Course Objectives: |
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: |
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 computer engineering principles, both theoretical and practical, and the ability to apply this knowledge to complex engineering problems. |
3 |
2) |
Ability to identify, formulate, and solve complex computer engineering problems using appropriate analysis and modeling techniques. |
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3) |
Ability to design and develop complex computer systems, devices, or products that meet specific requirements and operate under realistic constraints and conditions, using modern design methods. |
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4) |
Ability to develop, select and use modern techniques and tools used for the analysis and solution of complex computer engineering problems, and the ability to use information technologies effectively. |
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5) |
Ability to plan and conduct experiments, collect and analyze data, and interpret results in the study of complex computer engineering problems or 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; 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 computer engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in computer engineering; awareness of the legal consequences of computer engineering solutions. |
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