product and Quotient Rules
• The Chain Rule
• Implicit Differentiation
• Related Rates
• Linear Approximations and Differentials

3. APPLICATIONS OF DIFFERENTIATION

• Maximum and Minimum Values
• The Mean Value Theorem
• Derivatives and the Shape of Graphs
• Curve Sketching
• Optimization Problems
• Newton's Method
• Antiderivatives

4. INTEGRALS

• Areas and Distances
• The Definite Integral
• Evaluating Definite Integrals
• The Fundamental Theorem of Calculus
• The Substitution Rule

5. INVERSE FUNCTIONS

• The Natural Logarithmic Function
• The Natural Exponential Function<
• General Logarithmic ad Exponential Functions<
• Exponential Growth and Decay
• Inverse Trigonometric Functions
• Hyperbolic Functions
• Indeterminate Forms and l'Hospital Rule

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in MAT 191. The instructor determines the relative weights of these factors.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates and Make-Up Work

Due dates and policy regarding make-up work are set by the instructor.

### Schedule of Examinations

The instructor sets all test dates except the date of the final exam. The final exam is given at the date and time announced in the Schedule of Classes.