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 Coordinator
Course Lecturer(s)
Course Assistants
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;
  • 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
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 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.
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.
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.
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.
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.
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.

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