MAT1051 Calculus IBahçeşehir UniversityDegree Programs ENERGY SYSTEMS ENGINEERINGGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
ENERGY SYSTEMS ENGINEERING
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT1051 Calculus I Fall 3 2 4 7

Basic information

Language of instruction: English
Type of course: Must Course
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator : Instructor NERMINE AHMED EL SISSI
Course Lecturer(s): Prof. Dr. SÜREYYA AKYÜZ
RA DUYGU ÜÇÜNCÜ
Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN
RA AYSUN SOYSAL
Dr. Öğr. Üyesi MESUT NEGİN
Dr. Öğr. Üyesi MÜRÜVVET ASLI AYDIN
Assoc. Prof. HALE GONCE KÖÇKEN
Prof. Dr. NAFİZ ARICA
Dr. Öğr. Üyesi DOĞAN AKCAN
Recommended Optional Program Components: This is not defined for this course
Course Objectives: The purpose of the course is to give to the student a mathematical understanding of relations, functions, limits, continuity and differentiation and thus provide the necessary background so that a rational approach to problem solving is attained.

Learning Outcomes

The students who have succeeded in this course;
1 Understand and make calculations with numbers and functions, function’s types, and interpret different type of functions;
2 Calculate limit and asymptots and prove some basic evidence about limit and continuity.
3 Define derivatives s as a rate of change; apply linearization methods on nonlinear functions and use this on calculations.
4 Learn different derivation methods
5 Solve related rate problems
6 Use derivation methods in curve sketching
7 Calculate absolute and local maximum minimum values of univariate functions
8 Solve basic optimization problems;

Course Content

Relations, functions, limits, continuity, differentiation, rules of differentiation, The chain rule and implicit differentiation. Derivatives of trigonometric, exponential, logarithmic, inverse trigonometric functions.Related rates, linearization and differentials, extreme values, the Mean Value theorem, curve sketching, applied optimization problems. Indeterminate forms and L'Hopital's rule. Newton's method and antiderivatives.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Number systems and functions.
2) Functions and their properties.
3) Definition of limits and properties of limits.
4) Undefined limits, horizontal and vertical asymptotes. Continuity.
5) Definition of derivative. Tangents and derivative at a point. The derivative as a function.
6) The derivative as a rate of change. Differentiation rules.
7) Derivatives of functions. The chain rule and implicit differentiation.
8) Derivatives of functions (cont'd). Approximations and differentials.
9) Applications of the derivative. Related rate problems.
10) Applications of differentiation (cont'd). The Mean value theorem, maximum, minimum values, increasing and decreasing functions,
11) Curve sketching.
12) Indeterminate forms and L'Hopital's rule.
13) Optimization problems and Newton's method.
14) Linearization of non linear functions

Sources

Course Notes / Textbooks: Robert Adams, Christopher Essex, Calculus, Eight Edition, Pearson
References: James Stewart Calculus, 5th Ed. Brooks/Cole Publishing Company

C.H. Edwards,Jr. David E. Penney, Calculus with Analytic Geometry

Richard Silverman, Calculus with Analytic Geometry, Prentice Hall

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Midterms 1 % 40
Final 1 % 60
Total % 100
PERCENTAGE OF SEMESTER WORK % 40
PERCENTAGE OF FINAL WORK % 60
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Application 14 2 28
Study Hours Out of Class 14 3 42
Midterms 1 28 28
Final 1 30 30
Total Workload 170

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Build up a body of knowledge in mathematics, science and Energy Systems Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. 5
2) Ability to identify, formulate, and solve complex Energy Systems Engineering problems; select and apply proper modeling and analysis methods for this purpose. 4
3) Ability to design complex Energy systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose.
4) Ability to devise, select, and use modern techniques and tools needed for solving complex problems in Energy Systems Engineering practice; employ information technologies effectively.
5) Ability to design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Energy Systems Engineering. 3
6) Ability to cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Energy Systems-related problems
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions.
8) Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself.
9) Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Energy Systems Engineering applications.
10) Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11) Acquire knowledge about the effects of practices of Energys Systems Engineering on health, environment, security in universal and social scope, and the contemporary problems of Energys Systems engineering; is aware of the legal consequences of Energys Systems engineering solutions.