Course Details

CALCULUS 1

MATH151

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Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS Credits
1MATH151CALCULUS 15+0+056

Course Details
Language of Instruction English
Level of Course Unit Bachelor's Degree
Department / Program COMPUTER ENGINEERING
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course This course aims to teach the differential and integral part of single variable Calculus by
-Providing fundamental knowledge and skills to analyze the behavior of a single variable function in every aspect
-Constructing theoretical and conceptual understanding of essential mathematical tools to study single variable calculus.
-Developing the ability of using the notions and tools of basic mathematics to recognize and analyze a problem deduced from real life/nature and offering solutions to these problems by applying relevant computation and analysis techniques.
Course Content This course is an introduction to single variable calculus for engineering students and covers the fundamentals of differentiation and integration. In this context, taking limits of functions, differentiating, optimizing, graphing and integrating functions are being taught. By the end of the semester, the students will be able to demonstrate an understanding of a single variable function in every aspect by using the scientific skills gained during semester.
Course Methods and Techniques Analytic thinking and reasoning are always promoted during face to face lectures by encouraging students to get involved in the learning process by Q&A.
Prerequisites and co-requisities None
Course Coordinator Asist Prof.Dr. Çisem Güneş Aktaş cisem.gunesaktas@agu.edu.tr
Name of Lecturers Asist Prof.Dr. Çisem Güneş Aktaş cisem.gunesaktas@agu.edu.tr
Instructor Dr. Uğur Kayaş ugur.kayas@agu.edu.tr
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Supplementary Course Book : Single Variable by James Steward (any edition)
Lecture Slides and Lecture Templates , Problem Solving_Templates and Notes hared in cloud. Self recorded Lecture and Problem Solving videos as an asynchronised component
Course Book : Thomas' Calculus Early Transcendentals, Thomas, Weir, J. Hass, 14’th Global Edition, Pearson, ISBN-13: 9781292253114
Content is presented through slides and the templates as well as the written lecture notes are available in a shared ONeDrive account.
All the documents are shared in the cloud
All the documents are shared in the cloud
All the documents are shared in the cloud

Course Category
Mathematics and Basic Sciences %100
Engineering %0
Engineering Design %0
Social Sciences %0
Education %0
Science %0
Health %0
Field %0

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Yarıl yılSonu Sınavı/Dönem Projesinin Başarı Notuna Katkısı 1 % 35
Quiz/Küçük Sınav 11 % 20
Final examination 1 % 45
Total
13
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Kısa Sınav 11 1 11
Kişisel Çalışma 14 5 70
Ders dışı çalışma 2 14 28
Yüz Yüze Ders 14 5 70
Der Dışı Final Sınavı 1 2 2
Ders Dışı Ara Sınav 1 2 2
Total Work Load   Number of ECTS Credits 6 183

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To understand the concepts of limits and continuity of single variable functions
2 To establish the theoretical understanding of derivative of a function and build the geometric interpretation of it and to calculate the derivative of a given function.
3 To gain the ability of sketching a detailed graph of a function.
4 To apply derivative rules to optimize a given source.
5 To calculate the integral of a given function by using different techniques
6 To apply integration to find the area under a curve, to find length of a curve and to calculate the volume and surface area of the solid.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 2.1 Rates of Change and Tangent Lines to Curves, 2.2 Limit of a Function and Limit Laws, 2.4 One-sided Limits 2.5 Continuity Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving_Template Problem Solving_written Version Lecture Notes_Template Lecture Notes_written version Problem Solving_Template Problem Solving_written Version
2 2.6 Limit Involving Infinity: Asymptotes of Graphs 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving_Template Problem Solving_written Version
3 3.3 Differentiation Rules 3.4 The derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
4 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
5 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
6 4.1 Extreme Values of Functions 4.2 The Mean Value Theorem Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
7 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hopital’s Rule Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
8 4.6 Applied Optimization 4.7 Newton’s Method 4.8 Antiderivatives Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
9 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
10 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Substitution and Area Between Curves Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
11 6.1 Volumes Using Cross-Section 6.2 Volumes Using Cylindrical Shell Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
12 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 7.1 The Logarithm Defined as an Integral Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
13 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version
14 8.4 Integration of Rational Functions by Partial Fractions 8.7 Improper Integrals Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version Self-Recored videos Lecture Notes_Template Lecture Notes_written version Problem Solving _Template Problem Solving _written Version


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15
All 4 4 2 2 3 2 2
C1 4 4 2 2 3 2 2
C2 4 4 2 2 3 2 2
C3 4 4 2 2 3 2 2
C4 4 4 2 2 3 2 2
C5 4 4 2 2 3 2 2
C6 4 4 2 2 3 2 2

Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant


https://sis.agu.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=74875&lang=en
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