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It is the first course in the three half honors calculus sequence for college kids majoring in arithmetic, science or engineering. Topics embody limits, continuity, differentiation, purposes of differentiation, and integration. Applications of the derivative are lined in detail, including approximation of errors utilizing differentials, maxima and minima problems, curve sketching, optimization problems, and Newton’s methodology. Topics on integration embody Riemann sums, properties of definite integrals, integration by substitution and integrals involving logarithmic exponential and trigonometric functions. Introduction to analytic and numerical methods for solving differential equations. Use of arithmetic software program is an integral a part of the course.
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This is the first of three courses within the fundamental calculus sequence. Topics include the limit of a perform; the by-product of algebraic, trigonometric, exponential, and logarithmic features; and the definite integral. Applications of the by-product are covered in detail, together with approximations of error using differentials, maxima and minima issues, and curve sketching utilizing calculus.
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