| Math 212: Multivariable Calculus (Spring 2006) |
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| Home > Assignments> Quizzes |
| Quizzes |
(20 per cent) There will be quizzes given every week. These quizzes will almost always be take-home, weekend quizzes given out on class on Friday to be handed in in class on Monday. They will consist of relatively simple homework problems which you work on by yourself and will be a way in which you can assure yourself you are keeping up with the course. The quiz, and hints to the quiz will be posted on the web message board.
Most Fridays you will have a Take-Home Quiz to be handed-in on the following Monday.
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Topic | Hint | Date Assigned | Date Due |
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BONUS 11 |
Div, Grad, Curl | You need to use the vector calculus identity given to prove part (a) and then you can use part (a) as a new identity to help you prove part (b) | Mon Apr 24 | Wed Apr 26 |
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ELEVEN |
Line Integration | Recall the Fundamental Theorem of Line Integrals | Fri Apr 21 | Mon Apr 24 |
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BONUS 10 |
More Multiple Integration Practice | In (b) The volume as a double integral is probably easier to write down | Fri Apr 21 | Mon Apr 24 |
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TEN |
Multiple Integration | Without Fubini You Have No Hope. (Iterated integrals can be done in different orders if you change the limits of integration) | Wed Apr 12 | Mon Apr 17 |
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BONUS 9 |
Changing the Order of Integration for a Triple Integral | The Ultimate Fubini! (Think of a wedge of cheese. How many possible changes of order of integration are there for a triple integral?) | Wed Apr 12 | Mon Apr 17 |
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NINE |
Multiple Iterated Integrals | Remember Fubini! (Iterated integrals can be done in different orders if you change the limits of integration) | Fri Apr 7 | Mon Apr 10 |
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BONUS 8 |
Constrained Multivariable Optimization Practice | Remember the constraint equation itself must also always be satisfied (in addition to the Lagrange Multiplier equations). | Fri Mar 24 | Wed Mar 29 |
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EIGHT |
Lagrange Multipliers | Optimize the square of the distance, not the distance itself. | Fri Mar 24 | Mon Mar 27 |
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BONUS 7 |
Method of Lagrange (Constrained Multivariable Optimization) | Remember the constraint itself must also always be satisfied. | Fri Mar 24 | Wed Mar 29 |
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SEVEN |
Multivariable optmization | Recall that a multivariable function must attain a global max and global min on a closed bounded domain. To optimize a multivariable function on a domain involves single variable optimization. | Fri Mar 24 | Mon Mar 27 |
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BONUS 6 |
The Gradient and Gradient Fields | Remember a gradient field is a vector function of a vector variable which is obtained from a scalar function of a vector variable. To find this function, you have to reverse the Gradient operation. | Fri Mar 10 | Mon Mar 20 |
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SIX |
Multivariable chain rule | Remember when you take the chain rule to write the resulting derivative in terms of the proper variables. | Fri Mar 10 | Mon Mar 20 |
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BONUS 5 |
Approximating f(x,y) | This is similar to the tangent plane approximation to a function. | Fri Mar 3 | Mon Mar 6 |
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FIVE |
Multivariable limits | Remember a limit only exists if one gets the same answer by approaching the value from every direction. | Fri Mar 3 | Mon Mar 6 |
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BONUS 4 |
Tangent Planes | Think about what the 2-D slices look like when a particular variable is held constant. | Fri Feb 17 | Wed Feb 22 |
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FOUR |
Partial Derivatives | Think about what the meaning of the partial derivative of Q with respect t b. | Fri Feb 17 | Wed Feb 22 |
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BONUS 3 |
Determinants | Pick what row you use to compute the determinant very carefully! | Fri Feb 10 | Mon Feb 13 |
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THREE |
Homogeneous Linear Systems | An important series of questions which gets to the most fundamental ideas in Linear Systems | Fri Feb 10 | Mon Feb 13 |
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BONUS 2 |
Analytic Geometry | The distance between a point and a plane will be the shortest distance between that point and the plane. | Fri Feb 3 | Mon Feb 6 |
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TWO |
Vector Products | Practice with the vector cross product and scalar dot product. | Fri Feb 3 | Mon Feb 6 |
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BONUS 1 |
Planes | Recall what conditions one needs to have for the vectors in the plane and then think about what implications this has for the new points on the plane you select | Fri Jan 27 | Mon Jan 30 |
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ONE |
Vectors | Think about what must be true if the point (4,4,-2,2) lies on your computed line. | Fri Jan 27 | Mon Jan 30 |