Calculus 1A

Proofs, Parity, and Divisibility

Constructing and evaluating proofs of elementary integer statements. · 7 steps

Mathematical Induction

Proof by induction over the natural numbers. · 7 steps

Counting and Combinatorics

Counting arrangements and selections subject to constraints. · 7 steps

Functions, Domains, and Inverses

Function properties needed to analyze and transform functions. · 7 steps

Vectors, Dot Products, and Projections

Vector calculations in 2D and 3D using lengths, angles, and projections. · 7 steps

Cross Products, Lines, and Planes

Using 3D vector geometry to describe lines and planes. · 7 steps

Limits and Continuity in One Variable

Limits, one-sided behavior, and continuity of real-valued functions. · 7 steps

The Derivative and Differentiability

The derivative as a limit of difference quotients and a test of local behavior. · 7 steps

Differentiation Rules and Tangent Lines

Computing derivatives and using them to form local linear models. · 7 steps

Derivative Applications and Extreme Values

Using derivatives and the Extreme Value Theorem to locate absolute extrema. · 7 steps

Taylor Polynomials and Error Bounds

Approximating a function near a point with a Taylor polynomial and bounding its remainder. · 7 steps

Limits and Continuity of Multivariable Functions

Analyzing limits and continuity for functions of several variables. · 7 steps

Partial Derivatives and Tangent Planes

Using partial derivatives to describe local linear behavior of a surface. · 7 steps