| Week 1 |
- Visualization of geometric notions: points, lines, planes,
surfaces, regions.
- Distance formula and the method of completing the square.
- Vectors: representation, magnitude, direction, properties.
- Dot and cross products: properties.
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- Dot and cross products (review).
- Equations of lines and planes.
- Cylinders and quadric surfaces.
- Cylindrical and spherical coordinates.
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- Lines and planes (review).
- Cylinders and quadric surfaces (review).
- Functions and curves: vector functions, domain, range.
- Limit and continuity of a vector function.
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| Week 2 |
- Limit and continuity of a vector function (review).
- Derivatives and integrals of vector functions: tangential, normal
and binormal vectors, arclength.
- Functions of several variables(scalar functions): domain, range,
graph.
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- Domain of functions of several variables (review)
- Graph of functions of two variables, level curves and level surfaces (review).
- Limit and continuity of functions of several variables.
- Partial derivatives.
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- The chain rule.
- Implicit differentiation and Implicit function theorem.
- Higher derivatives, directional derivatives and the gradient vector.
- Maximizing the directional derivative.
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| Week 3 |
- Tangent planes.
- Linear approximations.
- Differentiability of a function of two variables.
- Tangent plane to level surfaces, normal line.
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| Week 4 |
- Tangent planes (review).
- Maximum and minimum values (review).
- Lagrange multipliers.
- Double integrals over rectangles.
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- Double integrals over rectangles (review).
- Iterated integrals, computations.
- Double integrals over general regions.
- Double integrals in polar coordinates.
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- Review of maximum and minimum values (homework problems)
- Triple integrals over boxes.
- Triple integrals over general solids.
- On the total differential of a function.
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| Week 5 |
- Triple integrals in cylindrical and spherical coordinates.
- The Jacobian of a transformation.
- Change of variables in multiple integrals.
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