2017–18–A
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).
Requirements and grading
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. 1. Limit of a function, continuity. 2. Derivative, basic derivative formulas. 3. Derivative of an inverse function; derivative of a composite function, the chain rule; derivative of an implicit function. 4. Derivatives of high order. 5. The mean value problem theorem. Indeterminate forms and l’Hopital’s rule. 6. Rise and fall of a function; local minimal and maximal values of a function. 7. Concavity and points of inflection. Asymptotes. Graphing functions. 8. Linear approximations and differentials. Teylor’s theorem and approximations of an arbitrary order. 9. Indefinite integrals: definition and properties. 10. Integration methods: the substitution method, integration by parts. 11. Definite integrals. The fundamental theorem of integral calculus (Newton-Leibniz’s theorem). 12. Calculating areas. Bibliography Thomas & Finney, Calculus and Analytic Geometry, 8th Edition, Addison-Wesley(World Student Series).
University course catalogue: 201.1.9711
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