## Course Detail

## Course Description

Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|

CALCULUS II | IND1210751 | Spring Semester | 4+0 | 4 | 6 |

Course Program | ( A ) Pazartesi 15:30-16:15 ( A ) Pazartesi 16:30-17:15 ( A ) Perşembe 10:00-10:45 ( A ) Perşembe 11:00-11:45 |

Prerequisites Courses | |

Recommended Elective Courses |

Language of Course | English |

Course Level | First Cycle (Bachelor's Degree) |

Course Type | Required |

Course Coordinator | Assist.Prof. Özge BİÇER ÖDEMİŞ |

Name of Lecturer(s) | Assist.Prof. Mohamed Khaled Mohamed Ismaıl KHALIFA |

Assistant(s) | |

Aim | To teach fundamental math contents, methods and techniques, and its applications for the study of Engineering. |

Course Content | This 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 Kazanımları | Teaching Methods | Assessment Methods |

1. Use the concept of polar coordinates to find areas, arc length of curves, and representations of conic sections. | 12, 14, 9 | A, 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, 9 | A, E |

3. Recognize multivariable functions to compute limits, partial derivatives and directional derivatives, extreme values, tangent planes graphically, numerically and algebraically. | 12, 14, 9 | A, E |

4. Use multiple integrals to compute areas and volumes. | 12, 14, 9 | A, E |

5. Determine convergence or divergence of sequences and series. | 12, 14, 9 | A, E |

6. Find Power and Taylor Series of a function. | 12, 14, 9 | A, E |

Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method |

Assessment Methods: | A: Traditional Written Exam, E: Homework |

## Course Outline

Order | Subjects | Preliminary Work |
---|---|---|

1 | Parametric Equations and Polar Curves | Polynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain rule. |

2 | Parametric Equations and Polar Curves | Polynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain Rule. |

3 | Vectors 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 |

4 | Vectors 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. |

5 | Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative | Single Variable Functions, Limit and Continuity, Derivative |

6 | Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative | Single Variable Functions, Limit and Continuity, Derivative |

7 | Extreme Values of Multivariable Functions, Lagrange Multiplier | Derivative, Extreme Values of Single Variable Functions |

8 | Extreme Values of Multivariable Functions, Lagrange Multiplier | Derivative, Extreme Values of Single Variable Functions |

9 | Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates | Definite Integrals, Polar Coordinates |

10 | Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates | Definite Integrals, Polar Coordinates |

11 | Infinite Sequences: Limits of Sequences of Numbers, Subsequences, Monotonic Sequence Theorem | Functions, Limit |

12 | Infinite Sequences and Series: Series of Nonnegative Terms, Alternating Series, Absolute and Conditional Convergence | |

13 | Power Series: Interval of Convergence, Radius of Convergence, Term by Term Differentiation, Term by Term Integration | Absolute Value, Integral, Derivative |

14 | Taylor 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 | |||||||

No | Program Qualification | Contribution Level | |||||

1 | 2 | 3 | 4 | 5 | |||

1 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||

2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||

3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | X | |||||

4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | ||||||

5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | ||||||

6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | ||||||

7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | ||||||

8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | ||||||

9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||

10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||

11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. |

## Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 30 | |

Rate of Final Exam to Success | 70 | |

Total | 100 |

ECTS / Workload Table | ||||||

Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||

Course Hours | 14 | 4 | 56 | |||

Guided Problem Solving | 14 | 2 | 28 | |||

Resolution of Homework Problems and Submission as a Report | 0 | 0 | 0 | |||

Term Project | 0 | 0 | 0 | |||

Presentation of Project / Seminar | 0 | 0 | 0 | |||

Quiz | 0 | 0 | 0 | |||

Midterm Exam | 14 | 3 | 42 | |||

General Exam | 14 | 4 | 56 | |||

Performance Task, Maintenance Plan | 0 | 0 | 0 | |||

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

Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|

CALCULUS II | IND1210751 | Spring Semester | 4+0 | 4 | 6 |

Course Program | ( A ) Pazartesi 15:30-16:15 ( A ) Pazartesi 16:30-17:15 ( A ) Perşembe 10:00-10:45 ( A ) Perşembe 11:00-11:45 |

Prerequisites Courses | |

Recommended Elective Courses |

Language of Course | English |

Course Level | First Cycle (Bachelor's Degree) |

Course Type | Required |

Course Coordinator | Assist.Prof. Özge BİÇER ÖDEMİŞ |

Name of Lecturer(s) | Assist.Prof. Mohamed Khaled Mohamed Ismaıl KHALIFA |

Assistant(s) | |

Aim | To teach fundamental math contents, methods and techniques, and its applications for the study of Engineering. |

Course Content | This 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 Kazanımları | Teaching Methods | Assessment Methods |

1. Use the concept of polar coordinates to find areas, arc length of curves, and representations of conic sections. | 12, 14, 9 | A, 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, 9 | A, E |

3. Recognize multivariable functions to compute limits, partial derivatives and directional derivatives, extreme values, tangent planes graphically, numerically and algebraically. | 12, 14, 9 | A, E |

4. Use multiple integrals to compute areas and volumes. | 12, 14, 9 | A, E |

5. Determine convergence or divergence of sequences and series. | 12, 14, 9 | A, E |

6. Find Power and Taylor Series of a function. | 12, 14, 9 | A, E |

Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method |

Assessment Methods: | A: Traditional Written Exam, E: Homework |

### Course Outline

Order | Subjects | Preliminary Work |
---|---|---|

1 | Parametric Equations and Polar Curves | Polynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain rule. |

2 | Parametric Equations and Polar Curves | Polynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain Rule. |

3 | Vectors 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 |

4 | Equations of lines and circles, Real space. | |

5 | Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative | Single Variable Functions, Limit and Continuity, Derivative |

6 | Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative | Single Variable Functions, Limit and Continuity, Derivative |

7 | Extreme Values of Multivariable Functions, Lagrange Multiplier | Derivative, Extreme Values of Single Variable Functions |

8 | Extreme Values of Multivariable Functions, Lagrange Multiplier | Derivative, Extreme Values of Single Variable Functions |

9 | Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates | Definite Integrals, Polar Coordinates |

10 | Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates | Definite Integrals, Polar Coordinates |

11 | Infinite Sequences: Limits of Sequences of Numbers, Subsequences, Monotonic Sequence Theorem | Functions, Limit |

12 | Infinite Sequences and Series: Series of Nonnegative Terms, Alternating Series, Absolute and Conditional Convergence | |

13 | Power Series: Interval of Convergence, Radius of Convergence, Term by Term Differentiation, Term by Term Integration | Absolute Value, Integral, Derivative |

14 | Taylor 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 | |||||||

No | Program Qualification | Contribution Level | |||||

1 | 2 | 3 | 4 | 5 | |||

1 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||

2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||

3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | X | |||||

4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | ||||||

5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | ||||||

6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | ||||||

7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | ||||||

8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | ||||||

9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||

10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||

11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. |

### Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 30 | |

Rate of Final Exam to Success | 70 | |

Total | 100 |