Course Details

CALCULUS 2

MATH152

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Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS Credits
2MATH152CALCULUS 25+0+056

Course Details
Language of Instruction English
Level of Course Unit Bachelor's Degree
Department / Program BIOENGINEERING
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course Bu ders, çok değişkenli kalkülüsün diferansiyel ve integral kısmını öğretmeyi amaçlamaktadır:

Seriler ve diziler hakkında anlayış kazandırmak, yakınsama-aykırılık belirleyerek toplamını bulma yeteneği sağlamak

Çok değişkenli bir fonksiyonun her yönünü analiz edebilmek için temel bilgi ve beceriler sunmak

Çok değişkenli kalkülüsü incelemek için gerekli matematiksel araçların teorik ve kavramsal anlayışını oluşturmak

Temel matematiksel kavramları ve araçları kullanma becerisini geliştirerek gerçek yaşam/doğadan türetilen bir problemi tanıma ve analiz etme, bu problemlere uygun hesaplama ve analiz tekniklerini uygulayarak çözümler sunmak.
Course Content This course is a continuation of single variable calculus and covers the fundamentals of differentiation and integration in 3-dimensional and bigger spaces which is called multi-variable calculus. In this context, series, taking limits, differentiating, optimizing, graphing and integrating in 3-d are being taught. By the end of the semester, the students will be able to demonstrate an understanding of a muti-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 ( MATH151 )
Course Coordinator Asist Prof.Dr. Çisem Güneş Aktaş cisem.gunesaktas@agu.edu.tr
Name of Lecturers Instructor Dr. Uğur Kayaş ugur.kayas@agu.edu.tr
Associate Prof.Dr. Ali Hakan Tor hakan.tor@agu.edu.tr
Asist Prof.Dr. Çisem Güneş Aktaş cisem.gunesaktas@agu.edu.tr
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Course Book: Text Book: Thomas' Calculus Early Transcendentals, Thomas, Weir, J. Hass, 14’th Global Edition, Pearson, ISBN-13: 9781292253114
Lecture Slides and Lecture Templates , Problem Solving_Templates and Notes shared in cloud. Self recorded Lecture and Problem Solving videos as an asynchronised component
Content is presented through slides and the templates as well as the written lecture notes and problem solving templates 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

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 distinguish sequences and series and relate them mathematically,
2 To determine convergence/divergence behavior of different types of series by using various convergence tests,
3 To calculate the partial derivative of several variable functions. Use these partial derivatives for application,
4 To evaluate double in both cartesian and polar coordinate system and triple integral in Cartesian, cylindrical and spherical,


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 9.1 Sequences 9.2 Infinite Series 9.3 Integral Test 9.4 Comparison Test 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
2 9.4 Comparison Test 9.5 The Ratio and Root Test 9.6 Alternating Series, Absolute and Conditional Convergence 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 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 Applications of Taylor Series 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 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 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 11.5 Lines and Planes in Space 10.1 Parametrizations of Plane Curves 10.2 Calculus with Parametric 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
6 12.1 Curves in Space and Their Tangents 12.2 Integrals of Vector Functions 12.3 Arc Length in Space 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 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 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 13.3 Partial Derivatives 13.4 The Chain 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
9 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes 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
10 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multipliers 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 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 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 10.3 Polar Coordinates 14.4 Double Integrals in Polar Form 11.6 Cylinders and Quadric Surfaces 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 14.5 Triple Integrals in Rectangular Coordinates 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 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 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple 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

Recommended Optional Programme Components
Veri yok

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
All 4 4 2 2 2 2 2
C1 3 3 2 1 2 2 2
C2 3 3 2 1 2 2 2
C3 3 3 2 1 2 2 2
C4 3 3 2 1 2 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=70784&lang=en
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