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Chapter PDFPremium Content - Image BankStudentInteractive AppletsConnect2Calculus VideosSection 1: Review of Formulas and Techniques StudenteProfessorIntegration Techniques - Review of Formulas (App)Section 2: Volume: Slicing, Disks, and Washers StudenteProfessorIntegration by Parts (App)Section 3: Volumes by Cylindrical Shells StudenteProfessorTrigonometric Techniques of Integration (App)Section 4: Integration of Rational Functions Using Partial Fractions StudenteProfessorIntegration of Rational Functions Using Partial Fractions (App)Section 5: Integration Tables and Computer Algebra Systems StudenteProfessorIntegration Tables and Computer Algebra Systems (App)Section 6: Improper Integrals StudenteProfessorThe Comparison Test (App)Chapter 7: First Order Differential Equations TeacherPremium Content - Chapter PDFPremium Content - Image BankStudentInteractive AppletsConnect2Calculus VideosSection 1: Modeling with Differential EquationsStudenteProfessorModeling with Differential Equations (App)Connect2Calculus VideosSection 2: Separable Differential Equations StudenteProfessorIVP with Implicit Solution (App)Connect2Calculus VideosSection 3: Direction Fields and Euler's Method StudenteProfessorDirection Fields and Euler's Method (App)Connect2Calculus VideosSection 4: Systems of First Order Differential Equations StudenteProfessorSystems of First Order Differentiable Equations (App)Chapter 8: Infinite Series TeacherPremium Content - 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Chapter PDFPremium Content - Image BankStudentInteractive AppletsConnect2Calculus VideosSection 1: Plane Curves and Parametric Equations StudenteProfessorThe Path of a Projectile (App)Connect2Calculus VideosSection 2: Calculus and Parametric Equations StudenteProfessorThe Path of the Scrambler (App)Connect2Calculus VideosSection 3: Arc Length and Surface Area in Parametric Equations StudenteProfessorSkiing Curved Path vs Straight Line (App)Connect2Calculus VideosSection 4: Polar Coordinates StudenteProfessorConverting an Equation from Rectangular to Polar Coordinates (App)Connect2Calculus VideosSection 5: Calculus and Polar Coordinates StudenteProfessorFinding the Area Between Two Polar Graphs (App)Connect2Calculus VideosSection 6: Conic Sections StudenteProfessorIdentifying the Features of an Ellipse (App)Section 7: Conic Sections in Polar Coordinates StudenteProfessorFocus and Directrix (App)Chapter 10: Vectors and the Geometry of Space TeacherPremium Content - Chapter PDFPremium Content - Image BankStudentInteractive AppletsConnect2Calculus VideosSection 1: Vectors in the Plane StudenteProfessorFinding a Position Vector (App)Connect2Calculus VideosSection 2: Vectors in Space StudenteProfessorVectors in Space (App)Section 3: The Dot Product StudenteProfessorCalculating Work (App)Connect2Calculus VideosSection 4: The Cross Product StudenteProfessorFinding the Distance from a Point to a Line (App)Connect2Calculus VideosSection 5: Lines and Planes in Space StudenteProfessorEquation of a Plane (App)Section 6: Surfaces in Space StudenteProfessorSketching a Paraboloid (App)Sketching an Elliptic Cone (App)Chapter 11: Vector-Valued Functions TeacherPremium Content - Chapter PDFPremium Content - Image BankStudentInteractive AppletsConnect2Calculus VideosSection 1: Vector-Valued Functions StudenteProfessorSketching the Curve Defined by a Vector-Valued Function (App)Connect2Calculus VideosSection 2: The Calculus of Vector-Valued Functions StudenteProfessorThe Calculus of Vector-Valued Functions (App)Section 3: Motion in Space StudenteProfessorFinding the Velocity and Acceleration Vectors (App)Connect2Calculus VideosSection 4: CurvatureStudenteProfessorFinding a Unit Tangent Vector (App)Connect2Calculus VideosSection 5: Tangent and Normal Vectors StudenteProfessorTangent and Normal Vectors (App)Section 6: Parametric Surfaces StudenteProfessorParametric Surfaces (App)Chapter 12: Functions of Several Variables and Differentiation TeacherPremium Content - Chapter PDFPremium Content - Image BankStudentInteractive AppletsConnect2Calculus VideosSection 1: Functions of Several Variables StudenteProfessorSketching Contour Plots (App)Section 2: Limits and Continuity StudenteProfessorThe Definition of a Limit (App)Section 3: Partial Derivatives StudenteProfessorPartial Derivatives (App)Section 4: Tangent Planes and Linear Approximations StudenteProfessorTangent Planes and Linear Approximations (App)Connect2Calculus VideosSection 5: The Chain Rule StudenteProfessorThe Chain Rule (App)Connect2Calculus VideosSection 6: The Gradient and Directional Derivatives StudenteProfessorFinding the Direction of Maximum Increase (App)Connect2Calculus VideosSection 7: Extrema of Functions of Several Variables StudenteProfessorExtrema and Functions of Several Variables (App)Connect2Calculus VideosSection 8: Constrained Optimization and Lagrange Multipliers StudenteProfessorFinding the Minimum Distance (App)Connect2Calculus VideosChapter 13: Multiple Integrals TeacherPremium Content - Chapter PDFPremium Content - Image BankStudentInteractive AppletsConnect2Calculus VideosSection 1: Double Integrals StudenteProfessorApproximate Limits of Integration (App)Section 2: Area, Volume, and Center of Mass StudenteProfessorArea, Volume and Center of Mass (App)Connect2Calculus VideosSection 3: Double Integrals in Polar Coordinates StudenteProfessorDouble Integrals in Polar Coordinates (App)Section 4: Surface IntegralsStudenteProfessorSurface Area (App)Section 5: Triple Integrals StudenteProfessorTriple Integrals (App)Connect2Calculus VideosSection 6: Cylindrical Coordinates StudenteProfessorCylindrical Coordinates (App)Section 7: Spherical Coordinates StudenteProfessorSpherical Coordinates (App)Section 8: Change of Variables in Multiple Integrals StudenteProfessorChange of Variables in Multiple Integrals (App)Connect2Calculus VideosChapter 14: Vector Calculus TeacherPremium Content - Chapter PDFPremium Content - Image BankStudentInteractive AppletsConnect2Calculus VideosSection 1: Vector Fields StudenteProfessorVector Fields (App)Connect2Calculus VideosSection 2: Line Integrals StudenteProfessorLine Integrals (App)Connect2Calculus VideosSection 3: Independence of Path and Conservative Vector Fields StudenteProfessorIndependence of Path and Conservative Vector Fields (App)Connect2Calculus VideosSection 4: Green's Theorem StudenteProfessorGreen's Theorem (App)Connect2Calculus VideosSection 5: Curl and Divergence StudenteProfessorCurl and Divergence (App)Connect2Calculus VideosSection 6: Surface Integrals StudenteProfessorSurface Integrals (App)Connect2Calculus VideosSection 7: The Divergence Theorem StudenteProfessorThe Divergence Theorem (App)Connect2Calculus VideosSection 8: Stokes' Theorem StudenteProfessorStokes' Theorem (App)Connect2Calculus VideosSection 9: Applications of Vector Calculus StudenteProfessorApplications of Vector Calculus (App)Chapter 15: Second Order Differential Equations TeacherPremium Content - Chapter PDFPremium Content - Image BankStudentInteractive AppletsConnect2Calculus VideosSection 1: Second-Order Equations with Constant Coefficients StudenteProfessorSecond Order Differential Equations (App)Section 2: Nonhomogeneous Equations: Undetermined Coefficients StudenteProfessorNonhomogeneous Equations: Undetermined Coefficients (App)Section 3: Applications of Second Order Equations StudenteProfessorApplications of Second Order Equations (App)Section 4: Power Series Solutions of Differential Equations StudenteProfessorPower Series Solution to a Differential Equation (App)
Section 1: A Brief Preview of Calculus: Tangent Lines and the Length of a CurveStudenteProfessorSlope of the Secant Line (App)Approximating the Curve with Two Line Segments (App)Section 2: The Concept of Limit StudenteProfessorA Limit That Does Not Exist (App)A Limit for Which Approximate Answers May be Deceptive (App)Section 3: Computation of Limits StudenteProfessorUsing the Squeeze Theorem to Verify the Value of a Limit (App)Section 4: Continuity and its Consequences StudenteProfessorIntermediate Value Theorem (App)An Illustration of the Intermediate Value Theorem (App)Connect2Calculus VideosSection 5: Limits Involving Infinity StudenteProfessorA Case Where Infinite One-Sided Limits Disagree (App)Finding Horizontal Asymptotes (App)Section 6: Formal Definition of the Limit StudenteProfessorFormal Definition of a Limit (App)Formal Definition of the Limit Using a Polynomial (App)Connect2Calculus VideosSection 7: Limits and Loss-of-Significance Errors StudenteProfessorAvoiding a Loss of Significance Error (App)Loss-of-Significance Involving a Trigonometric Function (App)
Section 1: Tangent Lines and Velocity StudenteProfessorFinding the Equation of a Tangent Line (App)A Secant Line Between Two Points and a Tangent Line at a Point (App)Connect2Calculus VideosSection 2: The Derivative StudenteProfessorSlope of a Tangent Line (App)A Function That is Not Differentiable at a Point (App)Connect2Calculus VideosSection 3: Computation of Derivatives: The Power Rule StudenteProfessorThe Power Rule and the Tangent Line (App)Finding the Equation of the Tangent Line (App)Connect2Calculus VideosSection 4: The Product and Quotient Rules StudenteProfessorProduct and Quotient Rules (App)Connect2Calculus VideosSection 5: The Chain Rule StudenteProfessorFinding the Velocity of a Hanging Weight (App)Concentration of a Chemical (App)Connect2Calculus VideosSection 6: Derivatives of Trigonometric FunctionsStudenteProfessorThe Derivative of Sine and Cosine (App)Connect2Calculus VideosSection 7: Derivatives of Exponential and Logarithmic FunctionsStudenteProfessorDerivatives of Exponential Functions (App)Finding the Velocity of a Hanging Weight (App)Connect2Calculus VideosSection 8: Implicit Differentiation and Inverse Trigonometric FunctionsStudenteProfessorFinding a Slope Implicitly (App)Connect2Calculus VideosSection 9: The Mean Value Theorem StudenteProfessorRolle's Theorem (App)An Illustration of the Mean Value Theorem (App)Connect2Calculus Videos
Section 1: Linear Approximations and Newton's Method StudenteProfessorIncrements and Differentials (App)Newton's Method (App)Connect2Calculus VideosSection 2: Indeterminate Forms and L'Hopital's RuleStudenteProfessorL'Hopital's Rule (App)Connect2Calculus VideosSection 3: Maximum and Minimum Values StudenteProfessorFinding Absolute Extrema on a Closed Interval (App)Finding Local Extrema of a Polynomial (App)Connect2Calculus VideosSection 4: Increasing and Decreasing Functions StudenteProfessorAn Increasing and Decreasing Function (App)Local Extrema and Fractional Exponents (App)Connect2Calculus VideosSection 5: Concavity and the Second Derivative Test StudenteProfessorConcave Up and Concave Down (App)Determining Concavity and Locating Inflection Points (App)Connect2Calculus VideosSection 6: Overview of Curve Sketching StudenteProfessorGraphing a Polynomial (App)Graphing a Rational Function (App)Connect2Calculus VideosSection 7: OptimizationStudenteProfessorMaximum Area (App)Finding the Maximum (App)Connect2Calculus VideosSection 8: Related Rates StudenteProfessorRelated Rates - Tracking a Fast Jet (App)Connect2Calculus VideosSection 9: Rates of Change in Economics and the Sciences StudenteProfessorA Simple Electric Circuit (App)Connect2Calculus Videos
Section 1: AntiderivativesStudenteProfessorFinding the Position of a Falling Object Given Its Acceleration (App)Section 2: Sums and Sigma Notation StudenteProfessorNonconstant velocity (App)Connect2Calculus VideosSection 3: AreaStudenteProfessorRiemann Sum (App)Approximating an Area with Rectangles (App)Connect2Calculus VideosSection 4: The Definite Integral StudenteProfessorEstimating Overall Change in Position (App)A Riemann Sum for a Function with Pos and Neg Values (App)Connect2Calculus VideosSection 5: The Fundamental Theorem of Calculus StudenteProfessorA Definite Integral with a Variable Upper Limit (App)Connect2Calculus VideosSection 6: Integration by Substitution StudenteProfessorIntegration by Substitution (App)Section 7: Numerical Integration StudenteProfessorMidpoint Rule (App)The (n + 1)-point Trapezoidal Rule (App)Section 8: The Natural Logarithm as an Integral StudenteProfessorNatural Logarithm (App)
Section 1: Area Between Curves StudenteProfessorFinding the Area Between Two Curves (App)An Area Computed by Integrating with Respect to y (App)Connect2Calculus VideosSection 2: Volume: Slicing, Disks, and Washers StudenteProfessorUsing the Method of Disks to Compute Volume (App)The Solid of Revolution Revolving about y (App)Connect2Calculus VideosSection 3: Volumes by Cylindrical Shells StudenteProfessorRevolving a Region Bounded by y = 0 and a Parabola (App)Solid of Revolution by Cylindrical Shells (App)Connect2Calculus VideosSection 4: Arc Length and Surface Area StudenteProfessorGraphs Similar Over an Interval (App)Surface of Revolution (App)Connect2Calculus VideosSection 5: Projectile Motion StudenteProfessorHeight of the Ball at Time t (App)The Motion of a Tennis Serve (App)Section 6: Applications of Integration to Physics and EngineeringStudenteProfessorComputing the Work Done Stretching a Spring (App)Connect2Calculus VideosSection 7: ProbabilityStudenteProfessorA Normal Distribution Curve (App)
Section 1: Review of Formulas and Techniques StudenteProfessorIntegration Techniques - Review of Formulas (App)Section 2: Volume: Slicing, Disks, and Washers StudenteProfessorIntegration by Parts (App)Section 3: Volumes by Cylindrical Shells StudenteProfessorTrigonometric Techniques of Integration (App)Section 4: Integration of Rational Functions Using Partial Fractions StudenteProfessorIntegration of Rational Functions Using Partial Fractions (App)Section 5: Integration Tables and Computer Algebra Systems StudenteProfessorIntegration Tables and Computer Algebra Systems (App)Section 6: Improper Integrals StudenteProfessorThe Comparison Test (App)
Section 1: Modeling with Differential EquationsStudenteProfessorModeling with Differential Equations (App)Connect2Calculus VideosSection 2: Separable Differential Equations StudenteProfessorIVP with Implicit Solution (App)Connect2Calculus VideosSection 3: Direction Fields and Euler's Method StudenteProfessorDirection Fields and Euler's Method (App)Connect2Calculus VideosSection 4: Systems of First Order Differential Equations StudenteProfessorSystems of First Order Differentiable Equations (App)
Section 1: Sequences of Real Numbers StudenteProfessorFinding the Limit of a Sequence (App)Connect2Calculus VideosSection 2: Infinite Series StudenteProfessorGeometric Series (App)Connect2Calculus VideosSection 3: The Integral Test and Comparison Tests StudenteProfessorUsing the Integral Test (App)Section 4: Alternating Series StudenteProfessorConvergence of the Partial Sums of an Alternating Series (App)Section 5: Absolute Convergence and the Ratio Test StudenteProfessorUsing the Ratio Test (App)Section 6: Power Series StudenteProfessorHalf-Open Interval of Convergence (App)Section 7: Taylor Series StudenteProfessorGraphing Taylor Polynomials (App)A Taylor Series Expansion of sin x (App)Connect2Calculus VideosSection 8: Applications of Taylor Series StudenteProfessorUsing Taylor Series to Approximate a Definite Integral (App)Section 9: Fourier Series StudenteProfessorFourier Series (App)
Section 1: Plane Curves and Parametric Equations StudenteProfessorThe Path of a Projectile (App)Connect2Calculus VideosSection 2: Calculus and Parametric Equations StudenteProfessorThe Path of the Scrambler (App)Connect2Calculus VideosSection 3: Arc Length and Surface Area in Parametric Equations StudenteProfessorSkiing Curved Path vs Straight Line (App)Connect2Calculus VideosSection 4: Polar Coordinates StudenteProfessorConverting an Equation from Rectangular to Polar Coordinates (App)Connect2Calculus VideosSection 5: Calculus and Polar Coordinates StudenteProfessorFinding the Area Between Two Polar Graphs (App)Connect2Calculus VideosSection 6: Conic Sections StudenteProfessorIdentifying the Features of an Ellipse (App)Section 7: Conic Sections in Polar Coordinates StudenteProfessorFocus and Directrix (App)
Section 1: Vectors in the Plane StudenteProfessorFinding a Position Vector (App)Connect2Calculus VideosSection 2: Vectors in Space StudenteProfessorVectors in Space (App)Section 3: The Dot Product StudenteProfessorCalculating Work (App)Connect2Calculus VideosSection 4: The Cross Product StudenteProfessorFinding the Distance from a Point to a Line (App)Connect2Calculus VideosSection 5: Lines and Planes in Space StudenteProfessorEquation of a Plane (App)Section 6: Surfaces in Space StudenteProfessorSketching a Paraboloid (App)Sketching an Elliptic Cone (App)
Section 1: Vector-Valued Functions StudenteProfessorSketching the Curve Defined by a Vector-Valued Function (App)Connect2Calculus VideosSection 2: The Calculus of Vector-Valued Functions StudenteProfessorThe Calculus of Vector-Valued Functions (App)Section 3: Motion in Space StudenteProfessorFinding the Velocity and Acceleration Vectors (App)Connect2Calculus VideosSection 4: CurvatureStudenteProfessorFinding a Unit Tangent Vector (App)Connect2Calculus VideosSection 5: Tangent and Normal Vectors StudenteProfessorTangent and Normal Vectors (App)Section 6: Parametric Surfaces StudenteProfessorParametric Surfaces (App)
Section 1: Functions of Several Variables StudenteProfessorSketching Contour Plots (App)Section 2: Limits and Continuity StudenteProfessorThe Definition of a Limit (App)Section 3: Partial Derivatives StudenteProfessorPartial Derivatives (App)Section 4: Tangent Planes and Linear Approximations StudenteProfessorTangent Planes and Linear Approximations (App)Connect2Calculus VideosSection 5: The Chain Rule StudenteProfessorThe Chain Rule (App)Connect2Calculus VideosSection 6: The Gradient and Directional Derivatives StudenteProfessorFinding the Direction of Maximum Increase (App)Connect2Calculus VideosSection 7: Extrema of Functions of Several Variables StudenteProfessorExtrema and Functions of Several Variables (App)Connect2Calculus VideosSection 8: Constrained Optimization and Lagrange Multipliers StudenteProfessorFinding the Minimum Distance (App)Connect2Calculus Videos
Section 1: Double Integrals StudenteProfessorApproximate Limits of Integration (App)Section 2: Area, Volume, and Center of Mass StudenteProfessorArea, Volume and Center of Mass (App)Connect2Calculus VideosSection 3: Double Integrals in Polar Coordinates StudenteProfessorDouble Integrals in Polar Coordinates (App)Section 4: Surface IntegralsStudenteProfessorSurface Area (App)Section 5: Triple Integrals StudenteProfessorTriple Integrals (App)Connect2Calculus VideosSection 6: Cylindrical Coordinates StudenteProfessorCylindrical Coordinates (App)Section 7: Spherical Coordinates StudenteProfessorSpherical Coordinates (App)Section 8: Change of Variables in Multiple Integrals StudenteProfessorChange of Variables in Multiple Integrals (App)Connect2Calculus Videos
Section 1: Vector Fields StudenteProfessorVector Fields (App)Connect2Calculus VideosSection 2: Line Integrals StudenteProfessorLine Integrals (App)Connect2Calculus VideosSection 3: Independence of Path and Conservative Vector Fields StudenteProfessorIndependence of Path and Conservative Vector Fields (App)Connect2Calculus VideosSection 4: Green's Theorem StudenteProfessorGreen's Theorem (App)Connect2Calculus VideosSection 5: Curl and Divergence StudenteProfessorCurl and Divergence (App)Connect2Calculus VideosSection 6: Surface Integrals StudenteProfessorSurface Integrals (App)Connect2Calculus VideosSection 7: The Divergence Theorem StudenteProfessorThe Divergence Theorem (App)Connect2Calculus VideosSection 8: Stokes' Theorem StudenteProfessorStokes' Theorem (App)Connect2Calculus VideosSection 9: Applications of Vector Calculus StudenteProfessorApplications of Vector Calculus (App)
Section 1: Second-Order Equations with Constant Coefficients StudenteProfessorSecond Order Differential Equations (App)Section 2: Nonhomogeneous Equations: Undetermined Coefficients StudenteProfessorNonhomogeneous Equations: Undetermined Coefficients (App)Section 3: Applications of Second Order Equations StudenteProfessorApplications of Second Order Equations (App)Section 4: Power Series Solutions of Differential Equations StudenteProfessorPower Series Solution to a Differential Equation (App)
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