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Course Code: 
MATH 132
Course Period: 
Autumn
Course Type: 
Core
P: 
3
Lab: 
2
Credits: 
4
ECTS: 
6
Prerequisite Courses: 
Course Language: 
İngilizce
Course Objectives: 
The aim of this course is to provide students with an understanding of sequences, series, analytic geometry in 3-space, limits and partial derivatives of functions of several variables, multiple integrals, line integrals of vector fields and their calculations.
Course Content: 

Applications of integrals; volumes of solids of revolution, arc length, areas of surfaces of revolution. Convergence of sequences. Convergence tests for series. Power, Taylor and Maclaurin series. Analytic geometry in 3-space. Functions of several variables, partial derivatives, extreme values. Double integrals

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination

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Course Learning Outcomes

Learning Outcomes Teaching Methods Assessment Methods
1) Knows the concepts of convergence of sequences and series and performs related calculations. 1,2 A
2) Knows the concepts of vectors, lines, planes and quadric surfaces in 3-space and performs related calculations. 1,2 A
3) Knows the concept of double integrals and some of its applications and performs related calculations. 1,2 A

 

Course Flow

Week Topics Study Materials
1 Volumes by slicing - Solids of revolution,   (From Textbook) 7.1,7.2
2 Arc Length and surface area, 7.3
3 Sequences and Convergence, Infinite Series, 9.1,9.2
4 Convergence Tests for Positive Series, 9.3
5 Absolute and Conditional Convergence, Power Series, 9.4,9.5
6 Taylor and Maclaurin Series, Applications of Taylor and Maclaurin Series, 9.6,9.7
7 Analytic Geometry in Three Dimensions, Vectors, 10.1,10.2
8 The Cross Product in 3-Space, Planes and Lines, 10.3,10.4
9 Quadric Surfaces, Functions of Several Variables, Limits and Continuity 10.5,12.1,12.2
10 Partial Derivatives, Higher-Order Derivatives, The Chain Rule 12.3,12.4,12.5
11 Linear Approximations, Differentials, Gradients and Directional Derivatives, Implicit Functions 12.6,12.7,12.8
12 Extreme Values, Extreme Values of Functions Defined on Restricted Domains, Lagrange Multipliers 13.1,13.2,13.3
13 Double Integrals, Iteration of Double Integrals in Cartesian Coordinates 14.1,14.2
14 Double Integrals in Polar Coordinates, Change of variables in double Integrals 14.4

 

 

Recommended Sources

Textbook R. A. Adams and C. Essex, Calculus, 7th Ed., Pearson (2010)
Additional Resources  

 

Material Sharing

Documents  
Assignments  
Exams  

 

 

Assessment

IN-TERM STUDIES NUMBER PERCENTAGE
Mid-terms 2 100
Quizzes 0 0
Assignments 0 0
Total   100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE 1 40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE   60
Total   100

 

Course’s Contribution to Program

No Program Learning Outcomes Contribution
1 2 3 4 5
1 The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)         X
2 Acquiring fundamental knowledge on fundamental research fields in mathematics         X
3 Ability form and interpret the relations between research topics in mathematics     X    
4 Ability to define, formulate and solve mathmatical problems         X
5 Consciousness of professional ethics and responsibilty X        
6 Ability to communicate actively          
7 Ability of self-development in fields of interest         X
8 Ability to learn, choose and use necessary information technologies          
9 Lifelong education          

 

ECTS

Activities Quantity Duration
(Hour)
Total
Workload
(Hour)
Course Duration (14x Total course hours) 14 5 70
Hours for off-the-classroom study (Pre-study, practice) 14 3 42
Mid-terms (Including self study) 2 8 16
Quizzes      
Assignments      
Final examination (Including self study) 1 12 12
Total Work Load     140
Total Work Load / 25 (h)     5.6
ECTS Credit of the Course     6