Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.
a. Functions: real numbers, inequalities, sets, intervals, Cartesian plane, lines, slopes,
exponents, domain, range, quadratic, polynomial, rational, exponential, piecewise and
composite functions, shifting, difference quotient, applications
b. Derivatives: limits, continuity, average and instantaneous rate of change, secant and
tangent lines, definition of derivative, power rule, product rule, quotient rule, chain
rule, higher-order derivatives, velocity, acceleration, nondifferentiable functions,
business applications
c. Applications of Derivative: relative extreme points, critical numbers, graphing, first-
derivative test, concavity, inflections points, second-derivative test, absolute extreme
values, applications of optimization, implicit differentiation, related rates
d. Exponential & Logarithmic Functions: graphing, compound interest, the number e,
exponential growth, natural logarithms, applications of logarithms, derivatives of
logarithmic and exponential functions, applications of derivatives
e. Integration: antiderivatives, indefinite integrals, integration rules, area under a curve,
definite integral, Fundamental Theorem of Integral Calculus, applications of integrals,
average value of a function, area between curves, applications of area, integration by
substitution, differentials
f. Integration Techniques and Differential Equations: integration by parts, integral
tables, improper integrals, numerical integration, trapezoidal approximation and error,
Simpson's Rule and error, differential equations, general and particular solutions,
separation of variables, applications of differential equations
g. Calculus of Several Variables: functions of two variables, graphing, relative extreme
points and saddle points, partial derivatives, functions of three or more variables,
higher-order partial derivatives, optimizing functions of several variables, critical
points, second-derivative test, applications, least squares, fitting exponential curves
with least squares, Lagrange Multipliers, total differentials and approximate changes,
multiple integrals.