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) |
Knows the basic concepts related to the theory and applications of chemistry, uses theoretical and applied knowledge, can select, develop and design methods. |
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2) |
Makes experimental planning and application for analysis, synthesis, separation and purification methods, provide solutions to the problems encountered and interpret the results. |
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3) |
Expresses the basic principles of sample preparation techniques and instrumental analysis methods used in qualitative and quantitative analysis of items, discusses their application areas. |
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4) |
Has knowledge about the sources, production, industrial applications and technologies of chemical substances. |
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5) |
Makes structural analyzes of chemical substances and interprets the results. |
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6) |
Work individually and in multidisciplinary groups, take responsibility, plan their tasks and use time effectively. |
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7) |
Follows the information in the field and communicates with colleagues by using English at a professional level. |
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8) |
Uses information and communication technologies along with computer software at the level required by the field. |
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9) |
Follows the national and international chemistry literature, transfers the knowledge gained orally or in writing. |
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10) |
Determines self-learning needs, manages/directs his/her learning. |
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11) |
Takes responsibility and adheres to the ethical values required by these responsibilities. |
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