# Extended Calculus I (MATH157) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Extended Calculus I MATH157 4 2 0 5 7.5
Pre-requisite Course(s)
N/A
Course Language English N/A Bachelor’s Degree (First Cycle) 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

### Course Category

Core Courses X

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

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Adequate knowledge of mathematics, physical sciences and the subjects specific to engineering disciplines; the ability to apply theoretical and practical knowledge of these areas in the solution of complex engineering problems. X
2 The ability to define, formulate, and solve complex engineering problems; the ability to select and apply proper analysis and modeling methods for this purpose. X
3 The ability to design a complex system, process, device or product under realistic constraints and conditions in such a way as to meet the specific requirements; the ability to apply modern design methods for this purpose. X
4 The ability to select, and use modern techniques and tools needed to analyze and solve complex problems encountered in engineering practices; the ability to use information technologies effectively.
5 The ability to design experiments, conduct experiments, gather data, and analyze and interpret results for investigating complex engineering problems or research areas specific to engineering disciplines. X
6 The ability to work efficiently in inter-, intra-, and multi-disciplinary teams; the ability to work individually.
7 (a) Sözlü ve yazılı etkin iletişim kurma becerisi; etkin rapor yazma ve yazılı raporları anlama, tasarım ve üretim raporları hazırlayabilme, etkin sunum yapabilme, açık ve anlaşılır talimat verme ve alma becerisi. (b) En az bir yabancı dil bilgisi; bu yabancı dilde etkin rapor yazma ve yazılı raporları anlama, tasarım ve üretim raporları hazırlayabilme, etkin sunum yapabilme, açık ve anlaşılır talimat verme ve alma becerisi. X
8 Recognition of the need for lifelong learning; the ability to access information, follow developments in science and technology, and adapt and excel oneself continuously.
9 Acting in conformity with the ethical principles; professional and ethical responsibility and knowledge of the standards employed in engineering applications.
10 Knowledge of business practices such as project management, risk management, and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development.
11 Knowledge of the global and social effects of engineering practices on health, environment, and safety issues, and knowledge of the contemporary issues in engineering areas; awareness of the possible legal consequences of engineering practices.
12 (a) Knowledge of (i) fluid mechanics, (ii) heat transfer, (iii) manufacturing process, (iv) electronics and control, (v) vehicle components design, (vi) vehicle dynamics, (vii) vehicle propulsion/drive and power systems, (viii) technical laws and regulations in automotive engineering field, and (ix) vehicle verification tests. (b) The ability to merge and apply these knowledge in solving multi-disciplinary automotive problems.
13 The ability to make use of theoretical, experimental, and simulation methods, and computer aided design techniques in automotive engineering field.
14 The ability to work in the field of vehicle design and manufacturing.

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