Find distances between points in space and find midpoints of line segments in space

Write the standard forms of the equations of spheres and find the centers and radii of spheres

Scalar Multiplication

Work- vectors

Find the dot product of two vectors and use the Properties of the Dot Product

Scalar projection of a vector

The cross product

Distance between a point and a plane

Sketch the quadric surface

Quadratic surfaces

Space curves and vector-valued functions

Space curves - A

Arc length parameter

Curvature

Formula for curvature

Find the first partial derivatives of functions of two variables

Multivariable functions: use a Cobb-Douglas production model

Read contour maps and sketch level curves of functions of two variables

Find the domains and ranges of functions of several variables

Limit of a function of two variables

Testing for continuity

Find the first partial derivatives of functions of two variables

Find the partial derivatives of functions of several variables

Second-Order Partial Derivatives

Linear Approximation and Differentials

Implicit differentiation

Find a directional derivative

Introduction to gradients

Understand the relative extrema of functions of two variables

Use the Second-Partials Test to find the relative extrema of functions of two variables

Find the maximum values of function using Lagrange Multipliers - A

Find the maximum values of function using Lagrange Multipliers - B

Use Lagrange multipliers with two constraints to find extrema of functions of several variables

Properties of Double Integrals

Iterated Integral in Two Variables

Calculate double integrals- Fubini's Theorem

Using Fubini's Theorem and Double Integrals to find Volume - A

Using Fubini's Theorem and Double Integrals to find Volume - B

Riemann sum

Double Integrals over a Rectangular Region

Use double integrals to find the volumes of solids - A

Use double integrals to find the volumes of solids - B

Evaluate double integrals

Iterated Integral in Two Variables

Properties of Double Integrals

Use Properties to Evaluate a Double Integral

Evaluate double integral using polar coordinate - A

Evaluate double integral using polar coordinate - B

Change to polar coordinates in a double integral

Moments and center of mass of a variable density planer lamina

Finding the center of mass

Finding the center of mass of a solid region - A

Finding the center of mass of a solid region - B

Use continuous probability density functions to answer questions about real-life situations

Find the expected values or means of continuous probability density functions

Definition of surface area

Surface area of a plane region

Find the surface area of the paraboloid

Triple integrals

Triple integrals: find the volume - A

Triple integrals: find the volume - B

Triple integrals in cylindrical coordinates- an overview

Triple integrals in spherical coordinates- an overview

Triple integrals in spherical coordinates

Change of Variables for Definite Integrals

Understand the concept of a Jacobian

Vector Fields - A

Vector Fields - B

Problem on Vector Field - A

Problem on Vector Field - B

Fundamental theorem for line integrals

Independence of path

Compute the Potential Function of a Conservative Vector Field

Curl

Divergence

Parametric surfaces

Problem on parametric surfaces

Surface area - B

Find the surface area of the paraboloid

Surface integrals

Problem on surface integrals - A

Problem on surface integrals - B

Divergence Theorem

Problem on Divergence Theorem - A

Problem on Divergence Theorem - B

Divergence Theorem

Fundamental theorem for line integrals

Second-order linear differential equation - A

Second-order linear differential equation - B 

Introduction to second-order nonhomogeneous linear equations - A

Introduction to second-order nonhomogeneous linear equations - B

Method of undetermined coefficients - A

Method of undetermined coefficients - B

The Domain and Range of a Function - A

Apply the Vertical Line Test

Even and Odd Symmetry of Functions

Increasing and decreasing functions on an interval

Cubic, square root, and reciprocal functions

Find the domain of a rational function

Graphs of Logarithmic Functions

Transformations of functions

Operations with Functions

Find the composition of two functions

Graph the function using graphing calculators

Properties of Exponents

Evaluate and graph natural exponential functions

Evaluate and graph natural exponential functions

Find the inverse of a function

Find the inverse of a function

Evaluate natural logarithms and graph natural logarithm functions Part I

Evaluate natural logarithms and graph logarithm functions Part II

Evaluate the other inverse trigonometric functions

Find the equation of the tangent line

Find average velocity - A

Average and Instantaneous Velocity

An introduction to limits

Find limits of functions graphically and numerically

Different limits from the Right and Left

Investigating infinite limits

Use the properties of limits to evaluate limits of functions

Evaluate a limit of a polynomial function

Limits of Polynomial and Rational Functions

Evaluate one-sided limits

Limits of radical functions

The Squeeze Theorem

Formal Definition of Limit - A

Formal Definition of Limit - B

A Formal Definition of an Infinite Limit

Determine the continuity of functions

Continuous and Discontinuous Functions

Properties of Continuity

The Intermediate Value Theorem

Use the Intermediate Value Theorem to help locate zeros of polynomial functions

Limits at Infinity

Find the horizontal asymptotes of functions and find limits at infinity

Evaluation of limits at infinity for a rational function

Properties of limits at infinity

Find the horizontal asymptotes of functions and find limits at infinity

Definition of limits at infinity

Slope of tangent lines to a point on a curve

Find the equation of the tangent line

Tangent line with slope m- Part I

Find average velocity - A

Find the instantaneous rates of change of functions at points

Find the average rates of change of functions over intervals - A

Find the average rates of change of functions over intervals - B

Use the limit definition to find the derivatives of functions

Find the Derivative of a Function using the definition

Notations for the Derivative Function

Nondifferentiable Functions

Find higher-order derivatives

Find derivatives using the General Power Rule

The Constant Multiple Rule

The Sum Rule and the Difference Rule

Find the derivatives of natural exponential functions

The product rule

Find the derivatives of functions using the Quotient Rule

Derivatives of trigonometric functions

Find derivatives using the Chain Rule

The Chain Rule

Implicit differentiation

Derivatives of Inverse trigonometric functions- an overview

Derivatives of logarithmic functions with bases other than e

Logarithmic Differentiation - A

Logarithmic Differentiation - B

Find average rate of change

Average Rate of Change

Radioactive Decay and Law of Cooling

Related rates- ripples in a pond

Linear Approximation and Differentials

Hyperbolic functions

Hyperbolic Functions and Their Derivatives

Extrema of a function and the Extreme Value Theorem

Relative Extrema and the graph of a function - A

Find absolute extrema of continuous functions on a closed interval

Rolle's Theorem

The Mean Value Theorem- an overview

The Mean Value Theorem

Increasing and decreasing functions on an interval

Use the First-Derivative Test to find the relative extrema of functions

Determine the intervals on which the graphs of functions are concave upward or concave downward

Concavity and inflection points

Apply the Second Derivative Test - A

Apply the Second Derivative Test - B

Approximate limits that produce indeterminate forms

Review of Indeterminate Forms

L'Hôpital's Rule- Part I

L'Hôpital's Rule- Part I

Use L'Hopital's Rule to evaluate limits

Use L'Hospital's Rule to evaluate limits

Curve sketching- finding intercepts, critical points, test values

Curve sketching- testing f, f' and f'' over intervals

Curve Sketching: A Summary

Curve sketching- conclusions of interval tests

Curve sketching with intercepts and interval tests

Curve Sketching with an Asymptote

Graph the function using graphing calculators

Use a graphing utility to evaluate functions, to find intercepts, and to find zeros of a function

Optimization- finding maximum volume- set up

Optimization- finding maximum volume- solution

Solve business and economics optimization problems

Solve business and economics optimization problems

Find Marginal cost, revenue, and profit, given linear total cost, total revenue, and profit functions

Situations in which Newton's Method Fails

Newton's Method

Related rates- ripples in a pond, an overview

Newton's Method of approximating zeros - an overview

Newton's method of approximating zeros

Antiderivatives

Understand the definition of antiderivative

Use antiderivatives to solve real-life problems

The Area Problem

Approximation of the area under a curve using rectangles

Area of a region in the plane

Application - Uniform Motion Problem

Area from Riemann Sums - A

Riemann sum

Area from Riemann Sums - B

Evaluation of a definite integral as a limit- Part I

Evaluation of a definite integral as a limit- Part II

Use the Midpoint Rule to approximate definite integrals

Properties of the Definite Integral-Part A

Properties of the Definite Integral-Part B

Evaluate definite integrals using the Fundamental Theorem of Calculus

Use basic integration rules to find antiderivatives

Indefinite integrals - overview

Rules for Integration

Evaluation of indefinite integrals

Use definite integrals to solve marginal analysis problems

A Simple Integral by Substitution

Use substitution to evaluate definite integrals Part I

Use substitution to evaluate definite integrals Part II

Substitution in an Indefinite Integral

Use properties of even and odd functions to help evaluate definite integrals

Find the areas of regions bounded by two graphs

Area Bounded by Two Curves

Calculate the area between two curves - B

Volume of Geometric Solids

The Disk Method

Apply the formula for the volume of a sphere: V = (4/3)Pi r³

Use the Washer Method to find volumes of solids of revolution with holes

Use vectors to find the work done by a force

Application: work done by a variable force - compressing a spring - A

Application: work done by a variable force - compressing a spring - B

Average value of a function

Mean Value Theorem for Integrals

Integration by parts- an overview

Integration by parts Part I

Integration by parts Part II

Use reduction formulas to find indefinite integrals

Integration by parts- integrand with a single term

Integrals of Trigonometric Functions

Integrals of other trig functions

Trigonometric substitution

Trigonometric substitution- an overview

Trigonometric substitution- rational powers

Integrals of Logarithmic Functions

Partial fractions decomposition- distinct linear and quadratic factors

Partial fractions decomposition- distinct linear factors

Partial fractions decomposition

Integrals of other trig functions

Integrate: using the table of integrals

Using tables to Evaluate Integrals

Use the Midpoint Rule to approximate definite integrals Part I

Use the Midpoint Rule to approximate definite integrals Part II

Use the Midpoint Rule to approximate definite integrals Part III

Using the Trapezoidal Rule to Approximate an Integral

The Trapezoidal Rule

Errors in the Trapezoidal Rule and Simpson's Rule

Simpson's Rule

Using Simpson's Rule to Approximate an Integral

Evaluate improper integrals with infinite limits of integration

Recognize improper integrals

Improper integrals

Improper integrals- an overview

Improper Integral with Infinite Interval

Evaluate improper integrals with infinite integrands

Improper Integral with Unbounded Discontinuity

Evaluate improper integrals with infinite integrands

Arc length parameter

Problem on hydrostatic force and pressure - A

Problem on hydrostatic force and pressure - B

Moments and center of mass of a variable density planer lamina

Finding the center of mass

Using Integrals to Find Consumer Surplus

Find the expected values or means of continuous probability density functions

Calculating Probability with Normal Distribution

The Concept of Differential Equations

Direction Fields

Separable Equations

Orthogonal trajectories

Logistic Growth

Exponential Growth and Decay

First-order linear differential equations

Applications of Differential Equations

Predator-prey differential equations

Analyzing predator-prey equations

Sketch the curve that is represented by a set of parametric equations

Arc length parameter

Surface area of a plane region

Plot points on the polar coordinate system

Graph polar equations by point plotting

Graph polar equations by point plotting

Graphing Polar equations with a calculator

Write equations of parabolas

Graph an ellipse with center at the origin

Write an equation of a hyperbola

Use Vertical and Horizontal Shifts to Sketch Functions

Polar equations of conics

Write the polar equation of a conic (ellipse, parabola, hyperbola) using eccentricity and the distance from the focus to the directrix

Write the terms of a sequence

Find the nth term of a sequence

Determine the convergence or divergence of sequences and find the limits of convergent sequences

Partial Sums

Sum Formula for Infinite Geometric Series

Use the nth-Term Test of Divergence to show that series diverge

Determine the convergence or divergence of p-series

Direct comparison test

Problem on direct comparison test

Alternating series

Problem on alternating series

Use the Ratio Test to determine the convergence or divergence of series - A

Use the Ratio Test to determine the convergence or divergence of series - B

Introduction to Power Series

Calculate Radius of Convergence for Power Series

Introduction to Taylor Series

A Taylor Series Example

Introduction to Taylor Polynomials

An Example with Taylor Polynomials - Part A

An Example with Taylor Polynomials - Part B

Use Taylor polynomials to determine the maximum errors of approximations - A

Use Taylor polynomials to determine the maximum errors of approximations - B