| Course Objectives: |
The course aims to teach the concepts of limit, continuity, derivative and integral in functions of one variable and to gain the ability to use these concepts in solving engineering problems. |
| Course Content: |
The content of the course consists of functions, graphs, limit, continuity, derivative definition, differentiation rules, chain rule, derivatives of implicit functions, applications of derivatives, definite integral, indefinite integral, applications of integral, transcendental functions. |
| Week |
Subject |
Related Preparation |
| 1) |
Functions and their graphs , combining functions, shifting and scaling graphs |
|
| 2) |
Trigonometric functions, exponential functions, inverse functions and logarithms |
|
| 3) |
Rates of change and tangent line to curves, limit of a function and limit laws, one-sided limits, continuity |
|
| 4) |
Limits involving infinity, asymptotes of graphs |
|
| 5) |
Tangent lines and derivative at a point, the derivative as a function, differentiation rules, the derivative as a rate of change, derivatives of trigonometric functions |
|
| 6) |
Chain rule, implicit differentiation |
|
| 7) |
Derivatives of inverse functions, derivatives of logaritms and exponential functions, erivatives of inverse trigonometric functions |
|
| 8) |
Midterm Exam |
|
| 9) |
Extreme values of functions, mean value theorem, monotonic functions and the first derivative test, concavity and curve sketching |
|
| 10) |
Concavity and curve sketching, indeterminate forms and L'hopital's rule, applied optimization, antiderivatives |
|
| 11) |
Area and estimating with finite sums, sigma notation and limits of finite sums, definite integral, fundamental theorem of calculus |
|
| 12) |
Indefinite integrals and substitution method, change of variable, area between curves, integrals of natural logarithm and exponential functions |
|
| 13) |
Volumes using cross-sections, volumes using cylindrical shells |
|
| 14) |
Using basic integration formulas, integration by parts, trigonometric integrals, trigonometric substitutions, integration of rational functions by partial fractions |
|
| |
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. |
3 |
| 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. |
|