e-Course [1413] - Advanced Math - Calculus
e-Course [1413] - Advanced Math - Calculus: Learn about limits of
functions, derivatives, differential calculus, the definite integral, anti-derivatives
and fundamental theories of calculus, applications of the integral, inverse and
transcendental functions, and differential equations.
e-Unit [14131] - Advanced Calculus - Limits Of Functions: Learn
about definition of a limit, asymptotic and unbounded behavior, and
continuity.
e-Lesson [141311] - Advanced Calculus - What’s A Limit?:
Learn about identifying if a limit exists for a graph or algebraic
expression, estimating limits from data tables, graphs, algebraic formulas
and trigonometric functions, and identifying properties of limits.
e-Lesson [141312] - Advanced Calculus - Asymptotic &
Unbounded Behavior: Learn to estimate limits at infinity, solve
limits at infinity algebraically, use limits to find asymptotes, reconstruct
the graph of a function from given limits, determine limits that compare
growth rates, compare relative magnitudes of functions, solve problems
comparing relative growth rates, and find when and why a limit does not
exist.
e-Lesson [141313] - Advanced Calculus - Continuity: Learn to
define continuity at a point, determine if a function is continuous at a
point, determine the type of discontinuity that may exist, describe
discontinuities in terms of limits, solve for parameters in continuous
functions, define and apply the Intermediate Value Theorem and the
Extreme Value Theorem.
e-Unit [14132] - Advanced Calculus - Derivatives: Learn about the
derivative at a point, computing and interpreting derivatives, and higher
order and implicit derivatives.
e-Lesson [141321] - Advanced Calculus - Derivative At A
Point: Learn to calculate average rates of change, estimate instantaneous
rates of change from graphs and tables, calculate instantaneous rates of
change using the limit function of a derivative, relate the slope of a
tangent line to the slopes of secant lines, find derivatives of functions,
estimate the graph of a derivative function from the original function and
vice versa, and identify Leibnitz and prime notations.
e-Lesson [141322] - Advanced Calculus - Computing &
Interpreting Derivatives: Learn to determine the derivative of basic
power functions and polynomials, determine derivatives of functions as
the sum, product and quotient of other functions, state the Product Rule
and the Quotient Rule, know derivatives of 6 basic trigonometric
functions, determine when a function is differentiable, determine the
derivative of piecewise functions, define and apply Rolle’s Theorem and
the Mean Value Theorem.
e-Lesson [141323] - Advanced Calculus - Higher Order &
Implicit Derivatives: Learn about determining higher order
derivatives, identifying places a graph is concave up or down from a
formula, use the second derivative to find inflection points, use higherorder derivatives to analyze rates of change, define and apply the Chain
Rule, determine the derivative for implicitly defined curves, and
calculate the slope of the tangent line at points on an implicitly defined
curve.
e-Unit [14133] - Advanced Calculus - Differential Calculus: Learn
about extrema and optimization, tangent and normal lines, rates of change
and related rates.
e-Lesson [141331] - Advanced Calculus - Extrema &
Optimization: Learn to define relative and absolute extrema, use the
first derivative number-line test and the second derivate test to identify
relative extrema and inflection points, and solve optimization problems
dealing with volume, area, time and distance.
e-Lesson [141332] - Advanced Calculus - Tangent & Normal
Lines: Learn to use implicit differentiation when necessary to write
equations of tangent and normal lines on a curve, identify points of local
linearity on a graph, use tangent line and local linearity approximation of
values of functions.
e-Lesson [141333] - Advanced Calculus - Rates Of Change &
Related Rates: Learn to translate descriptions of rates of change into
mathematical statements and vice versa, solve related-rates problems,
differentiate and calculate speed, velocity and acceleration from position
functions, and solve and graph rectilinear motion problems.
e-Unit [14134] - Advanced Calculus - Integrals: Learn about area
under a curve, definite integrals, and indefinite integrals.
e-Lesson [141341] - Advanced Calculus - Area Under A
Curve: Learn to use summation notation for sum of a series,
approximate area under a curve using midpoint, and endpoint
approximations, write Riemann sums to represent the approximations
and identify ways Riemann sum approximations can be improved, use
the trapezoid rule to approximate area under a curve, use numerical
methods to approximate the area under a curve, and identify typical error
of all approximation methods.
e-Lesson [141342] - Advanced Calculus - Definite Integrals:
Learn to calculate definite integrals geometrically for circles, trapezoids,
triangles and rectangles, identify area under a curve (and the definite
integral) as a limit of a Riemann sum, approximate definite integrals by
same methods as calculating area under a curve, identify the algebraic
properties of definite integrals, apply properties to solve problems related
to area, average values of functions for a given domain, position change
from velocity curves, and net change from rate of change functions.
e-Lesson [141343] - Advanced Calculus - Indefinite Integrals:
Learn to define and find antiderivatives of basic functions, solve simple
differential equations, and find antiderivatives for composite functions
with and without substitution.
e-Lesson [141344] - Advanced Calculus - Fundamental
Theorems: Learn to apply the First and Second Fundamental Theorems
to find derivatives of integral functions, use substitution to identify
equivalent definite integrals, solve definite integrals involving composite
functions, and use the chain rule and the First Fundamental Theorem to
analyze definite integrals with functions in the limits.
e-Unit [14135] - Advanced Calculus - Integral Applications: Learn
to use the definite integral to calculate area, volume, rate and rate of change.
e-Lesson [141351] - Advanced Calculus - Integrals & Area:
Learn to calculate area between two curves, calculate area of regions
bounded by multiple curves, use the definite integral and numerical
integration to find the average value of a function, and given area of a
function, find correct limits of integration for the definite integral.
e-Lesson [141352] - Advanced Calculus - Integrals & Volume:
Learn to find volumes by accumulating cross-sectional area, find the
volume of a solid of revolution (including rotating curves), calculate
volumes of solids with well-defined bases and cross-sectional shapes,
and given shape defined with a function or set of functions, determine
limits of integration for a specified volume.
e-Lesson [141353] - Advanced Calculus - Integrals & Rates:
Learn to calculate net and total changes from rates of change, and solve
problems here a quantity is accumulated or is averaged.
e-Unit [14136] - Advanced Calculus - Inverse & Transcendental
Functions: Learn about inverse functions, logarithmic and exponential
functions, derivatives involving transcendental functions, and integrals
involving transcendental functions.
e-Lesson [141361] - Advanced Calculus - Inverse Functions:
Learn about finding inverse functions from algebraic or trigonometric
functions, finding the derivatives of inverse algebraic and trigonometric
functions, analyze graphical properties of inverse functions, identify
domain restrictions of inverse trigonometric functions, find derivatives
for composite functions involving inverse trigonometric functions, and
apply inverse trigonometric functions to model situations.
e-Lesson [141362] - Advanced Calculus - Logarithmic &
Exponential Functions: Learn about identify algebraic, exponential
and logarithmic functions, apply laws of exponents and logarithms to
manipulate exponential and logarithmic functions, solve problems using
logarithmic and exponential functions as inverses, and write equations
that model exponential growth and decay.
e-Lesson [141363] - Advanced Calculus - Derivatives
Involving Transcendental Functions: Learn about finding the
derivative of logarithmic and exponential functions, use the derivative to
analyze curves and to optimize situations for all functions (algebraic,
trigonometric, inverse trigonometric, logarithmic, exponential and
combinations, and solve problems about rates of change and related rates
for all functions.
e-Lesson [141364] - Advanced Calculus - Integrals Involving
Transcendental Functions: Learn to find antiderivatives involving
transcendental functions, for all functions, solve problems related to area,
average values, volume, and motion, use the definite integral to
accumulate quantities for all functions, and use the Fundamental
Theorem of Calculus with transcendental functions.
e-Unit [14137] - Advanced Calculus - Differential Equations: Learn
about partial differentiation, and applications of partial differentiation
including problems involving slope fields.
e-Lesson [141371] - Advanced Calculus - Partial
Differentiation: Learn about partial derivatives, and implicit
differentiation.
e-Lesson [141372] - Advanced Calculus - Differentiation &
Slope Fields: Learn about the order of a differential equation, use a
slope field to sketch partial solutions of differential equations, match
slope fields and differential equations, separate variables in first-order
differential equations, solve first-order separable differential equations,
and translate word problems into differential equations.
e-Lesson [141373] - Advanced Calculus - Application Of
Partial Differentiation: Learn about problems involving small errors,
the tangent plane and normal line to a surface, tangent line and normal
plane to a skew curve, directional derivatives, maxima and minima, and
surface area.