# Extended Calculus I (MATH157) Ders Detayları

Course Name Corse Code Dönemi Lecture Hours Uygulama Saati Lab Hours Credit ECTS
Extended Calculus I MATH157 1. Semester 4 2 0 5 7.5
Pre-requisite Course(s)
N/A
Course Language İngilizce Service Courses Taken From Other Departments Lisans Face To Face Lecture, Question and Answer, Problem Solving. 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 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 understand improper integrals and sequences 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 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

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 40 100

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Accumulated knowledge on mathematics, science and mechatronics engineering; an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. X
2 An ability to differentiate, identify, formulate, and solve complex engineering problems; an ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. X
3 An ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; an ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions may include economics, environment, sustainability, producibility, ethics, human health, social and political problems.) X
4 An ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; an ability to use information and communications technologies effectively.
5 An ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies. X
6 An ability to work effectively on single disciplinary and multi-disciplinary teams; an ability for individual work; ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines.
7 An ability to express creative and original concepts and ideas effectively in Turkish and English language, oral and written, and technical drawings.
8 An ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; consciousness on the necessity of improvement and sustainability as a result of life-long learning; monitoring the developments on science and technology; awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation.
9 Consciousness on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself.
10 A knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project.
11 Knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; consciousness on these issues; awareness of legal results of engineering solutions.
12 Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions.
13 Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planing, improving or changing the norms with a criticism.

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