Midterm
1. Analytic Geometry
- Conic Sections
- Second-Degree Equations
2. Parametric and Polar Curves
- Parametric Equations; Tangent Lines and Arc Length for Parametric Curves
- Polar Coordinates
- Tangent Lines, Arc Length, and Area for Polar Curves
3. Three-Dimensional Space; Vectors
- Rectangular Coordinates in 3-Space; Spheres
- Vectors
- Dot Product; Projections
- Cross Product
- Parametric Equations of Lines
- Planes in 3-Space
- Quadric Surfaces
4. Vector-Valued Functions
- Introduction to Vector-Valued Functions
- Calculus of Vector-Value Functions
- Arc Length
- Unit Tangent, Normal Vectors, and Curvature
1. Analytic Geometry
- Conic Sections
- Second-Degree Equations
2. Parametric and Polar Curves
- Parametric Equations; Tangent Lines and Arc Length for Parametric Curves
- Polar Coordinates
- Tangent Lines, Arc Length, and Area for Polar Curves
3. Three-Dimensional Space; Vectors
- Rectangular Coordinates in 3-Space; Spheres
- Vectors
- Dot Product; Projections
- Cross Product
- Parametric Equations of Lines
- Planes in 3-Space
- Quadric Surfaces
4. Vector-Valued Functions
- Introduction to Vector-Valued Functions
- Calculus of Vector-Value Functions
- Arc Length
- Unit Tangent, Normal Vectors, and Curvature
5. Partial Derivatives
- Function of Two or More Variables
- Limits and Continuity
- Partial Derivatives
- Differentials and Local Linearity
- The Chain Rule
- Directional Derivatives and Gradients
- Maxima and Minima of Functions of Two Variables
6. Multiple Integrals
- Double Integrals
- Double Integral over Nonrectangular Regions
- Double Integrals in Polar Coordinates
- Triple Integrals
7. Topics in Vector Calculus
- Vectors Fields
- Line Integrals
- Independence of Path; Conservative Vector Fields
- Green''''''''''''''''s Theorem
- Surface Integrals
- The Divergence Theorem
- Stokes'''''''''''''''' Theorem
8. Fourier and Laplace analysis
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