| Biomedical Engineering (English) | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code: | MATH110 | ||||
| Course Name: | Calculus 2 | ||||
| Semester: | Spring | ||||
| Course Credits: |
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| Language of instruction: | English | ||||
| Course Condition: |
BENS101 - Calculus 1 | ENS101 - Calculus I | MATH109 - Calculus 1 |
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| Does the Course Require Work Experience?: | No | ||||
| Type of course: | Compulsory Courses | ||||
| Course Level: |
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| Mode of Delivery: | Face to face | ||||
| Course Coordinator: | Dr. Öğr. Üy. FUNDA ÖZDEMİR | ||||
| Course Lecturer(s): | Assist. Prof. Dr. FUNDA ÖZDEMIR | ||||
| Course Assistants: |
| Course Objectives: | The course aims to teach the improper integrals, sequences and series, differentiation, optimization and integration of functions of several variables, various coordinate systems and to gain the ability to use these concepts in solving engineering problems. |
| Course Content: | The content of the course consists of improper integrals, sequences and series, approximation of functions by series, functions of several variables, differentiation of functions of several variables, optimizing functions of several variables, integrating functions of several variables, integrals in Cartesian and polar coordinates. |
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The students who have succeeded in this course;
1) Compute the integrals over unbounded regions. 2) Learn the notion of convergence of series and use various tests to determine series convergence; find Taylor representations of functions and approximate functions via Taylor polynomial. 3) Understand and use the concept of a function of several variables, draw graphs in 3 dimensional spaces. 4) Compute partial derivatives, directional derivatives and write equations of tangent planes to surface; apply partial derivatives to find and test local extrema. 5) Evaluate double integrals in Cartesian and polar coordinates and triple integrals in Cartesian coordinates. |
| Week | Subject | Related Preparation |
| 1) | Improper integrals | |
| 2) | Sequences, infinite series | |
| 3) | The divergence and integral tests | |
| 4) | The ratio and alternating series tests | |
| 5) | Power series, Taylor series | |
| 6) | Vectors, dot product | |
| 7) | Cross product, planes and surfaces | |
| 8) | Midterm Exam | |
| 9) | Level curves, limits and continuity | |
| 10) | Partial derivatives, chain rule, directional derivatives, gradient, tangent planes | |
| 11) | Maximum/minimum problems | |
| 12) | Lagrange multipliers, double integrals over rectangular regions | |
| 13) | Double integrals over general regions or in polar coordinates | |
| 14) | Triple integrals |
| Course Notes / Textbooks: | Thomas, G.B. et al., Thomas’ Calculus, Pearson |
| References: | Calculus Early Transcendentals 2nd Edition (Global Edition), Briggs, Cochran & Gillett. |
| Course Learning Outcomes | 1 |
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| Program Outcomes | |||||||||||
| 1) Adequate knowledge of mathematics, science and biomedical engineering disciplines; Ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. | |||||||||||
| 2) Ability to identify, formulate and solve complex biomedical engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. | |||||||||||
| 3) Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | |||||||||||
| 4) Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in biomedical engineering practices; Ability to use information technologies effectively. | |||||||||||
| 5) Ability to design, conduct experiments, collect data, analyze and interpret results for the investigation of complex biomedical engineering problems or discipline-specific research topics. | |||||||||||
| 6) Ability to work effectively in disciplinary and multi-disciplinary teams; individual working skills. | |||||||||||
| 7) Ability to communicate effectively orally and in writing; knowledge of at least one foreign language, ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | |||||||||||
| 8) Awareness of the necessity of lifelong learning; the ability to access information, follow developments in science and technology, and constantly renew oneself. | |||||||||||
| 9) Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practices. | |||||||||||
| 10) Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship, innovation; information about sustainable development. | |||||||||||
| 11) Information about the effects of biomedical engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; Awareness of the legal consequences of biomedical engineering solutions. | |||||||||||
| No Effect | 1 Lowest | 2 Average | 3 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Adequate knowledge of mathematics, science and biomedical engineering disciplines; Ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. | |
| 2) | Ability to identify, formulate and solve complex biomedical engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. | |
| 3) | Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | |
| 4) | Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in biomedical engineering practices; Ability to use information technologies effectively. | |
| 5) | Ability to design, conduct experiments, collect data, analyze and interpret results for the investigation of complex biomedical engineering problems or discipline-specific research topics. | |
| 6) | Ability to work effectively in disciplinary and multi-disciplinary teams; individual working skills. | |
| 7) | Ability to communicate effectively orally and in writing; knowledge of at least one foreign language, ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | |
| 8) | Awareness of the necessity of lifelong learning; the ability to access information, follow developments in science and technology, and constantly renew oneself. | |
| 9) | Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practices. | |
| 10) | Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship, innovation; information about sustainable development. | |
| 11) | Information about the effects of biomedical engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; Awareness of the legal consequences of biomedical engineering solutions. |
| Semester Requirements | Number of Activities | Level of Contribution |
| Midterms | 1 | % 40 |
| Final | 1 | % 60 |
| total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 40 | |
| PERCENTAGE OF FINAL WORK | % 60 | |
| total | % 100 | |
| Activities | Number of Activities | Preparation for the Activity | Spent for the Activity Itself | Completing the Activity Requirements | Workload | ||
| Course Hours | 13 | 0 | 3 | 39 | |||
| Application | 13 | 0 | 2 | 26 | |||
| Study Hours Out of Class | 13 | 0 | 3 | 39 | |||
| Midterms | 1 | 13 | 2 | 15 | |||
| Final | 1 | 23 | 2 | 25 | |||
| Total Workload | 144 | ||||||