Math& 151 ~ Calculus I  
 
 
 

Course Description
Limits and continuity, differentiation and applications, Mean value theorem, applications of differentiation, related rates, curve sketching, min-max problems, concavity, and anti-derivatives.

Pre-requisite
Math 142 with a grade of C or higher, or equivalent math placement score.

Mode of Delivery (Modes)
Lecture

Offered
Fall, Winter, Spring

Required for:
MATH 152, MATH 204, PHYS 221 (or concurrent), ENGR &214


Course Content

Text: Calculus: Early Transcendentals, 5th Ed., Stewart, Cengage

1. Functions and Models
1.1 Four Ways to Represent a Function
1.2 Mathematical Models: A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4Graphing Calculators and Computers
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
1.7 Principles of Problem Solving

2. Limits and Derivatives
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function

3. Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic Functions
3.7 Rates of Change in the Natural and Social Sciences
3.8 Exponential Growth and Decay
3.9 Related Rates
3.10 Linear Approximations and Differentials
3.11 Hyperbolic Functions

4. Applications of Differentiation
4.1 Maximum and Minimum Values
4.2 Applied Project: The Calculus of Rainbows
4.3 The Mean Value Theorem
4.4 How Derivatives Affect the Shape of a Graph
4.5 Indeterminate Forms and L'Hospital's Rule
4.6 Summary of Curve Sketching
4.7 Graphing with Calculus and Calculators
4.8 Optimization Problems
4.9 Applications to Business and Economics
4.10 Newton's Method
4.11 Antiderivatives