A library of functions -- Key concept: the derivative -- Short-cuts to differentiation -- Using the derivative -- Key concept: the definite integral -- Constructing antiderivatives -- Integration -- Using the definite integral -- Sequences and series -- Approximating functions using series -- Differential equations -- Functions of several variables -- A fundamental tool: vectors -- Differentiating functions of several variables -- Optimization: local and globlal extrema -- Integrating functions of several variables -- Parameterization and vector fields -- Line integrals -- Flux integrals -- Calculus of vector fields.