Limits - unbounded - limits at infinity - trigonometric limits - continuity - continuity at a point - squeeze theorem - Intermediate Value Theorem Derivatives - derivative at a point - differentiation rules - chain rule - Rolle's Theorem - Mean Value Theorem - implicit differentiation - logarithmic differentiation - rate of change - curve sketching - differentials - linear approximation - max-min - Newton's method - related rates - slope & tangent Integration - Riemann sums - definite integral - indefinite integral - Fundamental Theorems of Calculus - improper integral - approximate definite integral - integration by parts - trig substitution - partial fractions - u substitution - area - volume of revolution -- disc method -- shell method -- washer method - MVT for integrals - arclength - surface of revolution - numerical integration (Other Topics) - algebra - approximation - differential equations - domain & range - factoring - finding roots - fixed point - geometry - graphing intro - growth & decay - history - inequalities - infinite series - modelling - non-calculus - optimization - paradoxes - parametric equations - trig identities
automaticity building computation creating counterexamples creating examples estimating forming a strategy generalization illustrative counterexample illustrative example math language multiple representations multiple solutions multistep problem plotting prediction proof qualitative sketching state a definition or theorem using a definition using a formula using a theorem classic problem exam question at UT tricks true-false word problem biology application chemistry application economics application physics application
linear quadratic cubic higher polynomial rational root exponential logarithm trigonometric inverse trig hyperbolic trig piecewise strange functions absolute value general inverses implicitly defined abstract function composite
Any 1 - Typical 2 - Hard 3 - Very Hard