MAT1051 Calculus IBahçeşehir UniversityDegree Programs CIVIL ENGINEERINGGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
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
Dr. Öğr. Üyesi MESUT NEGİN
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


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
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) Adequate knowledge in mathematics, science and civil engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems. 5
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. 2
3) Ability to design a complex system, process, structural and/or structural members to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
4) Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in civil engineering applications; ability to use civil engineering technologies effectively.
5) Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or civil engineering research topics. 3
6) Ability to work effectively within and multi-disciplinary teams; individual study skills.
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing.
8) Awareness of the necessity of lifelong learning; ability to access information to follow developments in civil engineering technology.
9) To act in accordance with ethical principles, professional and ethical responsibility; having awareness of the importance of employee workplace health and safety.
10) Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of civil engineering solutions.