Calculus I (Differential)
Limits made rigorous, then the derivative and everything it can do.
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Limits and Continuity
Limit laws, squeeze theorem, continuity, and the Intermediate Value Theorem.
The Derivative and Differentiation Rules
Definition, power/product/quotient rules, and derivatives of trig, exponential and log functions.
Chain Rule and Implicit Differentiation
Composite functions, implicit curves, logarithmic differentiation, and inverse-function derivatives.
Related Rates
Modelling linked changing quantities.
Extrema and Curve Sketching
Critical points, Mean Value Theorem, concavity, and complete curve analysis.
Optimization
Applied max-min problems with constraints.
Linear Approximation, Differentials and L'Hôpital
Tangent-line approximation, Newton's method, and indeterminate forms.