Topic outline

• CALCULUS 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 Coordinates - Final Assessment

This is the final assessment for Parametric Equations and Polar Coordinates. (Available when you subscribe.)

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• Vectors 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
2.7. Cylindrical and Spherical Coordinates
Final Assessment

• Vector-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 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 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 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 Equations

7.1. Second-Order Linear Equations
7.2. Nonhomogeneous Linear Equations
7.3. Applications
7.4. Series Solutions of Differential Equations
Final Assessment