# Calculus 1 for engineering

### Course topics

In this course the basic concepts of one-dimensional analysis (a limit, a derivative, an integral) are introduced and explored in different applications: graphing functions, approximations, calculating areas etc.

- Limit of a function, continuity.
- Derivative, basic derivative formulas.
- Derivative of an inverse function; derivative of a composite function, the chain rule; derivative of an implicit function.
- Derivatives of high order.
- The mean value problem theorem. Indeterminate forms and l’Hopital’s rule.
- Rise and fall of a function; local minimal and maximal values of a function.
- Concavity and points of inflection. Asymptotes. Graphing functions.
- Linear approximations and differentials. Teylor’s theorem and approximations of an arbitrary order.
- Indefinite integrals: definition and properties.
- Integration methods: the substitution method, integration by parts.
- Definite integrals. The fundamental theorem of integral calculus (Newton-Leibniz’s theorem).
- Calculating areas.

##### Bibliography

**Thomas & Finney**, *Calculus and Analytic Geometry*, 8th Edition, Addison-Wesley (World Student Series).

### Course Information

- University course catalogue:
- 201.1.9711
- Level:
- Service
- Credits:
- 5.0

##### Recently Given

- 2024–25–A
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- 2022–23–B (Dr. Natalia Gulko)
- 2022–23–A (Prof. Izhar Oppenheim)
- 2021–22–B (Dr. Natalia Gulko)
- 2021–22–A (Prof. Tom Meyerovitch)
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- 2019–20–B

###### Departments

- Software and information systems engineering
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