The first midterm will be on Tuesday, March 12th, from 7:30 to 9:30 pm in Science Center Hall D.

There will be a coursewide review held on Sunday, March 10th from 7 to 9pm in Science Center Hall E - everyone is welcome to come.  Remember also to take advantage of the Math Question Center which meets from Sunday to Thursday from 8 to 10 pm in Loker.

Please find below a pretty exhaustive list of what we have covered up to this point.  On the midterm you should be prepared to answer questions from any of these topics.  Note that this midterm covers material just up through section 11.4 on the Tangent Plane - it will not cover anything after that (i.e. it will not include sections 11.5, 11.6 and 11.7 even though we are going over them right now in class).  Also be sure to read through the list of topics that will not be included in this first midterm (these are located at the bottom of the list).

Topics for first midterm:

• Basic definitions for multidimensional spaces
• Coordinate systems: rectangular, cylindrical, spherical - their use, conversion between systems
• Distance formulas (between points, computation of distance between points and lines, points and planes, etc.)
• Standard basis vectors, i, j and k and their use
• Basic vector definitions, operations:
• Notation:  <x, y, z> =  x i + y j + z k
• Addition/subtraction, finding magnitude of vectors, finding unit vectors
• Dot products and their geometric significance (i.e. a · b = |a| |b| cosine(angle between a and b), finding magnitude of a vector in terms of dot products)
• Scalar and vector projections - computation, understanding
• Cross products - computation and geometric significance (no scalar triple products on midterm)
• Equations of lines and planes -
• For lines: vector and parametric equations  (no symmetric equations on page 677 section 9.5)
• For planes: vector equations, scalar equations, linear equations
• Normal vectors for planes, use for finding angle between planes
• Vector Functions
• Use in finding parametric equations for space curves
• Ability to find and identify simple space curves and their parametrizations - circles, helixes, parametrization of intersections (such as in example 5 on page 707)
• Differentiation of vector functions:
• Computation, knowledge/use of differentiation rules (Theorem 3 page 714)
• Note, no integrals for vector functions on midterm (page 715 in section 10.2)
• Finding tangent vectors for space curves, tangent lines
• Computing Arc Length for space curves
• No parametrizing space curves with respect to arc length (bottom of page 718, section 10.3)
• No Curvature computations (in section 10.3)
• No Normal and Binormal vectors (in section 10.3)
• Surfaces
• Recognition of equations and traces for several simple quadric surfaces: ellipsoids, elliptic paraboloids, cones and hyperbolic paraboloids (all on page 691)
• Parametric equations for surfaces - understanding of grid curves
• Knowledge of basic examples such as for cylinders, spheres,
• Finding parametrizations, such as parametric equations for surfaces of rotation (page 740, section 10.5)
• Multivariable functions
• Depiction through use of graphs, level curves
• Knowledge of basic examples: linear functions, cones, paraboloids, parabolic cylinder (page 687)
• Partial derivatives:
• Computation (use of analytic definition, in (4) page 768, when necessary, such as for 11.3 problem  #78)
• Geometric significance (rate of change of function in x, y direction)
• Skip implicit differentiation (page 771 section 11.3)
• Notation, computation of higher partial derivatives (page 772) and knowledge of Clairaut's Theorem (on equivalence of mixed partials)
• Skip partial differential equations section and the Cobb-Douglas Production Function (in 11.3)
• Tangent Planes - finding equations for, using partial derivatives
• Use of tangent plane for approximating differentiable functions
• Knowledge of the meaning of a differentiable function: one whose linear approximation given by the tangent plane is a good approximation (compare to the z = 0 tangent plane approximation for the function given in figure 4, page 782) (you do not need to know the full blown definition given in (7), bottom of page 782)
• Skip differentials (in section 11.4, page 784 through 786)
• Skip tangent planes to parametric surfaces (in section 11.4)
• Note there are a number of topics in the textbook that we did not cover in class, and which  will not be covered on the exam:
• No scalar triple products (in section 9.4)
• No symmetric equations (in section 9.5)
• No integrals of vector functions (in section 10.2)
• Nothing  in section 10.3 after page 718 (starting with parametrizing space curves by arc length at bottom of 718)
• Nothing in section 10.4 (skipped completely)
• No implicit differentiation (in section 11.3)
• No partial differential equations, Cobb-Douglas Production Function (in 11.3)
• Also, to save you a bit of worry, the following topics that we did cover will not be tested on the midterm:
• Section 11.2 on Limits and Continuity
• Finding tangent planes for parametric surfaces (in section 11.4)

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Old Exams for practise:

• Note that although the class is similar from last year to this year, there are differences in terms of the timing of  what was covered during the semester.  For instance on the spring 2001 mid-term, you don't need to know how to do  #4 or #5 parts c,d at this point since we haven't covered those topics yet. In addition to using the following practice tests, you should really go through your old homework problems - they will give you more of a sense of what you need to know for this semester's midterms.
• We will keep posting solutions to these exams, but do be sure to try to do them first on your own!
• Midterm practice exam l  (Solutions)
• Midterm practice exam 2  (Solutions)
• Midterm 1 Spring 2000  (Solutions)
• Midterm 1 Spring 2001  (skip #4 and #5 parts c and d)  (Solutions)
• Midterm 1 Fall 2001  (Solutions)

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Answers to Review Problems for Chapters 9, 10 and 11 from our textbook:

• Since what we've covered is a bit different from what other semesters have covered in the past, another good way to get ready for the midterm is to do the review problems at the end of each chapter that we've covered.  Posted below are the answers to these review problems.  By doing these review problems, you'll be able to get practise for our midterm that's more specifically geared to what we've covered so far this semester.
• Note that certain problems (such as #10 in review for chapter 9) are on topics we have specifically excluded from the midterm (see list of such topics above), so there are some problems that you shouldn't expect to be able to do - you should be able to figure out which ones these are by checking the list of topics covered/not covered.
• Since we've only covered up through 11.4 in chapter 11, not all of the answers were scanned in for that chapter, only the ones that were relevant for us at this point.
• Answers to Chapter 9 Review questions
• Answers to Chapter 10 Review questions
• Answers to Chapter 11 Review questions