Academic staff member responsible for the design of the course syllabus
(name, surname, academic title/scientific degree, email address and signature)
|
Dr. Emre Eroğlu eeroglu@epoka.edu.al
|
Main Course Lecturer (name, surname, academic title/scientific degree, email address
and signature) and Office Hours:
|
Dr. Emre Eroğlu eeroglu@epoka.edu.al
|
Second Course Lecturer(s) (name, surname, academic title/scientific degree, email
address and signature) and Office Hours:
|
NA
|
Language: |
English
|
Compulsory/Elective: |
Compulsory
|
Study program: (the study for which this course is offered) |
Bachelor in Civil Engineering (3 years)
|
Classroom and Meeting Time: |
|
Teaching Assistant(s) and Office Hours: |
NA
|
Code of Ethics: |
Code of Ethics of EPOKA University
Regulation of EPOKA University "On Student Discipline"
|
Attendance Requirement: |
|
Course Description: |
Infinite series, power series, Taylor series. Vectors, lines and planes in space. Functions of several variables: Limit, continuity, partial derivatives, the chain rule, directional derivatives, tangent plane approximation and differentials, extreme values, Lagrange multipliers. Double and triple integrals with applications. The line integral.
|
Course Objectives: |
The students will demonstrate an understanding of the calculus of exponential, logarithmic, and inverse trigonometric functions. The students will also develop a basic understanding of advanced integration techniques, infinite sequences and series as well as selected topics from parametric equations, polar coordinates, and conic sections.
|
BASIC CONCEPTS OF THE COURSE
|
1 |
Infinite series, power series, Taylor series.
|
2 |
Vectors, lines and planes in space.
|
3 |
Functions of several variables
|
4 |
mit, continuity, partial derivatives, the chain rule, directional derivatives, tangent plane approximation and differentials,
|
5 |
Lagrange multipliers.
|
6 |
Double and triple integrals with applications.
|
7 |
The line integral.
|
Week |
Topics |
1 |
Application of integrals: volumes of solids by disc, washer and cylindrical shell methods, arc length of curves and surfaces of revolution. |
2 |
Integration by Substitution, Integration by Parts, Trogonometric IntegrationImproper integrals, their types. Divergence and convergence. Evaluation. |
3 |
Differential Equations,Direction Fields,Euler’s Method,Separable equations,Orthogonal Trajectories |
4 |
Differential Equations,1st Order Linear Equations |
5 |
Differential Equations,2nd Order Linear Equations |
6 |
Parametric Equation, Polar coordinates. Tangents, Area, arc length. |
7 |
Infinite sequences. Divergence and convergence. Monotone sequences. Upper and lower bounds.Divergence test. |
8 |
Integral test, comparison test, limit comparison test,ratio test, root test, alternating series test. |
9 |
Absolute convergence. Strategy for series, estimations. Power series and functions. Taylor series. Applications of series. |
10 |
Functions of several variables. Limits. |
11 |
Partial derivatives, directional derivatives. |
12 |
Elements from vector calculus: line integrals, Green's Theorem, Stokes' Theorem and the Divergence Theorem. |
13 |
Double integrals, triple integrals, their applications. |
14 |
Double integrals, triple integrals, their applications. |
No |
Program Competencies |
Cont. |
Bachelor in Civil Engineering (3 years) Program |
1 |
an ability to apply knowledge of mathematics, science, and engineering |
5 |
2 |
an ability to design a system, component, or process to meet desired needs |
5 |
3 |
an ability to function on multidisciplinary teams |
4 |
4 |
an ability to identify, formulate, and solve engineering problems |
5 |
5 |
an understanding of professional and ethical responsibility |
5 |
6 |
an ability to communicate effectively |
4 |
7 |
the broad education necessary to understand the impact of engineering solutions in a global and societal context |
5 |
8 |
a recognition of the need for, and an ability to engage in life long learning |
5 |
9 |
a knowledge of contemporary issues |
4 |
10 |
an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice |
3 |
11 |
skills in project management and recognition of international standards and methodologies |
3 |