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Course Detail

Course Description

CourseCodeSemesterT+P (Hour)CreditECTS
CALCULUS II-Spring Semester4+046
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of CourseEnglish
Course LevelFirst Cycle (Bachelor's Degree)
Course TypeRequired
Course CoordinatorAssist.Prof. Özge BİÇER ÖDEMİŞ
Name of Lecturer(s)Prof.Dr. Gülçin Mihriye MUSLU, Assist.Prof. Tuğba ASLAN KHALİFA
Assistant(s)
AimTo teach fundamental math contents, methods and techniques, and its applications for the study of Engineering.
Course ContentThis course contains; Parametric Equations and Polar Curves,Parametric Equations and Polar Curves,Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces ,Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces ,Functions of Several Variables: Limits and Continuity, Partial
Derivatives, Directional Derivative,Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative,Extreme Values of Multivariable Functions, Lagrange Multiplier,Extreme Values of Multivariable Functions, Lagrange Multiplier,Multiple Integrals: Double Integrals, Areas, Double
Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical
Coordinates,Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates,Infinite Sequences: Limits of Sequences of Numbers, Subsequences, Monotonic Sequence Theorem,Infinite Sequences and Series: Series of Nonnegative Terms, Alternating Series, Absolute and Conditional Convergence,Power Series: Interval of Convergence, Radius of Convergence, Term by Term Differentiation, Term by Term Integration,Taylor Series.
Dersin Öğrenme KazanımlarıTeaching MethodsAssessment Methods
1. Use the concept of polar coordinates to find areas, arc length of curves, and representations of conic sections.12, 14, 9A, E
2. Apply dot or cross product to calculate angles between vectors, orientation of axes, areas of triangles and parallelograms in space, scalar and vector projections, volumes of parallelepipeds and distance between a point and a plane in the space.12, 14, 9A, E
3. Recognize multivariable functions to compute limits, partial derivatives and directional derivatives, extreme values, tangent planes graphically, numerically and algebraically.12, 14, 9A, E
4. Use multiple integrals to compute areas and volumes.12, 14, 9A, E
5. Determine convergence or divergence of sequences and series.12, 14, 9A, E
6. Find Power and Taylor Series of a function.12, 14, 9A, E
Teaching Methods:12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method
Assessment Methods:A: Traditional Written Exam, E: Homework

Course Outline

OrderSubjectsPreliminary Work
1Parametric Equations and Polar CurvesPolynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain rule.
2Parametric Equations and Polar CurvesPolynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain Rule.
3Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces Equations of lines and circles, Real space
4Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces Equations of lines and circles, Real space.
5Functions of Several Variables: Limits and Continuity, Partial
Derivatives, Directional Derivative
Single Variable Functions, Limit and Continuity, Derivative
6Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional DerivativeSingle Variable Functions, Limit and Continuity, Derivative
7Extreme Values of Multivariable Functions, Lagrange MultiplierDerivative, Extreme Values of Single Variable Functions
8Extreme Values of Multivariable Functions, Lagrange MultiplierDerivative, Extreme Values of Single Variable Functions
9Multiple Integrals: Double Integrals, Areas, Double
Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical
Coordinates
Definite Integrals, Polar Coordinates
10Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical CoordinatesDefinite Integrals, Polar Coordinates
11Infinite Sequences: Limits of Sequences of Numbers, Subsequences, Monotonic Sequence TheoremFunctions, Limit
12Infinite Sequences and Series: Series of Nonnegative Terms, Alternating Series, Absolute and Conditional Convergence
13Power Series: Interval of Convergence, Radius of Convergence, Term by Term Differentiation, Term by Term IntegrationAbsolute Value, Integral, Derivative
14Taylor Series
Resources
Thomas’ Calculus, 12th ed., G. B. Thomas, Jr. and M. D. Weir and J. Hass, Addison-Wesley

Course Contribution to Program Qualifications

Course Contribution to Program Qualifications
NoProgram QualificationContribution Level
12345
1
1. An ability to apply knowledge of mathematics, science, and engineering
X
2
2. An ability to identify, formulate, and solve engineering problems
X
3
3. 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
X
4
4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
5
5. An ability to design and conduct experiments, as well as to analyze and interpret data
6
6. An ability to function on multidisciplinary teams
7
7. An ability to communicate effectively
8
8. A recognition of the need for, and an ability to engage in life-long learning
9
9. An understanding of professional and ethical responsibility
10
10. A knowledge of contemporary issues
11
11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context

Assessment Methods

Contribution LevelAbsolute Evaluation
Rate of Midterm Exam to Success 30
Rate of Final Exam to Success 70
Total 100
ECTS / Workload Table
ActivitiesNumber ofDuration(Hour)Total Workload(Hour)
Course Hours14456
Guided Problem Solving14228
Resolution of Homework Problems and Submission as a Report000
Term Project000
Presentation of Project / Seminar000
Quiz000
Midterm Exam14342
General Exam14456
Performance Task, Maintenance Plan000
Total Workload(Hour)182
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(182/30)6
ECTS of the course: 30 hours of work is counted as 1 ECTS credit.

Detail Informations of the Course

Course Description

CourseCodeSemesterT+P (Hour)CreditECTS
CALCULUS II-Spring Semester4+046
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of CourseEnglish
Course LevelFirst Cycle (Bachelor's Degree)
Course TypeRequired
Course CoordinatorAssist.Prof. Özge BİÇER ÖDEMİŞ
Name of Lecturer(s)Prof.Dr. Gülçin Mihriye MUSLU, Assist.Prof. Tuğba ASLAN KHALİFA
Assistant(s)
AimTo teach fundamental math contents, methods and techniques, and its applications for the study of Engineering.
Course ContentThis course contains; Parametric Equations and Polar Curves,Parametric Equations and Polar Curves,Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces ,Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces ,Functions of Several Variables: Limits and Continuity, Partial
Derivatives, Directional Derivative,Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative,Extreme Values of Multivariable Functions, Lagrange Multiplier,Extreme Values of Multivariable Functions, Lagrange Multiplier,Multiple Integrals: Double Integrals, Areas, Double
Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical
Coordinates,Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates,Infinite Sequences: Limits of Sequences of Numbers, Subsequences, Monotonic Sequence Theorem,Infinite Sequences and Series: Series of Nonnegative Terms, Alternating Series, Absolute and Conditional Convergence,Power Series: Interval of Convergence, Radius of Convergence, Term by Term Differentiation, Term by Term Integration,Taylor Series.
Dersin Öğrenme KazanımlarıTeaching MethodsAssessment Methods
1. Use the concept of polar coordinates to find areas, arc length of curves, and representations of conic sections.12, 14, 9A, E
2. Apply dot or cross product to calculate angles between vectors, orientation of axes, areas of triangles and parallelograms in space, scalar and vector projections, volumes of parallelepipeds and distance between a point and a plane in the space.12, 14, 9A, E
3. Recognize multivariable functions to compute limits, partial derivatives and directional derivatives, extreme values, tangent planes graphically, numerically and algebraically.12, 14, 9A, E
4. Use multiple integrals to compute areas and volumes.12, 14, 9A, E
5. Determine convergence or divergence of sequences and series.12, 14, 9A, E
6. Find Power and Taylor Series of a function.12, 14, 9A, E
Teaching Methods:12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method
Assessment Methods:A: Traditional Written Exam, E: Homework

Course Outline

OrderSubjectsPreliminary Work
1Parametric Equations and Polar CurvesPolynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain rule.
2Parametric Equations and Polar CurvesPolynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain Rule.
3Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces Equations of lines and circles, Real space
4Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces Equations of lines and circles, Real space.
5Functions of Several Variables: Limits and Continuity, Partial
Derivatives, Directional Derivative
Single Variable Functions, Limit and Continuity, Derivative
6Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional DerivativeSingle Variable Functions, Limit and Continuity, Derivative
7Extreme Values of Multivariable Functions, Lagrange MultiplierDerivative, Extreme Values of Single Variable Functions
8Extreme Values of Multivariable Functions, Lagrange MultiplierDerivative, Extreme Values of Single Variable Functions
9Multiple Integrals: Double Integrals, Areas, Double
Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical
Coordinates
Definite Integrals, Polar Coordinates
10Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical CoordinatesDefinite Integrals, Polar Coordinates
11Infinite Sequences: Limits of Sequences of Numbers, Subsequences, Monotonic Sequence TheoremFunctions, Limit
12Infinite Sequences and Series: Series of Nonnegative Terms, Alternating Series, Absolute and Conditional Convergence
13Power Series: Interval of Convergence, Radius of Convergence, Term by Term Differentiation, Term by Term IntegrationAbsolute Value, Integral, Derivative
14Taylor Series
Resources
Thomas’ Calculus, 12th ed., G. B. Thomas, Jr. and M. D. Weir and J. Hass, Addison-Wesley

Course Contribution to Program Qualifications

Course Contribution to Program Qualifications
NoProgram QualificationContribution Level
12345
1
1. An ability to apply knowledge of mathematics, science, and engineering
X
2
2. An ability to identify, formulate, and solve engineering problems
X
3
3. 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
X
4
4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
5
5. An ability to design and conduct experiments, as well as to analyze and interpret data
6
6. An ability to function on multidisciplinary teams
7
7. An ability to communicate effectively
8
8. A recognition of the need for, and an ability to engage in life-long learning
9
9. An understanding of professional and ethical responsibility
10
10. A knowledge of contemporary issues
11
11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context

Assessment Methods

Contribution LevelAbsolute Evaluation
Rate of Midterm Exam to Success 30
Rate of Final Exam to Success 70
Total 100

Numerical Data

Student Success

Ekleme Tarihi: 09/10/2023 - 10:50Son Güncelleme Tarihi: 09/10/2023 - 10:51