## MATH 210 Calculus III Spring, 2013  11:00 -11:50  MTRF....KA104 Course Assignments and Schedule

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Last updated: 1-21-2013 Work in progress!

Assignment Problem List (Work in progress) 1-21-2013
*Early or Just in time:
When two due dates are given,
the first date is for preparation and/or starting problems,
the second date is for completion of problem work

 Week/Day Monday Tuesday Thursday Friday 1 1/21 MLK Day No Class Introduction-  Begin review Variables- relations-functions.  What is calculus? Differential Equations? 13.1 Introduction to 3-dimensional coordinate geometry. More on 3 dim. coordinate geometry.  Introduction to vectors. 2 1/28  More on Vectors and visualization  of vector algebra More vector stuff. 13.2 "1 variable controlling 2"  11.1 Parametric curves and vectors. Visualizations: Transformations and graphs.  More on vectors and functions "1 variable controlling 2," 2 controlling 1". 3 2/4 More on vector algebra 12.5 Lines: parametric and vector equations 2 &3 dim.. 11.1 Parametric curves .  Visualizations:13.1, 13.2 Vector functions, tangent vectors and velocity. The tangent problem 11.2 "1 variable controlling 2 (or 3) ."Begin:Derivatives,Tangent lines, Differential equations and integrals . 13.2 Tangent lines, Lengths: segments, vectors, arcs. 10.2, 10.3, 13..3 speed 13.4  Acceleration Arc length as an integral of speed. Smooth curves. 4 2/11 Smooth curves. Finish up 1 variable controlling 2 and 3. The calculus of the"vector" derivative The Dot Product. 12.3. More on dot products. Geometry of dot product with angles. Orthogonal vectors. Lines in the plane with dot products. Planes in Space. Projections and Dot products. Work and dot products More Calculus for r'(t). 5  Summary #1 Due 2/18 2/18Begin "2 controlling 1 variable" Tables and Scalar fields. Level Curves. Linear Functions, Equations: Revisit Planes in Space. Graphs and level curves of  functions of 2 and 3 variables. Application of derivative calculus The graph of a function of 2 variables. Begin Partial Derivative. Linear (Affine)Functions- lines, planes and vectors. 6 2/25  More! on tangents, partial derivatives, planes and "Tangent Planes". Second order Partial derivatives. The Differentials.Concepts and definitions Differentials, C1 and differentiable functions. Geometry of differentiability- Tangent planes. 7  Summary #2 Due 3/8 POW Optional 3-7 3/4 The Chain Rule (1-2-1) [Limits and Continuity. Closeness, Approximations.?] Implicit Differentiation What is continuity? What does differentiable mean? Implicit Differentiation Gradient and level curve/surfaces. 8 Exam #1 Self Scheduled Wednesday 3/13 3/11 Chain Rule(2-2-1) (Review for exam #1) Begin Directional derivatives and the gradient. Geometry of the gradient. More Gradient and level surfaces Tangent planes from gradients. 3/18 to 3/22 No Classes. Spring Break 9 3/25 . More on Tangent Planes. Testing for extremes. The discriminant test. Quadratic forms. Odds and ends .Taylor and functions of 2 variables. (Synopsis) Extrema on compact sets LaGrange Multiplier 10 Summary #3 Due 4-5 or 4-8 4/1 No Class CC Day. Start Integration over rectangles More on Integration and iterated integrals Fubini's Theorem. Beginning-basic properties.applications volumes. Integration over compact regions. 11 What about 4 variables: 1-3, 3-1, 2-2 ?  5 variables? 2-3, 3-2? 4/8 Average Value The area problem.11.2(?) More Integration over compact regions Properties of integration in the plane. 12 Summary #4 Due 4/15 Examples for changing order of Integration- factors in integration [e^(-x^2-y^2)] Polar coordinates review assigned. Begin Integration with Polar Coordinates. Polar coordinates review. Begin Integration with Polar Coordinates. More integration with Polar Coordinates. The integral of exp(-x2). 13 Exam #2 Self Scheduled TBA 4/22 Cross Product More Integration in the plane. Quadric Surfaces 13.6?   Cross products More on planes and normal vectors with cross products.. Begin Integration in 3D. Cartesian coordinate 14 4/29 .Applications of integration in the plane and space to mass, probability and means? Integration in Cylindrical and spherical coordinates More work on integration and spherical coordinates. Applications?  Surface Integrals.I A first look at other integration with one or two controlling variables. Vector fields and line integrals. Integration Over curves. Curvature Formulae 13.3 15Summary #5 Due 5/6 FT of calculus for line integrals. Finish Surface Area and Surface integrals II. More  Integration. Conservative fields. More on conservative fields. Green's theorem. Briefly 2-3 visualized More! Application to tangent plane. Applications of integration in the plane and space to mass. Linear regression and "least squares." Review.!?

 16 Final Examination Self scheduled Review Session: Sunday TBA Monday May 13 10:20-12:10 Tuesday May 14 10:20-12:10 Wednesday, May 15 12:40-14:30 Friday, May 17 10:20-12:10.