|
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
, Valmir Bame
|
|
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 Computer Engineering (3 years)
|
| Classroom and Meeting Time: |
Thursday E-110
|
| 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: |
N/A
|
| Course Description: |
Functions, Limits, continuity and derivatives. Applications. Extreme values, the Mean Value Theorem and its applications. Graphing. The definite integral. Area and volume as integrals. The indefinite integral. Transcendental functions and their derivatives. L'Hopital's rule. Techniques of integration. Improper integrals. Applications. Parametric curves. Polar coordinates.
|
| Course Objectives: |
The objective of this course is to provide a good background on single variable calculus, including limits, derivatives, applications of derivatives, and integration.
|
|
BASIC CONCEPTS OF THE COURSE
|
| 1 |
Overview of the essential functions. The domain and range. Odd and even functions
|
| 2 |
Bijections. Inverse functions
|
| 3 |
One-sided limits. Infinite limits, vertical asymptotes.
|
| 4 |
Limits at infinity, horizontal asymptotes
|
| 5 |
The concept of the derivative
|
| 6 |
Techniques of differentiation
|
| 7 |
Monotony and local extreme values
|
| 8 |
L'Hospital's rule.
|
| 9 |
Implicit differentiation.
|
| 10 |
Techniques of integration
|
| Week |
Topics |
| 1 |
Functions and models.Overview of the essential functions.The domain and range.Odd and even functions. |
| 2 |
New functions from old ones. One-to-one and onto functions. Bijections. Inverse functions. |
| 3 |
The concept of the limit, precise definition. One-sided limits. Infinite limits, vertical asymptotes. |
| 4 |
Limits at infinity, horizontal asymptotes. Indeterminate forms. The sandwich theorem. Continuity. |
| 5 |
The concept of the derivative.The formal definition of the derivative.Constructing the table of der. |
| 6 |
Techniques of differentiation. The sum, product, ratio and chain rule. Higher order derivatives. |
| 7 |
Application of derivatives: Monotony and local extreme values. Concavity and inflection points. Sketching graphs of functions. |
| 8 |
Midterm exam. |
| 9 |
Applications of derivatives: mean value theorem, L'Hospital's rule. |
| 10 |
Applications of derivatives: optimization problems. |
| 11 |
Related rate problems. Implicit differentiation. |
| 12 |
Introduction to integrals.The fundamental theorem of calculus. |
| 13 |
Techniques of integration. The substitution rule, integration by parts, integration of rational functions. |
| 14 |
Improper integrals. |
| 1 |
Students will be able to find the domain and range for different polynomial and rational functions |
| 2 |
Students will be able to find limits of functions and determine continuity of functions. |
| 3 |
Find derivatives of algebraic and some trigonometric functions, and use derivatives to solve applied problems. |
| 4 |
Find integrals of some algebraic and trigonometric functions, and use integrals to solve applied problems. |
| 5 |
Find indefinite and improper integrals using different integration techniques, apply L'Hopital's rule |
| 6 |
Represent area as a definite integral and interpret the result in applications. |
| No |
Program Competencies |
Cont. |
| Bachelor in Computer Engineering (3 years) Program |
| 1 |
Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice. |
5 |
| 2 |
Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations |
5 |
| 3 |
Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects. |
5 |
| 4 |
Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies. |
4 |
| 5 |
Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions. |
4 |
| 6 |
Ability of identifying the potential resources for information or knowledge regarding a given engineering issue. |
4 |
| 7 |
The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence. |
4 |
| 8 |
Ability for effective oral and official communication skills in foreign language. |
3 |
| 9 |
Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology. |
5 |
| 10 |
Engineering graduates with well-structured responsibilities in profession and ethics. |
3 |
| 11 |
Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues. |
2 |
| 12 |
Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity. |
2 |
