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MATH 151 Calculus-I 

AIM & OBJECTIVES The Development of calculus in the 17th Century represents one of the greatest intellectual accomplishments in human history. Today, calculus provides students with necessary foundation, understanding and skills that are needed to be successful in college courses such as physics, chemistry, engineering and business. The objective of this course is to introduce the fundamental ideas of the differential and integral calculus of functions of one variable. CATALOGUE DESCRIPTION Limits and continuity. Derivatives. Rules of differentiation. Higher order derivatives. Chain rule. Related rates. Rolle's and the mean value theorem. Critical Points. Asymptotes. Curve sketching. Integrals. Fundamental Theorem. Techniques of integration. Definite integrals. Application to geometry and science. Indeterminate forms. L'Hôpital's Rule. Improper integrals. Sequences, Infinite Series, Alternating series, Ratio, Root, Comparison Test GENERAL LEARNING OUTCOMES On successful completion of the course, the students should be able to: recognize properties of functions and their inverses; recall and use properties of polynomials, rational functions, exponential, logarithmic, trigonometric and inverse-trigonometric functions; understand the terms domain and range; sketch graphs, using function, its first derivative, and the second derivative; use the algebra of limits, and l’Hôspital’s rule to determine limits of simple expressions; apply the procedures of differentiation accurately, including implicit and logarithmic differentiation; apply the differentiation procedures to solve related rates and extreme value problems; obtain the linear approximations of functions and to approximate the values of functions; perform accurately definite and indefinite integration, using integration by parts, substitution, inverse substitution; understand and apply the procedures for integrating rational functions; perform accurately improper integrals; understand and apply the tests for determining convergence or divergence of series. RELATION TO OTHER COURSES Math 151 Calculus-I is the first course of a series of Engineering Mathematics Courses. Math 151 is prerequisite to Math 152 Calculus-II and to Math 203 Ordinary Differential Equations courses (or similar differential equations courses)
E.M.U. Calculus Website Eastern Mediterranean University

MATH 152 Calculus-II 

AIM & OBJECTIVES Calculus was first invented to meet the mathematical needs of scientists of the sixteenth and seventeenth centuries, needs that mainly mechanical in nature. Nowadays it is a tool used almost everywhere in the modern world to describe change and motion. Its use is widespread in science, engineering, medicine, business, industry, and many other fields. Calculus also provides important tools in understanding functions and has led to the development of new areas of mathematics including real and complex analysis, topology, and non-euclidean geometry. The objective of this course is to introduce the fundamental ideas of the differential and integral calculus of functions of several variables. CATALOGUE DESCRIPTION Power series, Taylor & Maclaurin series, Lines and planes, Vectors, Dot and Cross Product, Lines and Planes, Vector Valued Functions, Differentiation and Integration of Vector Valued Functions, Functions of several variables, Limits and Continuity, Partial Differentiation, Chain Rule, Tangent plane, Critical points, Global and Local Extrema, Directional Derivatives, Gradient, Divergence and Curl, Multiple integrals with applications, Triple integrals with applications, Triple integrals in Cylindrical and Spherical coordinates, Line-, Surface- and Volume Integrals, Independence of path, Green’s Theorem, Conservative Vector Fields, Divergence Theorem, Stokes’ Theorem. GENERAL LEARNING OUTCOMES On succesful completion of the course, the students should be able to: understand how to approximate functions with polynomials; explain the properties of power series; find the radius and the interval of convergence of a power series, indicating at which points the series converges absolutely/conditionally; construct Taylor and Maclaurin series for a given function; use Taylor and Maclaurin series for approximation of functions and estimate the error; use power series to calculate limits; understand and apply two and three dimensional Cartesian coordinate system; recognize and classify the equations and shapes  of quadratic surfaces; use the properties of vectors and operations with vectors; recognize and construct the equations of lines and planes; operate with vector functions, find their derivatives and integrals, find the arc length; understand and use the concept of a function of several variables, find it’s domain; calculate the limits of multivariable functions and prove the nonexistence of a limit; find partial derivatives using the properties of differentiable multivariable functions and basic rules; apply partial derivatives for finding equations of tangent planes, normal lines, and for extreme values; evaluate double integrals in Cartesian and polar coordinates and triple integrals in Cartesian and cylindrical coordinates; apply multiple integrals for computing areas and volumes; understand and use integration in vector fields; find line integrals and flux using Green’s Theorem; find circulation of a vector field using Stoke’s theorem; use Divergence Theorem to find the flux of a vector field RELATION TO OTHER COURSES This course provides the mathematical background for engineering students and is very important, for instance, for advanced courses on partial differential equations or numerical analysis.
SPRING TERM 2018 - 2019
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