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Course Syllabus
Organization:
Subject:
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New Uzbekistan University
MATH 111- Calculus 1
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Credit units:
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6 ECTS
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Instructor(s):
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Dr. Bobir Toshmatov, DSc
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Instructor(s):
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Dr. Makhmudov Muzaffar, PhD
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Email:
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b.toshmatov@
newuzbekistanuniversity.org
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Email:
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m.makhmudov@
newuzbekistanuniversity.uz
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Office number:
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609
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Office number:
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609
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Teaching Assistant:
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Mrs. Gulkhayo Rayimova
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Email:
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g.rayimova@
newuzbekistanuniversity.uz
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Office number:
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601
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Course description
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This course is an introduction to differential and integral calculus of functions of one variable. The main topics covered include limits and continuity, derivatives, applications of derivatives, definite and indefinite integrals, and applications of integrals. Topics include:
Concepts of Function, Limits and Continuity
Differentiation Rules, Application to Graphing, Rates, Approximations, and Extremum Problems
Definite and Indefinite Integration
The Fundamental Theorem of Calculus
Applications to Geometry: Area, Volume, and Arc Length
Applications to Science: Average Values, Work, and Probability
Techniques of Integration
Approximation of Definite Integrals, Improper Integrals
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Course objectives Related to Program Outcomes
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After completing this course, students should demonstrate competency in the following skills:
Use both the limit definition and rules of differentiation to differentiate functions.
Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.
Apply differentiation to solve applied max/min problems.
Apply differentiation to solve related rates problems.
Evaluate integrals both by using Riemann sums and by using the Fundamental Theorem of Calculus.
Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution.
Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions and integration by parts.
Use L’Hospital’s rule to evaluate certain indefinite forms.
Determine convergence/divergence of improper integrals and evaluate convergent improper integrals.
Determine the convergence/divergence of an infinite series and find the Taylor series expansion of a function near a point.
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