| Prerequisites: MATH 151
Frequency: Fall/Spring Terms
Credit: (4-2)5
Content: Sequences, infinite series, power series, Taylor's series.
Vectors, lines and planes in space. Space curves. Limit, continuity and
differentiability of function of several variables, extreme values, method
of Lagrange multipliers. Vector valued functions, their continuity and
differentiation. Double and triple integrals with applications. Line integrals.
Green’s Theorem.
Goals: Calculus was first discovered to meet the needs of the
scientists of the sixteenth and seventeenth centuries. Diferential calculus
deals with the problem of calculating rates of change. It enables us to
define slope of curves, to calculate velocities, accelerations of moving
bodies and to predict the times when planets
would be closest together or farthest apart. Integral calculus
deals with the problem of determining a function from information about
its rate of change. It enables us to calculate the future location of a
body from its present position, to find the areas of irregular regions
in the plane, to measure the lengths of curves, and to find the volumes
and masses of arbitrary solids. The goal of this course is to present a
modern view of calculus enhanced by the use of technology.
Course Outline:
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(1 Week) Sequences, Series. Convergence
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(1 Week) Absolute Convergence. Power Series
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(1 Week) Taylor and Binomial Series
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(1 Week) Vectors in Space
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(1 Week) Planes, Lines. Quadratic Surfaces
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(1 Week) Functions, continuity and partial derivatives of
functions of several variables.
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(1 Week) Differentials. The Gradient. The Jacobian
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(1 Week) Extrema (Linear Programming omitted)
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(2 Week) Double integrals, trible integral in various coordinate
systems.
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(1 Week) Vector Functions and Parametrization.
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Vector and Scalar Fields.
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(1 Week) The Line Integral. Green’s Theorem
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(1 Week) Catch up-Review
Suggested textbook: Robert A.Adams; Calculus: A Complete
Course, 3rd Edition, Addison-Wesley, 1995
Courrent
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