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 mathematical 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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Course Notes / Textbooks: |
Giordano, Frank R., Hass, Joel, Weir, Maurice D., Thomas, George B., Thomas' Calculus, 11th Edition, ISBN 9780321185587, 2004, Addison-Wesley. |
References: |
Calculus: A Complete Course, Richard A. Adams, Prentice Hall, 6th ed, 2006. |
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Program Outcomes |
Level of Contribution |
1) |
Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline. |
2 |
2) |
Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems. |
3 |
3) |
Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques. |
2 |
4) |
Have the ability to think analytically and use the time effectively in the process of deduction. |
3 |
5) |
Have the ability to search the literature, understand and interpret scientific articles. |
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6) |
Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License. |
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7) |
Have the ability to work efficiently in interdisciplinary teams. |
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8) |
Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations. |
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9) |
Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards. |
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10) |
Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria. |
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11) |
Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves. |
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