A general single-variable and multivariable Early Transcendentals calculus textbook by Rogawski/Adams/Franzosa 4e (2019). Covers Calc 1, Calc 2, and Calc 3 across Ch 1-16.
Functions, families of functions, trigonometric, inverse, exponential, and logarithmic functions - review of precalculus content used throughout calculus.
Limit concept introduced via tangent lines and instantaneous velocity; evaluating limits algebraically; continuity; trigonometric limits; limits at infinity; IVT; formal definition.
Definition of the derivative; differentiation rules including product, quotient, chain; implicit differentiation; derivatives of transcendentals; related rates.
Linearization; extrema; MVT; concavity; L'Hopital's Rule; curve sketching; applied optimization; Newton's Method.
Approximating area; Riemann sums; the definite integral; FTC Parts I and II; Net Change Theorem; the substitution method; further transcendental functions.
Area between curves; volumes by slicing/disk/washer/cylindrical shells; arc length and surface area; work.
Derivatives and integrals of exponential, logarithmic, inverse trigonometric, and hyperbolic functions; growth/decay applications.
Integration by parts; trigonometric integrals and substitution; partial fractions; strategies; improper integrals; numerical integration.
Fluid pressure and force; Taylor polynomials and approximations.
Solving separable differential equations and modeling with them.
Sequences; infinite series; convergence tests; absolute and conditional convergence; power series; Taylor series.
Parametric curves; arc length and speed for parametric curves; polar coordinates; area and arc length in polar form.
Vectors in the plane and 3-space; dot and cross products; lines and planes in 3-space; quadric surfaces; cylindrical and spherical coordinates.
Vector-valued functions; their calculus; arc length and speed; curvature; motion in 3-space.
Functions of several variables; partial derivatives; differentiability; gradient and directional derivatives; chain rules; optimization; Lagrange multipliers.
Double and triple integrals; iterated integration; integration in polar/cylindrical/spherical coordinates; change of variables.