ECTS - Extended Calculus I
Extended Calculus I (MATH157) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Extended Calculus I | MATH157 | Diğer Bölümlere Verilen Ders | 4 | 2 | 0 | 5 | 7.5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Service Courses Given to Other Departments |
| 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 sequence Math 157-158 is an extension of the standard calculus course that contains vector calculus and the line integral in addition to the standard complete introduction to the concepts and methods of differential and integral calculus . It is taken by some of the engineering students who needs these topics in their departments. Math 157 is designed 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, sequences. |
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 P.5 Combining Functions to Make New Functions | pp:3-39 |
| 2 | P.6 Polynomials and Rational Functions P.7 Trigonometric Functions 1.1 Examples of Velocity, Growth Rate, and Area | pp:39-63 |
| 3 | 1.2 Limits of Functions 1.3 Limits at Infinity and Infinite Limits 1.4 Continuity 1.5 The Formal Definition of Limit | pp:63-92 |
| 4 | 2.1 Tangent Lines and Their Slopes 2.2 The Derivative 2.3 Differentiation Rules 2. 4 The Chain Rule 2.5 Derivatives of Trigonometric Functions | pp:94-125 |
| 5 | 2.6 Higher-Order Derivatives 2.7 Using Differentials and Derivatives 2.8 The Mean Value Theorem 2.9 Implicit Differentiation | pp:125-147 |
| 6 | 3.1 Inverse Functions 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) | pp:163-187 |
| 7 | Midterm | |
| 8 | 3.5 The Inverse Trigonometric Functions 3.6 Hyperbolic Functions (only their definition and derivatives) 4.1 Related Rates 4.3 Indeterminate Forms | pp:190-203 pp:213-219 pp:227-232 |
| 9 | 4.4 Extreme Values 4.5 Concavity and Inflections 4.6 Sketching the Graph of a Function | pp:232-252 |
| 10 | 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 |
| 11 | 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 |
| 12 | 5.6 The Method of Substitution 5.7 Areas of Plane Regions 6.1 Integration by Parts | pp:316-337 |
| 13 | 6.2 Integrals of Rational Functions 6.3 Inverse Substitutions 6.5 Improper Integrals | pp:337-353 pp:359-367 |
| 14 | 7.1 Volumes by Slicing – Solids of Revolution 7.2 More Volumes by Slicing 7.3 Arc Length and Surface Area (only Arc Length) | pp:390-407 |
| 15 | 9.1 Sequences and Convergence | pp:495-502 |
| 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 | |
| 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 skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | |||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | |||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | |||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | |||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | |||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | |||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | |||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | |||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | |||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | |||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | |||||
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 | 4 | 56 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | |||
| Prepration of Final Exams/Final Jury | 1 | 16 | 16 |
| Total Workload | 168 | ||