Calculus

Understanding how functions behave without sudden breaks.

A practical introduction to how calculus measures change in real situations.

Understanding how slope shows change between quantities.

Understanding how tangent lines behave near curves and how they give local approximations.

Explore the nuances of derivatives in calculus, focusing on their application in measuring instantaneous change.

Explore the nuances of differentiating products of functions using the product rule.

Explore the intricacies of the Chain Rule in Calculus, focusing on differentiating composite functions.

Explore how derivatives are applied in real-world scenarios such as motion, growth, and optimization.

Explore techniques to find optimal solutions in calculus.

Advanced mastery of integrals: judgment, restraint, and calibration in ambiguous accumulation scenarios.

Mastering judgment in using integrals to compute area, focusing on ambiguous cases, hidden costs, and restraint.

Advanced judgment in evaluating definite integrals under ambiguous and high-stakes conditions.

Mastery of the subtle connections between differentiation and integration, focusing on judgment and restraint in ambiguous cases.

Mastering judgment in using integration by parts under ambiguous and high-stakes conditions. For advanced learners only.

Advanced judgment in variable substitution for integrals: recognizing when, why, and how to restrain action.

Mastering judgment in handling improper integrals: infinite intervals and discontinuities.

Mastering judgment in modeling change with differential equations under uncertainty and stress.

Mastering calculus in multiple dimensions, focusing on judgment and restraint in complex systems.

Advanced calibration of calculus judgment under ambiguity, stress, and nonlinear consequences.