A general single-variable and multivariable calculus course based on the textbook by Briggs, Cochran, Gillett, and Schulz, organized by Pearson around an "intuition before formality" approach with strong graphical motivation.
A review of functions, their representations, and the elementary function families used throughout the calculus course (linear, polynomial, rational, algebraic, exponential, logarithmic, and trigonometric functions and their inverses).
A development of the limit concept from intuitive ideas through formal techniques, including one-sided limits, infinite limits, limits at infinity, and continuity, culminating in the precise epsilon-delta definition.
The derivative as instantaneous rate of change, computed first from the limit definition and then through differentiation rules: power, product, quotient, chain, implicit, and derivatives of trigonometric, logarithmic, exponential, and inverse trig functions, with related-rates applications.
Geometric and modeling applications of the derivative including extreme-value problems, the Mean Value Theorem, curve sketching, optimization, l'Hopital's rule, Newton's method, and antiderivatives.
The definite integral developed via Riemann sums, the Fundamental Theorem of Calculus connecting differentiation and integration, properties of integrals, and the substitution method.
Geometric and physical applications of definite integration including area between curves, volumes by slicing and shells, arc length, surface area of revolution, and work-and-force problems.
A more rigorous treatment of the natural logarithm and exponential, modeling problems using exponential growth and decay, and the hyperbolic functions and their inverses.
Strategies for evaluating integrals beyond direct substitution: integration by parts, trigonometric integrals and substitutions, partial fraction decomposition, numerical integration methods, and improper integrals.
Differential equations as mathematical models, with separable equations developed in depth from antiderivative methods. (Sections 9.1 Basic Ideas, 9.2 Direction Fields and Eulers Method, 9.4 Special First-Order Linear Equations, and 9.5 Modeling with Differential Equations are temporarily omitted from this Briggs ordering pending DCM content production for the corresponding topics.)
Sequences and their convergence behavior, leading to infinite series and a battery of convergence tests for series of constants.
Power series and their intervals of convergence; Taylor and Maclaurin series representations of common functions; using power series to approximate function values and integrals.
Parametric equations, polar coordinates, and calculus operations adapted to these representations including derivatives, area, and arc length. (Section 12.4 Conic Sections is temporarily omitted from this Briggs ordering pending DCM content production for that topic.)
Vectors in the plane and in three-dimensional space, dot and cross products, lines and planes, and quadric surfaces, providing the geometric foundation for vector and multivariable calculus.
Vector-valued functions describing curves in space, with calculus operations (differentiation and integration), motion problems including velocity, acceleration, curvature, and the Frenet frame.
Multivariable functions and their graphs and level curves, limits and continuity, partial derivatives, the chain rule, directional derivatives, gradients, tangent planes, extrema, and Lagrange multipliers.
Iterated and multiple integrals over rectangular and general regions, polar, cylindrical, and spherical coordinates, and the change-of-variables theorem with Jacobians. (Section 16.6 Integrals for Mass Calculations is temporarily omitted from this Briggs ordering pending DCM content production for the corresponding multivariable centers-of-mass topic.)