General
Сдать экзамен по курсу "Calculus: Single Variable"
This course provides a brisk, challenging, and dynamic treatment of differential and integral calculus, with an emphasis on conceptual understanding and applications to the engineering, physical, and social sciences.
Для получения сертификата надо выполнить задания по каждой главе (по 4% от оценки) и сдать экзамен (80% от оценки).
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Chapter 1: Functions
Functions- The Exponential
- Taylor Series
Computing Taylor Series- Convergence
- Expansion Points
- Limits
- L'Hôpital's rule
- Orders of Growth
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Chapter 2: Differentiation
- Derivatives
- Differentiation Rules
- Linearization
- Higher Derivatives
- Optimization
- Differentials
- Differentiation Operator
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Chapter 3: Integration
- Indefinite Integrals
- A Simple O.D.E.
- More O.D.E.s
- O.D.E. Linearization
- Integration by Substitution
- Integration by Parts
- Trig Substitution
- Partial Fractions
- Definite Integrals
- The F.T.I.C.
- Improper Integrals
- Trigonometric Integrals
- Tables and Software
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Chapter 4: Applications
- Simple Areas
- Complex Areas
- Simple Volumes
- Complex Volumes
- Volume and Dimension
- Arclength
- Surface Area
- Work
- Elements
- Averages
- Centroids
- Moments and Gyrations
- Fair Probability
- Probability Densities
- Expectation and Variance
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Chapter 5: Discretization
- Sequences
- Differences
- Discrete Calculus
- Numerical O.D.E.s
- Numerical Integration
- Infinite Series
- Convergence Tests I
- Convergence Tests II
- Absolute & Conditional
- Power Series
- Taylor Series Redux
- Approximation and Error
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Conclusion
- Calculus Redux
- Foreshadowing
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Экзамен по курсу
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