© Eastern Mediterranean University

## 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)

## 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