A general calculus course based on the textbook by Stewart, Clegg, and Watson covering single-variable and multivariable calculus
A review of functions and their representations, mathematical models including linear, polynomial, power, rational, algebraic, trigonometric, exponential, and logarithmic functions, transformations, and inverse functions
A development of the limit concept including one-sided limits, limit laws, the precise epsilon-delta definition, continuity, limits at infinity, and the introduction of the derivative as a rate of change and as a function
A development of the standard differentiation rules for polynomials, exponentials, trigonometric, logarithmic, and inverse trigonometric functions, the chain rule, implicit differentiation, related rates, linear approximation, and hyperbolic functions
Applications of derivatives including extrema, the Mean Value Theorem, monotonicity, concavity, l'Hospital's Rule, curve sketching, optimization, Newton's Method, and antiderivatives
Riemann sums, the definite integral, the Fundamental Theorem of Calculus, indefinite integrals, the Net Change Theorem, and the substitution rule
Areas between curves, volumes by cross-sections and by cylindrical shells, and work as applications of the definite integral
Integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, a strategy for integration, approximate integration, and improper integrals
Arc length and surface area as applications of the definite integral and applications to physics and engineering
An introduction to first-order differential equations including separable equations
Curves defined parametrically, calculus on parametric curves, polar coordinates, and calculus in polar coordinates
Sequences, series and the standard convergence tests, power series, Taylor and Maclaurin series, and applications of Taylor polynomials
Three-dimensional coordinates, vectors, the dot and cross products, equations of lines and planes, and quadric surfaces
Vector-valued functions, derivatives and integrals of vector functions, arc length and curvature, and motion in space
Functions of several variables, partial derivatives, the multivariable chain rule, directional derivatives, gradients, extrema, and Lagrange multipliers
Double and triple integrals over regions, integrals in polar, cylindrical, and spherical coordinates, applications of double integrals, and change of variables