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Fall and Spring: 10 units Definite and indefinite integrals; inverse functions, logarithmic, exponential, and hyperbolic functions; applications of integration, integration by substitution and by parts. Integration by trigonometric substitution and partial fractions; arclength; improper integrals; Simpson's and Trapezoidal Rules for numerical integration; separable differential equations, first order linear differential equations, homogeneous second order linear differential equations with constant coefficients. 3 hours lecture, 2 hours recitation. Prerequisite: 21-115. Includes the second half of 21-120 and the first half of 21-122 and is offered to achieve flexible placement of entering students. Suggestions of what a student starting calculus should know. |