ECTS - Calculus I
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) |
|---|
| N/A |
| 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 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 | Adequate knowledge in mathematics, science and subjects specific to the energy systems engineering discipline; the ability to apply theoretical and practical knowledge of these areas to complex engineering problems. | X | ||||
| 2 | The ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose. | |||||
| 3 | The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. | |||||
| 4 | The ability to develop, select and utilize modern techniques and tools essential for the analysis and determination of complex problems in energy systems engineering applications; the ability to utilize information technologies effectively. | |||||
| 5 | The ability to design experiments, conduct experiments, gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the energy systems engineering discipline. | |||||
| 6 | The ability to work effectively in inter/inner disciplinary teams, the ability to work individually. | |||||
| 7 | a)Effective oral and writen communication skills in Turkish; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and to receive clear and understandable instructions. b)The knowledge of at least one foreign language; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and to receive clear and understandable instructions. | |||||
| 8 | Recognition of the need for lifelong learning; the ability to access information, to follow recent developments in science and technology. | |||||
| 9 | a)The ability to behave according to ethical principles, awareness of professional and ethical responsibility; b)knowledge of the standards utilized in energy systems engineering applications. | |||||
| 10 | Knowledge on business practices such as project management, risk management and change management; awareness about entrepreneurship, innovation; knowledge on sustainable development. | |||||
| 11 | a) Knowledge on the effects of energy systems engineering applications on the universal and social dimensions of health, environment and safety; b) and awareness of the legal consequences of engineering solutions. | |||||
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 | ||