Calculus I (MATH151) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Calculus I MATH151 1. Semester 4 2 0 5 7
Pre-requisite Course(s)
Course Language English
Course Type Compulsory Departmental Courses
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives The course is designed to fill the gaps in students knowledge that they have in their pre-college education and then to give them computational skills in one-variable differential and integral calculus to handle engineering problems
Course Learning Outcomes The students who succeeded in this course;
  • understand, define and use functions, and represent them by means of graphs
  • understand fundamental concepts of limit and continuity
  • understand the meaning of derivative and calculate derivatives of one-variable functions
  • use derivatives to solve problems involving maxima, minima, and related rates
  • understand integration, know integration techniques, use them to solve area, volume and other problems
Course Content Preliminaries, limits and continuity, differentiation, applications of derivatives, L`Hopital's Rule, integration, applications of integrals, integrals and transcendental functions, integration techniques and improper integrals, squences.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 P.1 Real Numbers and the Real Line, P.2 Cartesian Coordinates in the Plane, P.3 Graphs of Quadratic Equations, P.4 Functions and Their Graphs, pp:3-33
2 P.5 Combining Functions to Make New Functions, P.6 Polynomials and Rational Functions, P.7 Trigonometric Functions, pp:33-57
3 1.1 Examples of Velocity, Growth Rate, and Area, 1.2 Limits of Functions, 1.3 Limits at Infinity and Infinite Limits, 1.4 Continuity, pp:58-87
4 1.5 The Formal Definition of Limit, 2.1 Tangent Lines and Their Slopes, 2.2 The Derivative, 2.3 Differentiation Rules, pp:87-114
5 2.4 The Chain Rule, 2.5 Derivatives of Trigonometric Functions, 2.6 Higher-Order Derivatives, pp:115-129
6 2.7 Using Differentials and Derivatives, 2.8 The Mean Value Theorem, 2.9 Implicit Differentiation, 3.1 Inverse Functions, pp:129-147 pp:163-169
7 Midterm
8 3.2 Exponential and Logarithmic Functions, 3.3 The Natural Logarithm and Exponential, 3.4 Growth and Decay (Theorem 4, Theorem 5, Theorem 6 and Examples for these theorems), 3.5 The Inverse Trigonometric Functions, pp:169-187 pp:190-197
9 3.6 Hyperbolic Functions (only their definition and derivatives), 4.1 Related Rates, 4.3 Indeterminate Forms, pp:198-203 pp:213-219 pp:227-232
10 4.4 Extreme Values, 4.5 Concavity and Inflections, 4.6 Sketching the Graph of a Function, pp:232-252
11 4.8 Extreme-Value Problems, 4.9 Linear Approximations, 2.10 Antiderivatives and Initial Value Problems (Antiderivatives, The Indefinite Integral), 5.1 Sums and Sigma Notation, pp:258-271 pp:147-150 pp:288-293
12 5.2 Areas as Limits of Sums, 5.3 The Definite Integral, 5.4 Properties of the Definite Integral, 5.5 The Fundamental Theorem of Calculus, pp:293-316
13 5.6 The Method of Substitution, 5.7 Areas of Plane Regions, 6.1 Integration by Parts, pp:316-337
14 6.2 Integrals of Rational Functions, 6.3 Inverse Substitutions, 6.5 Improper Integrals, pp:337-353 pp:359-367
15 7.1 Volumes by Slicing – Solids of Revolution, 7.2 More Volumes by Slicing, 7.3 Arc Length and Surface Area (only Arc Length), Review, pp:390-407
16 Final Exam


Course Book 1. Calculus: A complete Course, R. A. Adams, C. Essex, 7th Edition; Pearson Addison Wesley
Other Sources 2. Thomas’ Calculus Early Transcendentals, 11th Edition.( Revised by M. D. Weir, J.Hass and F. R. Giardano; Pearson , Addison Wesley)
3. Calculus: A new horizon, Anton Howard, 6th Edition; John Wiley & Sons
4. Calculus with Analytic Geometry, C. H. Edwards; Prentice Hall
5. Calculus with Analytic Geometry, R. A. Silverman; Prentice Hall

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 60
Final Exam/Final Jury 1 40
Toplam 3 100
Percentage of Semester Work 60
Percentage of Final Work 40
Total 100

Course Category

Core Courses X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Acquires sufficient knowledge in mathematics, natural sciences, and related engineering disciplines; gains the ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. X
2 Gains the ability to identify, define, formulate, and solve complex engineering problems; acquires the skill to select and apply appropriate analysis and modeling methods for this purpose. X
3 Gains the ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions, and applies modern design methods for this purpose.
4 Develops the skills to develop, select, and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in industrial engineering applications; gains the ability to effectively use information technologies.
5 Gains the ability to design experiments, conduct experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or discipline-specific research topics. X
6 Acquires the ability to work effectively in intra-disciplinary and multidisciplinary teams, as well as individual work skills. X
7 Acquires effective oral and written communication skills in Turkish; at least one foreign language proficiency; gains the ability to write effective reports, understand written reports, prepare design and production reports, make effective presentations, and give and receive clear instructions.
8 Develops awareness of the necessity of lifelong learning; gains the ability to access information, follow developments in science and technology, and continuously renew oneself.
9 Acquires the consciousness of adhering to ethical principles, and gains professional and ethical responsibility awareness. Gains knowledge about the standards used in industrial engineering applications.
10 Gains knowledge about practices in the business life such as project management, risk management, and change management. Develops awareness about entrepreneurship and innovation. Gains knowledge about sustainable development.
11 Gains knowledge about the universal and social dimensions of the impacts of industrial engineering applications on health, environment, and safety, as well as the problems reflected in the engineering field of the era. Gains awareness of the legal consequences of engineering solutions.
12 Gains skills in the design, development, implementation, and improvement of integrated systems involving human, material, information, equipment, and energy.
13 Gains knowledge about appropriate analytical and experimental methods, as well as computational methods, for ensuring system integration.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 4 64
Application 16 2 32
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury
Prepration of Final Exams/Final Jury 1 18 18
Total Workload 156