Calculus I (MATH151) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Calculus I MATH151 4 2 0 5 7
Pre-requisite Course(s)
N/A
Course Language English
Course Type N/A
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

Sources

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
Major Area Courses
Supportive Courses X
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 Adequate knowledge in mathematics, science and computing fields; ability to apply theoretical and practical knowledge of these fields in solving engineering problems related to information systems. X
2 Ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose. X
3 Ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; 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 information systems engineering applications; ability to use information technologies effectively. X
5 Ability to gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the information systems discipline.
6 Ability to work effectively in inter/inner disciplinary teams; ability to work individually. X
7 a. Effective oral and written communication skills in Turkish; ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. b. Knowledge of at least one foreign language; ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
8 Recognition of the need for lifelong learning; the ability to access information and follow recent developments in science and technology with continuous self-development.
9 a. Ability to behave according to ethical principles, awareness of professional and ethical responsibility. b. Knowledge of the standards utilized in information systems engineering applications.
10 a. Knowledge on business practices such as project management, risk management and change management. b. Awareness about entrepreneurship, and innovation. c. Knowledge on sustainable development.
11 a. Knowledge of the effects of information systems engineering applications on the universal and social dimensions of health, environment, and safety. b. Awareness of the legal consequences of engineering solutions.
12 An ability to design, develop, operate and manage cost-effective information systems by assembling the most appropriate software and hardware, arranging appropriate personnel, and defining necessary procedures, in order to enable public and private sector organizations to do their jobs more effectively and be more competitive. X
13 Skills in finding solutions to business problems using information technologies.

ECTS/Workload Table

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