MATH 140
    
    COURSE DESCRIPTION:  (GQ) Calculus with Analytic Geometry I (4:4:0)
    Derivatives, differentials, applications, integrals.  Students may
    take only one course for credit from among MATH 110, 140, 140A and
    140B.  During Spring and Fall semesters the course is offered in 
    60 fifty minute lectures, four per week; in the summer session it
    is offered in 40 seventy-five minute lectures, five per week.
    
    PREREQUISITES: MATH 022, 026; or MATH 040; or MATH 41; or
    satisfactory performance on the mathematics (both algebra and
    trigonometry) proficiency examination.

                                    TOPICS
    
    LIMITS AND RATES OF CHANGE
         The Tangent and Velocity Problems
         The Limit of a Function
         Calculating Limits using the Limit Laws
         The Precise Definition of a Limit
         Continuity
         Tangents, Velocities, and Other Rates of Change
    
    THE DERIVATIVE
         Derivatives
	 Differentiation Formulas
	 Rates of Change in the Natural and Social Sciences
 	 Derivatives of Trigonometric Functions
	 The Chain Rule
	 Implicit Differentiation
	 Higher Derivatives
	 Related Rates
	 Differentials; Linear and Quadratic Approximations
	 Newton's Method
    
    THE MEAN VALUE THEOREM AND CURVE SKETCHING
         Maximum and Minimum Values
	 The Mean Value Theorem
	 Monotonic Functions and the First Derivative Test
	 Concavity and Points of Inflection
	 Limits at Infinity: Horizontal Asymptotes
	 Curve Sketching
	 Graphing with Calculus and Calculators
	 Applied Maximum and Minimum Problems
	 Applications to Economics
	 Antiderivatives
    
    INTEGRALS
         Sigma Notation
	 Area
	 The Definite Integral
	 The Fundamental Theorem of Calculus
	 The Substitution Rule

    APPLICATIONS OF INTEGRATION
	 Areas between Curves
	 Volume
	 Volumes by Cylindrical Shells
	 Work
	 Average Value of a Function
    
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