- Limits and Continuity
- calculations of limits
- limit theorems
- continuity at a point and on an interval
- essential and removable discontinuities
- Intermediate Value Theorem
- The Derivative
- rates of change and tangent lines
- differentiation from definition
- differentiation formulas and rules
- chain rule
- implicit differentiation
- higher derivatives
- the differential and differential approximations
- linear approximations
- applications to related rates
- Inverse Functions: Exponential, Logarithmic and Inverse Trigonometric Functions
- definitions, properties, and graphs
- differentiation of logarithmic and exponential functions (any base)
- logarithmic differentiation
- differentiation of inverse trigonometric functions
- applications to related rates
- limits involving combinations of exponential, logarithmic, trigonometric, and inverse trigonometric functions
- L'Hôpital's rule
- Graphing and Algebraic Functions
- increasing and decreasing functions
- local extrema
- Rolle's Theorem and Mean Value Theorem
- curve sketching
- concavity; inflection points
- asymptotic behaviour; limits at infinity; infinite limits
- applied maximum and minimum problems
- antidifferentiation
- rectilinear motion
- Parametric Equations and Polar Coordinates
- parametric representation of curves in R²
- derivatives and tangent lines of functions in parametric form
- tangent lines to graphs in polar form
- definitions and relationships between polar and Cartesian coordinates
- graphing of r = f(?)
- Optional Topics (included at the discretion of the instructor).
- a formal limit proof (using epsilonics)
- application of the absolute value and greatest integer functions
- proofs of the rules of differentiation (differentiation formulas) for algebraic functions
- proofs of the differentiation formulas for trigonometric functions from the definition of derivative
- a proof of L'Hôpital's rule for the case of "0/0"
- Newton’s Method
제가 다음 학기에 해외대학에서 들으려고하는 수학 과목인데 많이어렵나요???
이름만 들으면 어려워보이는데..
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