COURSE INFORMATION FORM

Faculty Faculty of Engineering Program B.Sc. in Civil Engineering Required

B.Sc. in Computer Engineering Required B.Sc. in Electrical-Electronics Engineering Required B.Sc. in Industrial Engineering Required B.Sc. in Mechanical Engineering Required

Semester Fall 2015-2016

Course Code MATH 115 Course Title in English

Calculus I

Course Title in Turkish

Diferansiyel ve İntegral Hesap I

Language of Instruction

English

Type of Course Flipped Classroom/Lecture/Exercise Level of Course Undergraduate Course Category (by % of Content)

Basic Science Basic Engineering Engineering Design General Education 100 - - -

Semester Offered Fall Contact Hours per Week

Lecture: 4 hours Recitation: - Lab:- Other:-

Estimated Student Workload

176 hours per semester

Number of Credits 7 ECTS Grading Mode Standard Letter Grade Pre-requisites None

Expected Prior Knowledge

None

Co-requisites None Registration Restrictions

Only Undergraduate Students

Overall Educational Objective

To acquire a basic knowledge and understanding of important concepts of differentiation and integration of a single variable.

Course Description This course provides a comprehensive introduction to some fundamental aspects of function of a single variable, trigonometric functions, limit, continuity of a function, differentiation of a single variable function, extremum of a function, mean value theorem, L’Hospital’s rule, antiderivative and the indefinite integral, definite integrals, fundamental theorem of calculus, applications of the definite integral, the exponential and logarithmic function, the inverse trigonometric functions, hyperbolic functions and their inverses, integration techniques.

Course Description in Turkish Bu derste; diferansiyel ve integral hesabın temel kavramları şu konu başlıklar altında kapsamlı bir

şekilde incelenmektedir: Tek değişkenli fonksiyonlar, trigonometrik fonksiyonlar, limit, süreklilik, tek değişkenli fonksiyonların türevi, bir fonksiyonun ekstremum değerleri, ortalama değer teoremi, L’Hospital kuralı, antitürev ve belirsiz integral, belirli integral, diferansiyel ve integral hesabın esas teoremi, belirli integralin uygulamaları, üstel fonksiyon, logaritma, ters trigonometric fonksiyonlar, hiperbolik fonksiyonlar ve ters hiperbolik fonksiyonlar, integral teknikleri.

Course Learning Outcomes and Competences

Upon successful completion of the course, the learner is expected to:

1. Calculate limit at a point and limit at infinity of single variable functions. 2. Solve applied optimization extrema problems and sketch graphs of functions.

3. Evaluate definite and indefinite integrals using integration techniques. 4. Apply definite integrals for calculating arc-lengths, volumes, area of surface of revolution,

center of mass and moments of inertia. 5. Calculate, differentiate and integrate exponential functions, logarithmic functions,

trigonometric and inverse trigonometric functions and hyperbolic and inverse hyperbolic functions

Relation to Student Outcomes and Competences: N=None S=Supportive H=Highly Related Relationship of the Course with the Student Outcomes and Competences Level Assessed by N/S/H

(Related Learning Outcomes and Activities)

Exam, Project, HW, Lab, Presentation, etc.

(a) an ability to apply knowledge of mathematics, science, and engineering. H (1,2,3,4)

Exams, Quizzes, Homework

(b) an ability to design and conduct experiments, as well as to analyze and interpret data.

(c) an ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability.

(d) an ability to function on multidisciplinary teams.

S

Flipped Classroom Practice

(e) an ability to identify, formulate, and solve engineering problems.

(f) an understanding of professional and ethical responsibility.

(g) an ability to communicate effectively. S

Flipped Classroom Practice

(h) the broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context.

(i) a recognition of the need for, and an ability to engage in life-long learning.

S Flipped Classroom

Practice

(j) a knowledge of contemporary issues.

(k) an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.

Prepared by and Date Assoc. Prof. Dr. Ali Çınar and Asst. Prof. Dr. İrem Zeynep Yıldırım / September 2016 Name of Instructor Assoc. Prof. Dr. Ali Çınar

Asst. Prof. Dr. İrem Zeynep Yıldırım Course Contents Week Topic 1. Function of a single variable, trigonometric functions 2. Limit and continuity 3. The derivative of a function 4. Applications of the derivative 5. Curve sketching and L’Hospital’s rule 6. Antiderivative, the indefinite and definite integral 7. The fundamental theorem of calculus 8. Applications of definite integrals 9. Applications of definite integrals

10. Inverse of a function. Transcendental functions: Logarithmic and exponential functions 11. Transcendental functions: Inverse trigonometric functions

12. Transcendental functions: Hyperbolic and inverse hyperbolic functions

13. Integration techniques: Integration by parts, integration by partial fractions

14. Integration techniques: Trigonometric integrals, trigonometric substitutions

15. Final Examination Period.

16. Final Examination Period.

Required/Recommended Readings

Thomas' Calculus, 13th Ed., G. Thomas, M. Weir, J. Hass, F. Giordano, Pearson/ Addison Wesley, 2015

Teaching Methods Lectures/contact hours using “flipped classroom” as an active learning technique Homework and Projects Review questions as homework Laboratory Work - Computer Use - Other Activities - Assessment Methods

Types of assessment: Number Ratio (%) Midterm Exams 2 30 (each contributing 15%) Quizzes 2 10 (each contributing 5%) Flipped Classroom Practice 28 15 Watching the videos and taking online test 22 5 Final Exam 1 40 Total 100

Course Administration Instructor’s office and phone number: 5th Floor, (0212) 3953653 Office hours: Cinar : Monday 13:00- 15:00. Yildirim: Tuesdays 15:00-17:00 Email address: cinara@mef.edu.tr , yildirimz@mef.edu.tr Rules for attendance: Classroom participation contributes to 15% of the final grade. Missing a quiz: Provided that proper documents of excuse are presented, each missed quiz by the student will be given a grade by taking the average of all of the other quizzes. No make-up will be given. Missing a midterm: Provided that proper documents of excuse are presented, each missed midterm by the student will be given the grade of the final exam. No make-up will be given. Missing a final: Faculty regulations. A reminder of proper classroom behavior, code of student conduct: YÖK Regulations Statement on plagiarism: YÖK Regulations (http://www.mef.edu.tr/tr/yonetmelikler)

ECTS Student Workload Estimation

Activity No/Weeks Calculation ExplanationNo/Weeks

per Semester

(A)

Preparing for the Activity

(B)

Spent in the Activity Itself

(C)

Completing the Activity

Requirements (D)

Lecture/Flipped Classroom14 2 4 2 112 A*(B+C+D)

Quizzes 2 6 1 14 A*(B+C+D)

Midterm(s) 2 12 2 28 A*(B+C+D)

Assingment, Project, Presentation 0 A*(B+C+D)

Final Examination 1 20 2 22 A*(B+C+D)

Total Workload 176

Total Workload/25 7.04

ECTS 7

Hours

PROGRAM CRITERIA

1. Breadth in mechanical engineering practice, analysis and design with 18 required courses in mechanical engineering, and depth in one or more fields with 4 mechanical engineering electives. 2. Knowledge of chemistry and calculus-based physics with depth in at least one of these; ability to apply advanced mathematics through multivariate calculus and differential equations; familiarity with statistics and linear algebra. 3. Ability to work professionally in both thermal and mechanical systems areas, including the design and realization of such systems. Key verbs for cognitive domain in writing learning outcomes and competences:

Key Verbs: Remembering: defines, describes, identifies, knows, labels, lists, matches, names, outlines, recalls, recognizes, reproduces, selects, states. Understanding: comprehends, converts, defends, distinguishes, estimates, explains, extends, generalizes, gives an example, infers, interprets, paraphrases, predicts, rewrites, summarizes, translates. Applying: applies, changes, computes, constructs, demonstrates, discovers, manipulates, modifies, operates, predicts, prepares, produces, relates, shows, solves, uses. Analyzing: analyzes, breaks down, compares, contrasts, diagrams, deconstructs, differentiates, discriminates, distinguishes, identifies, illustrates, infers, outlines, relates, selects, separates. Evaluating: appraises, compares, concludes, contrasts, criticizes, critiques, defends, describes, discriminates, evaluates, explains, interprets, justifies, relates, summarizes, supports. Creating: categorizes, combines, compiles, composes, creates, devises, designs, explains, generates, modifies, organizes, plans, rearranges, reconstructs, relates, reorganizes, revises, rewrites, summarizes, tells, writes. Key verbs for affective domain in writing learning outcomes and competences: Receiving Phenomena: asks, chooses, describes, follows, gives, holds, identifies, locates, names, points to, selects, sits, erects, replies, uses. Responding to Phenomena: answers, assists, aids, complies, conforms, discusses, greets, helps, labels, performs, practices, presents, reads, recites, reports, selects, tells, writes. Valuing: completes, demonstrates, differentiates, explains, follows, forms, initiates, invites, joins, justifies, proposes, reads, reports, selects, shares, studies, works. Organizing: adheres, alters, arranges, combines, compares, completes, defends, explains, formulates, generalizes, identifies, integrates, modifies, orders, organizes, prepares, relates, synthesizes. Internalizing values: acts, discriminates, displays, influences, listens, modifies, performs, practices, proposes, qualifies, questions, revises, serves, solves, verifies.