Course Detail
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| CALCULUS II | - | Fall Semester | 4+0 | 4 | 6 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Mohamed Khaled Mohamed Ismaıl KHALIFA |
| Name of Lecturer(s) | Assist.Prof. Özge BİÇER ÖDEMİŞ |
| 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 | An ability to apply knowledge of mathematics, science, and engineering | X | |||||
| 2 | An ability to identify, formulate, and solve engineering problems | X | |||||
| 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 | An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | ||||||
| 5 | An ability to design and conduct experiments, as well as to analyze and interpret data | ||||||
| 6 | An ability to function on multidisciplinary teams | ||||||
| 7 | An ability to communicate effectively | ||||||
| 8 | A recognition of the need for, and an ability to engage in life-long learning | ||||||
| 9 | An understanding of professional and ethical responsibility | ||||||
| 10 | A knowledge of contemporary issues | ||||||
| 11 | The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context | ||||||
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 | - | Fall Semester | 4+0 | 4 | 6 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Mohamed Khaled Mohamed Ismaıl KHALIFA |
| Name of Lecturer(s) | Assist.Prof. Özge BİÇER ÖDEMİŞ |
| 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 | An ability to apply knowledge of mathematics, science, and engineering | X | |||||
| 2 | An ability to identify, formulate, and solve engineering problems | X | |||||
| 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 | An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | ||||||
| 5 | An ability to design and conduct experiments, as well as to analyze and interpret data | ||||||
| 6 | An ability to function on multidisciplinary teams | ||||||
| 7 | An ability to communicate effectively | ||||||
| 8 | A recognition of the need for, and an ability to engage in life-long learning | ||||||
| 9 | An understanding of professional and ethical responsibility | ||||||
| 10 | A knowledge of contemporary issues | ||||||
| 11 | The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 30 | |
| Rate of Final Exam to Success | 70 | |
| Total | 100 | |