Catalog Description: CALCULUS WITH ANALYTIC GEOMETRY I (4) Derivatives,differentials, applications. Integration, applications. Analytic geometry. (Students may take only one course for credit from Math 110, 140 and 140A)

Prerequisite: Math 22, 26; or Math 40, or Math 41; or satisfactory performance on the mathematics proficiency examination (both algebra and trigonometry).

Text: Calculus, third edition, Stewart, Brooks/Cole Publishing

CHAPTER 1 LIMITS AND RATES OF CHANGE 
1.1  The Tangent and Velocity Problems 
1.2  The Limit of a Function
1.3  Calculating Limits Using the Limit Laws
1.5  Continuity
1.6  Tangents, Velocities and Other Rates of Change

CHAPTER 2 DERIVATIVES
2.1  Derivatives
2.2  Differentiation Formulas
2.3  Rates of Change in the Natural Sciences
2.4  Derivatives of Trigonometric Functions
2.5  The Chain Rule
2.6  Implicit Differentiation
2.7  Higher Derivatives
2.8  Related Rates
2.9  Differentials; Linear Approximations
2.10 Newton's Method

CHAPTER 3 THE MEAN VALUE THEOREM AND CURVE SKETCHING
3.1  Maximum and Minimum Values
3.2  The Mean Value Theorem
3.3  Monotonic Functions and the First Derivative Test
3.4  Concavity and Points of Inflection
3.5  Limits at Infinity; Horizontal Asymptotes
3.6  Curve Sketching
3.8  Applied Maximum and Minimum Problems
3.10 Antiderivatives  

CHAPTER 4 INTEGRALS
4.1  Sigma Notation
4.2  Area
4.3  The Definite Integral
4.4  The Fundamental Theorem of Calculus
4.5  The substitution Rule

CHAPTER 5 APPLICATIONS OF INTEGRATION
5.1  Areas between Curves
5.2  Volumes
5.3  Volumes by Cylindrical Shells

CHAPTER 6 LOGARITHMIC AND EXPONENTIAL FUNCTIONS
6.1  Inverse Functions
6.2  Exponential Functions and their Derivatives
6.3  Logarithmic Functions
6.4  Derivatives of Logarithmic Functions
6.5*  Exponential Growth and Decay
6.7  The Hyperbolic Functions