ECTS - Calculus I
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 Lecturer(s) |
|
| 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;
|
| 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 | 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 | An ability to apply knowledge of mathematics, science and engineering to Industrial Engineering; an ability to apply theoretical and practical knowledge to model and solve engineering problems. | X | ||||
| 2 | An ability to identify, formulate and solve complex engineering problems; an ability to select and apply proper analysis and modeling methods. | X | ||||
| 3 | An ability to design a complex system, process, tool or component to meet desired needs within realistic constraints; an ability to apply modern design. | |||||
| 4 | An ability to develop, select and put into practice techniques, skills and modern engineering tools necessary for engineering practice; an ability to use information technology effectively. | |||||
| 5 | An ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or disciplinary research topics. | X | ||||
| 6 | An ability to work individually, on teams, and/or on multidisciplinary teams. | X | ||||
| 7 | Ability to communicate effectively in Turkish orally and in writing; knowledge of at least one foreign language; effective report writing and understand written reports, preparing design and production reports, making effective presentations, giving and receiving clear and understandable instruction. | |||||
| 8 | A recognition of the need for, and an ability to engage in life-long learning; an ability to use information-seeking tools and to follow the improvements in science and technology. | |||||
| 9 | An ability to behave according to the ethical principles, an understanding of professional and ethical responsibility. Information on standards used in industrial engineering applications. | |||||
| 10 | Knowledge of business applications such as project management, risk management and change management. A recognition of entrepreneurship, innovativeness. Knowledge of sustainable improvement. | |||||
| 11 | Information on the effects of industrial engineering practices on health, environment and security in universal and societal dimensions and the information on the problems of the in the field of engineering of the era. Awareness of the legal consequences of engineering solutions. | |||||
| 12 | An ability to design, development, implementation and improvement of integrated systems that include human, materials, information, equipment and energy. | |||||
| 13 | Knowlede on appropriate analytical, computational and experimental methods to provide system integration. | |||||
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 | ||