## MATH 210 Calculus III  Spring, 2003 MTRF 10:00 -10:50  SH 116  Course Assignments

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Last updated: 2-6-03

MATH 210: Calculus III Spring,2002
 Week /Day Monday Tuesday Thursday Friday 1 1/21 Introduction-  Begin review Variables- relations-functions.  What is calculus? Differential Equations? 1/23 Introduction to 3-dimensional coordinate geometry. 1/24 13.1 Introduction to vectors. 2 1/27 13.2 "1 variable controlling 2"  11.1 Parametric curves .  Visualizations: Transformations and graphs. 1/28 More on vectors and functions "1 variable controlling 2," 2 controlling 1". 1/30 More on vector algebra. 1/31 Lines: parametric and vector equations 2 &3 dim. 13.5
 Week/Day Monday Tuesday Thursday Friday 3 2/3 The tangent problem 11.2 "1 variable controlling 2 (or 3)." Vector functions, tangent vectors and velocity. 14.1, 14.2 2/4Tangent lines, Lengths: segments, vectors, arcs. 11.2, 11.3, 14.3 speed 2/6 Smooth curves. Acceleration 14.4  Arc length as an integral of speed. 2/7 Differential equations and integrals of vector functions. 4  Summary #1 Due 2-11 2/10 The Dot Product. 13.3. 2/11 More on dot products.  Finish up 1 variable controlling 2 and 3. The calculus of the"vector" derivative 2/13 More on dot products 2/14  The Calculus for r'(t). 5 2/17 Curvature Formulae 14.3 2/18 Begin "2 controlling 1 variable".  Scalar fields.Graphs and level curves of 2/20 2/21 Begin Partial Derivatives
 Week/Day Monday Tuesday Thursday Friday 6 Summary #2 Due 2-25 2-24 Second order Partial derivatives. Linear (Affine)Functions- lines, planes and vectors. 2-25 More on Planes and "Tangent Planes". What is continuity? What does differentiable mean? 2/27  Differentials.Concepts and definitions. 2/28 [Limits and Continuity. Closeness, Approximations. ?]  Differentials, C1 and differentiable functions.The geometry of differentiability- Tangent planes. 7 3-3 The Chain Rule (1-2-1)  chain rule 3-4Chain Rule(2-2-1)  Directional derivatives and the gradient. 3-6 Geometry of the gradient. 3-7 More on gradient. 8 Summary #3 Due 3-10 Exam #1 Self Scheduled for Wednesday 3-12 3-10 Finish Gradient and level curve/surfaces.  Extremes.. 3-11.Testing for extremes. Extrema on compact sets 3-13 More Extremes and odds and ends. 3-14  Finish discussion of the discriminant test. Quadratic forms. 9 3-17 No Class (Break) 3-18 3-20 3-21 10 3-24  LaGrange Multiplier 3-25 Linear regression and "least squares." 15.7 problem 51. 3-27 Quadric Surfaces 13.6 What about 4 variables: 1-3, 3-1, 2-2 ?  5 variables? 2-3, 3-2? 3-28 Breath? 11Summary #4 Due 4-3 3-31  NO Classs  C.C. Day 4-1Start Integration over rectangles 4-3 More on Integration and iterated integrals. 4-4 Average Value  The area problem.11.2(?) Fubini's Theorem. 12 4-7  Beginning-basic properties.applications volumes. Integration over compact regions. 4-8 More Integration over compact regions.Properties of integration in the plane. 4-10 Cross products 4-11 .. More on planes and normal vectors with cross products..
 Week/Day Monday Tuesday Thursday Friday 13 4-14 More Integration in the plane.  Cross Product  Application to tangent plane. 4-15 Begin Polar coordinates 4-17 Polar coordinates- curves in the plane. Tangents. 4-18 Arc length in Polar coordinates  Begin Integration with polar coordinates. 14 Exam #2  4-23 4-21  More Integration with Polar Coordinates. The integral of exp(-x2).  . 4-22 Begin Integration in 3D. Cartesian coordinates 4-24 Applications of integration in the plane and space to mass. Start Cylindrical  coordinates. 4-25 No class! 15 4-28  Integration in Cylindrical. Begin spherical coordinates 4-29 More Integration in Cylindrical and spherical coordinates 5-1 Integration in spherical coordinates. Integration surface Area. Briefly 2-3 visualized. 5-2 More work on integration and shperical coordinaates. 16 Talks 5-5 Vector fields and line integrals  2-2 Transformations and vector fields. 5-6 Integration Over curves. Vector fields and line integrals 5-8 Talks 5-9 Talks Green's theorem?Review.!?

Assignment Problem List I ( as of 1-30-03)