## MTH 233 Section Objectives

##### Section 2.1
1. Describe vectors in the plane, and write them in component form and in terms of basis vectors.
2. Compute the magnitude of a vector in 2-space.
3. Describe and perform basic operations on vectors in 2-space.
##### Section 2.2
1. Distinguish 3-dimensional space from 2-dimensional space.
2. Work with the rectangular coordinate system in 3-space.
3. Perform and describe basic operations on vectors in 3-space.
4. Compute the magnitude of a vector in 3-space.
##### Section 2.3
1. Compute the dot product of two vectors.
2. Find and use the projection of one vector onto another.
3. Find the direction cosines of a vector.
4. Use the dot product in applications involving orthogonality, work, angles between vectors, projections, etc.
##### Section 2.4
1. Compute the cross product of two vectors.
2. Find a vector orthogonal to two given vectors.
3. Use the cross product in applications of area, volume, and torque.
##### Section 2.5
1. Find parametric or symmetric equations for a line in space.
2. Find the equation of a plane in space.
3. Find the distance from a point to a line.
4. Find the distance from a point to a plane.
5. Find the angle between two planes.
##### Section 2.6
1. Identify cylinders as 3-dimensional surfaces.
2. Recognize quadric surfaces from their graphs or equations.
3. Roughly sketch the graph of a quadric surface.
4. Sketch the traces of a quadric surface.
##### Section 2.7
1. Convert among rectangular, cylindrical, and spherical coordinates.
##### Section 3.1
1. Recognize and use equations for vector-valued functions.
2. Sketch and/or describe the graph of a vector-valued function.
3. Find limits of vector-valued functions.
4. Determine the points of continuity of a vector-valued function.
##### Section 3.2
1. Evaluate and use the derivative of a vector-valued function.
2. Compute the unit tangent vector for a vector-valued function.
3. Integrate vector-valued functions.
##### Section 3.3
1. Determine the length of a plane or space curve defined by a vector-valued function.
2. Find the arc-length parameterization for a smooth curve.
3. Find the curvature of a smooth curve at a point.
4. Compute the principal unit normal vector for a smooth curve.
##### Section 3.4
1. Find the tangential and normal components of acceleration.
2. Solve a projectile motion problem in space.
##### Section 4.1
1. Recognize a function of two variables and identify its domain and range.
2. Sketch or describe the graph of a function of two variables.
3. Recognize a function of three or more variables and identify its domain and range.
4. Identify and describe the level curves or surfaces of a function of several variables.
##### Section 4.2
1. Compute the limit of a multi-variable function.
2. Use the two-path test to show that a limit does not exist.
3. Determine the points of discontinuity of a function of several variables.
##### Section 4.3
1. Compute the partial derivatives of a function of several variables.
2. Compute higher-order partial derivatives.
3. Describe the conditions for equality of higher-order mixed partial derivatives.
4. Interpret partial derivatives as slopes.
##### Section 4.4
1. Determine if a function of two variables is differentiable.
2. Compute the total differential of a function and use it to approximate change.
3. Find an equation of the plane tangent to a given surface at a point.
4. Find parametric equations for the line normal to a given surface at a point.
5. Use tangent planes (i.e., linearizations) to approximate function values.
##### Section 4.5
1. State and use the chain rules for any number of independent and intermediate variables.
2. Use implicit differentiation.
##### Section 4.6
1. Compute directional derivatives and interpret them as slopes.
3. Use gradient vectors as normal vectors.
4. Use gradient vectors to determine the direction of maximum increase/decrease.
##### Section 4.7
1. Find the critical points of a function of two variables.
2. Use the second partials test to classify critical points.
3. Use critical points and boundary points to find the absolute extrema for functions of two variables.
##### Section 4.8
1. Use Lagrange multipliers to solve a constrained optimization problem.
##### Sections 5.1 & 5.2
1. Write a double integral as an iterated integral and evaluate.
2. Use a double integral to compute the area of a region, the volume under a surface, or the volume between two surfaces.
3. Change the order of integration.
##### Section 5.3
1. Evaluate a double integral in polar coordinates.
2. In applications of double integrals, convert from rectangular to polar coordinates or vice versa.
3. Use double integrals in polar coordinates to compute areas and volumes.
##### Section 5.4
1. Write a triple integral as an iterated integral and evaluate.
2. Use a triple integral to compute the volume of a space region.
3. Use a triple integral to compute the average value of a function over a space region.
4. Change the order of integration.
##### Section 5.5
1. Evaluate a triple integral by converting to cylindrical coordinates.
2. Evaluate a triple integral by converting to spherical coordinates.
##### Section 5.6
1. Use a triple integral to find the mass of a solid in space.
##### Sections 6.1-6.3
1. Evaluate line integrals.

Last updated January 7, 2022

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