## Topic outline

- CALCULUS VOLUME 3CALCULUS VOLUME 3
This comprehensive course contains 7 sections with 50 self-grading lessons, including final assessments. The first section is available to try for free.

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- Parametric Equations and Polar CoordinatesParametric Equations and Polar Coordinates
- Plot a curve described by parametric equations.
- Convert the parametric equations of a curve into the form $y=f(x).$
- Recognize the parametric equations of basic curves, such as a line and a circle.
- Recognize the parametric equations of a cycloid.

1.2 Calculus of Parametric Curves

1.3 Polar Coordinates

1.4 Area and Arc Length in Polar Coordinates

1.5 Conic SectionsClick the link above to get the access codes and instructions to add this trial course to your LMS.

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- Parametric Equations and Polar Coordinates - Final AssessmentParametric Equations and Polar Coordinates - Final Assessment
This is the final assessment for

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The full course includes all 50 lessons, including 7 Final Assessments with Instructor Answer Keys.

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- Vectors in SpaceVectors in Space
2.1. Vectors in the Plane

2.2. Vectors in Three Dimensions

2.3. The Dot Product

2.4. The Cross Product

2.5. Equations of Lines and Planes in Space

2.6. Quadric Surfaces

2.7. Cylindrical and Spherical Coordinates

Final Assessment - Vector-Valued FunctionsVector-Valued Functions
3.1. Vector-Valued Functions and Space Curves

3.2. Calculus of Vector-Valued Functions

3.3. Arc Length and Curvature

3.4. Motion in Space

Final Assessment - Differentiation of Functions of Several VariablesDifferentiation of Functions of Several Variables
4.1. Functions of Several Variables

4.2. Limits and Continuity

4.3. Partial Derivatives

4.4. Tangent Planes and Linear Approximations

4.5. The Chain Rule

4.6. Directional Derivatives and the Gradient

4.7. Maxima/Minima Problems

4.8. Lagrange Multipliers

Final Assessment - Multiple IntegrationMultiple Integration
5.1. Double Integrals over Rectangular Regions

5.2. Double Integrals over General Regions

5.3. Double Integrals in Polar Coordinates

5.4. Triple Integrals

5.5. Triple Integrals in Cylindrical and Spherical Coordinates

5.6. Calculating Centers of Mass and Moments of Inertia

5.7. Change of Variables in Multiple Integrals

Final Assessment - Vector CalculusVector Calculus
6.1. Vector Fields

6.2. Line Integrals

6.3. Conservative Vector Fields

6.4. Green’s Theorem

6.5. Divergence and Curl

6.6. Surface Integrals

6.7. Stokes’ Theorem

6.8. The Divergence Theorem

Final Assessment - Second-Order Differential EquationsSecond-Order Differential Equations
7.1. Second-Order Linear Equations

7.2. Nonhomogeneous Linear Equations

7.3. Applications

7.4. Series Solutions of Differential Equations

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