(11 Courses Available)
Finding the average value of a function on an interval (K-A)
Connecting position, velocity, and acceleration functions using integrals (K-A)
Using accumulation functions and definite integrals in applied contexts (K-A)
Finding the area between curves expressed as functions of x (K-A)
Finding the area between curves expressed as functions of y (K-A)
Volumes with cross sections: squares and rectangles (K-A)
Volumes with cross sections: triangles and semicircles (K-A)
Volume with disc method: revolving around x- or y-axis (K-A)
Volume with disc method: revolving around other axes (K-A)
Volume with washer method: revolving around x- or y-axis (K-A)
Volume with washer method: revolving around other axes (K-A)
The arc length of a smooth, planar curve and distance traveled (K-A)
Using the mean value theorem (K-A)
Extreme value theorem, global versus local extrema, and critical points (K-A)
Determining intervals on which a function is increasing or decreasing (K-A)
Using the first derivative test to find relative (local) extrema (K-A)
Using the candidates test to find absolute (global) extrema (K-A)
Determining concavity of intervals and finding points of inflection: graphical (K-A)
Determining concavity of intervals and finding points of inflection: algebraic (K-A)
Using the second derivative test to find extrema (K-A)
Sketching curves of functions and their derivatives (K-A)
Connecting a function, its first derivative, and its second derivative (K-A)
Solving optimization problems (K-A)
Exploring behaviors of implicit relations (K-A)
Interpreting the meaning of the derivative in context (K-A)
Straight-line motion: connecting position, velocity, and acceleration (K-A)
Rates of change in other applied contexts (non-motion problems) (K-A)
Introduction to related rates (K-A)
Solving related rates problems (K-A)
Approximating values of a function using local linearity and linearization (K-A)
Using L'Hopital's rule for finding limits of indeterminate forms (K-A)
Optional videos (K-A)
Modeling situations with differential equations (K-A)
Verifying solutions for differential equations (K-A)
Sketching slope fields (K-A)
Approximating solutions using Euler's method (K-A)
Reasoning using slope fields (K-A)
Finding general solutions using separation of variables (K-A)
Finding particular solutions using initial conditions and separation of variables (K-A)
Exponential models with differential equations (K-A)
Logistic models with differential equations (K-A)
The chain rule: introduction (K-A)
The chain rule: further practice (K-A)
Implicit differentiation (K-A)
Differentiating inverse functions (K-A)
Differentiating inverse trigonometric functions (K-A)
Selecting procedures for calculating derivatives: strategy (K-A)
Selecting procedures for calculating derivatives: multiple rules (K-A)
Calculating higher-order derivatives (K-A)
Further practice connecting derivatives and limits (K-A)
Optional videos (K-A)
Defining average and instantaneous rates of change at a point (K-A)
Defining the derivative of a function and using derivative notation (K-A)
Estimating derivatives of a function at a point (K-A)
Connecting differentiability and continuity: determining when derivatives do and do not exist (K-A)
Applying the power rule (K-A)
Derivative rules: constant, sum, difference, and constant multiple: introduction (K-A)
Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule (K-A)
Derivatives of cos(x), sin(x) and ln(x) (K-A)
The product rule (K-A)
The quotient rule (K-A)
Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions (K-A)
Optional videos (K-A)
Defining convergent and divergent infinite series (K-A)
Working with geometric series (K-A)
The nth-term test for divergence (K-A)
Integral test for convergence (K-A)
Harmonic series and p-series (K-A)
Comparison tests for convergence (K-A)
Alternating series test for convergence (K-A)
Ratio test for convergence (K-A)
Determining absolute or conditional convergence (K-A)
Alternating series error bound (K-A)
Finding Taylor polynomial approximations of functions (K-A)
Lagrange error bound (K-A)
Radius and interval of convergence of power series (K-A)
Finding Taylor or Maclaurin series for a function (K-A)
Representing functions as power series (K-A)
Optional videos (K-A)
Exploring accumulations of change (K-A)
Approximating areas with Riemann sums (K-A)
Riemann sums, summation notation, and definite integral notation (K-A)
The fundamental theorem of calculus and accumulation functions (K-A)
Interpreting the behavior of accumulation functions involving area (K-A)
Applying properties of definite integrals (K-A)
The fundamental theorem of calculus and definite integrals (K-A)
Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule (K-A)
Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals (K-A)
Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals (K-A)
Integrating using substitution (K-A)
Integrating functions using long division and completing the square (K-A)
Optional videos (K-A)
Using integration by parts (K-A)
Integrating using linear partial fractions (K-A)
Evaluating improper integrals (K-A)
Defining limits and using limit notation (K-A)
Estimating limit values from graphs (K-A)
Estimating limit values from tables (K-A)
Determining limits using algebraic properties of limits: limit properties (K-A)
Determining limits using algebraic properties of limits: direct substitution (K-A)
Determining limits using algebraic manipulation (K-A)
Selecting procedures for determining limits (K-A)
Determining limits using the squeeze theorem (K-A)
Exploring types of discontinuities (K-A)
Defining continuity at a point (K-A)
Confirming continuity over an interval (K-A)
Removing discontinuities (K-A)
Connecting infinite limits and vertical asymptotes (K-A)
Connecting limits at infinity and horizontal asymptotes (K-A)
Working with the intermediate value theorem (K-A)
Optional videos (K-A)
Defining and differentiating parametric equations (K-A)
Second derivatives of parametric equations (K-A)
Finding arc lengths of curves given by parametric equations (K-A)
Defining and differentiating vector-valued functions (K-A)
Solving motion problems using parametric and vector-valued functions (K-A)
Defining polar coordinates and differentiating in polar form (K-A)
Finding the area of a polar region or the area bounded by a single polar curve (K-A)
Finding the area of the region bounded by two polar curves (K-A)
Calculator-active practice (K-A)
