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 |
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2) |
Trigonometric functions, exponential functions, inverse functions and logarithms |
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3) |
Rates of change and tangent line to curves, limit of a function and limit laws, one-sided limits, continuity |
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4) |
Limits involving infinity, asymptotes of graphs |
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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 |
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6) |
Chain rule, implicit differentiation |
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7) |
Derivatives of inverse functions, derivatives of logaritms and exponential functions, erivatives of inverse trigonometric functions |
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8) |
Midterm Exam |
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9) |
Extreme values of functions, mean value theorem, monotonic functions and the first derivative test, concavity and curve sketching |
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10) |
Concavity and curve sketching, indeterminate forms and L'hopital's rule, applied optimization, antiderivatives |
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11) |
Area and estimating with finite sums, sigma notation and limits of finite sums, definite integral, fundamental theorem of calculus |
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12) |
Indefinite integrals and substitution method, change of variable, area between curves, integrals of natural logarithm and exponential functions |
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13) |
Volumes using cross-sections, volumes using cylindrical shells |
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14) |
Using basic integration formulas, integration by parts, trigonometric integrals, trigonometric substitutions, integration of rational functions by partial fractions |
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Program Outcomes |
Level of Contribution |
1) |
Adequate knowledge in mathematics, science and software engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems. |
3 |
2) |
Ability to identify, formulate, and solve complex software engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. |
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3) |
Ability to design, implement, verify, validate, measure and maintain a complex software system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. |
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4) |
Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in software engineering applications; ability to use information technologies effectively. |
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5) |
Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or software engineering research topics. |
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6) |
Ability to work effectively within and multidisciplinary teams; individual study skills. |
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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. |
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8) |
Awareness of the necessity of lifelong learning; the ability to access information, to follow developments in science and technology and to renew continuously. |
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9) |
To act in accordance with ethical principles, professional and ethical responsibility; information on the standards used in engineering applications. |
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10) |
Information on business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; information about sustainable development. |
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11) |
Knowledge of the effects of software engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in software engineering; awareness of the legal consequences of software engineering solutions. |
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