Organization: Subject

Course Syllabus

Organization: Subject:	New Uzbekistan University MATH 111- Calculus 1	Credit units:	6 ECTS
Instructor(s):	Dr. Bobir Toshmatov, DSc	Instructor(s):	Dr. Makhmudov Muzaffar, PhD
Email:	b.toshmatov@ newuzbekistanuniversity.org	Email:	m.makhmudov@ newuzbekistanuniversity.uz
Office number:	609	Office number:	609
Teaching Assistant:	Mrs. Gulkhayo Rayimova	Email:	g.rayimova@ newuzbekistanuniversity.uz
Office number:	601

Course description

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

Course objectives Related to Program Outcomes

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.