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 (6/97)