An AP-Calc-targeted single+multi-variable calculus course based on Larson and Edwards (12e).
A review of essential precalculus material including graphs of equations, linear models, functions and their graphs, and the trigonometric functions used throughout calculus
An introduction to the concept of a limit, methods for finding limits graphically, numerically, and analytically, the formal definition of a limit, continuity, and infinite limits as a precursor to vertical asymptotes
The definition of the derivative as a limit and as a rate of change, basic differentiation rules, the product, quotient, and chain rules, implicit differentiation, and related rates
Using the derivative to analyze functions: extrema, the mean value theorem, monotonicity, concavity, curve sketching, limits at infinity, optimization, Newton's method, and differentials
Antiderivatives and indefinite integration, the area problem, Riemann sums, the definite integral, the fundamental theorem of calculus, integration by substitution, and numerical integration
The natural logarithm and exponential functions defined via integration, inverse functions, exponential and logarithmic differentiation and integration, inverse trigonometric functions, and hyperbolic functions
Introduction to first-order ordinary differential equations: growth and decay applications, separation of variables, and the logistic equation
Using integration to compute areas between curves, volumes of solids of revolution by disks and shells, arc length, surfaces of revolution, work, and fluid pressure
Advanced integration techniques including integration by parts, trigonometric integrals and substitutions, partial fractions, evaluation of indeterminate forms via L'Hopital's rule, and improper integrals
Sequences, infinite series and convergence tests, power series, and Taylor and Maclaurin series
Plane curves expressed parametrically, polar coordinates, and area and arc length in polar coordinates
Vectors in two and three dimensions, the dot and cross products, lines and planes in space, surfaces in space, and cylindrical and spherical coordinates
Vector-valued functions, their calculus, motion in space, and arc length and curvature for space curves
Multivariable functions, limits, partial derivatives, differentials, the chain rule, directional derivatives, gradients, tangent planes, extrema of functions of two variables, and Lagrange multipliers
Iterated integrals, double and triple integrals over general regions, change of variables to polar, cylindrical, and spherical coordinates, and Jacobians