A general single-variable and multivariable Early Transcendentals calculus textbook by Anton/Bivens/Davis 12e (2021). Covers Calc 1, Calc 2, and Calc 3 across Ch 0-15.
Functions, function families, inverse and exponential/logarithmic functions — review.
Intuitive and rigorous limits, computing limits, infinite limits, limits at infinity, continuity.
Tangent lines, the derivative function, basic differentiation rules, product/quotient, trig, chain rule.
Implicit differentiation, derivatives of log/exp/inverse-trig, related rates, linearization, L'Hôpital.
Curve sketching, optimization, rectilinear motion, Newton's method, Rolle's/MVT.
Antiderivatives, indefinite/definite integrals, FTC, substitution.
Area, volumes, arc length, surface area, work, fluid pressure, hyperbolic functions.
Integration by parts, trig integrals/substitution, partial fractions, numerical integration, improper. §7.7 split-bundled.
Modeling, separation of variables.
Sequences, series, convergence tests, Taylor and Maclaurin series, power series operations.
Parametric curves, polar coordinates, calculus in polar.
3D coords, vectors, dot/cross products, lines/planes, quadric surfaces, cyl/spherical coords.
Vector-valued functions, calculus of, change of param, TNB, curvature, motion.
Multivariable functions, partials, chain rule, directional derivatives, tangent planes, optimization.
Double/triple integrals, polar/cyl/sph coords, change of variables.