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) |
Build up a body of knowledge in mathematics, science and Mechanical Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. |
3 |
2) |
Identify, formulate, and solve complex Mechanical Engineering problems; select and apply proper modeling and analysis methods for this purpose. |
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3) |
Design complex Mechanical systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. |
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4) |
Devise, select, and use modern techniques and tools needed for solving complex problems in Mechanical Engineering practice; employ information technologies effectively. |
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5) |
Design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Mechanical Engineering. |
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6) |
Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Mechanical-related problems. |
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7) |
Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions. |
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8) |
Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself. |
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9) |
Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Mechanical Engineering applications. |
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10) |
Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development. |
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11) |
Acquire knowledge about the effects of practices of Mechanical Engineering on health, environment, security in universal and social scope, and the contemporary problems of Mechatronics engineering; is aware of the legal consequences of Mechanical engineering solutions. |
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