Mathematics I Chapters

Representing functions of one variable; Polynomial, trigonometric, exponential, and logarithmic functions; Domain and range; Graphs of functions.

Precise definition of limits and continuity; Limits at infinity; Continuity; Horizontal, vertical, and slant asymptotes.

Tangents and velocity; Rate of change; Review of derivatives; Differentiability; Mean value theorem; Indeterminate forms; L'Hospital's Rule.

Curve sketching; Maxima and minima; Optimization problems; Newton's method.

Review of antiderivatives; Rectilinear motion; Indefinite integrals and net change; Definite integrals; Fundamental theorem of calculus; Improper integrals.

Area between curves; Volume using cylindrical shells; Approximate integration; Arc length; Surface area of revolution.

Introduction; First-order equations; Separable equations; Linear equations; Second-order linear differential equations; Non-homogeneous linear equations; Methods of solving ODEs.

Introduction to sequences and series; Convergence tests; Power series; Taylor and Maclaurin series.

Vectors in 2D and 3D; Applications; Dot and cross products; Equations of lines and planes; Derivatives and integrals of vector functions; Arc length; Curvature.

Limits and continuity; Partial derivatives; Tangent planes; Maxima and minima; Double and triple integrals.