## MATH 210 Calculus III Spring, 2015  10:00 -10:50  MTRF....Art_027 Course Assignments and Schedule

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Last updated: 2-25-2015 Work in progress!

Assignment Problem List (Work in progress) 2-25-2015
*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 1/19 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 1/26  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 2/2 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 More on DE's and integrals. 13.4  Smooth curves and parametrization (?) 4 Summary #1 Due 2/10 POW #1 Submit Thursday 2/13 2/9 Smooth curves. Definite intgrals: Change in position - a vector. Arc length as an integral of speed. Lengths: segments, vectors, arcs. 10.2, 10.3, 13..3 speed Arc length as an integral. velocity, speed Finish up 1 variable controlling 2 and 3. The calculus of the"vector" derivative The Dot Product. 12.3. Geometry of dot product with angles. Orthogonal vectors. Orthogonal vectors. acceleration More on dot products. 5 2/16 Lines in the plane with dot products. Planes in Space. More Calculus for r'(t). Projections and Dot products. Work and dot product More on Work and dot products? Finish Velocity and Acceleration with example? Unit tangent vector. Revisit lines in the plane and Planes in Space. Begin "2 controlling 1 variable" Tables .Scalar fields Level Curves and surfaces of  functions of 2 and 3 Begin visualize function with mapping diagram. Linear (Affine)Functions and Equations: lines, planes and vectors. 6 Summary #2 Due 2/26 2/23 Begin the graph and mapping diagram of a function of 2 variables. Graphs and mapping diagrams Begin Partial Derivative. More!  tangents, partial derivatives, planes and "Tangent Planes". Second order Partial derivatives. Start Differentials.Concepts and definitions 7  POW #2 Due March 5. Work for a Moving Particle. 3/2 Differentials, C1 and differentiable functions. Geometry of differentiability-Tangent Planes The Chain Rule (1-2-1) [Limits and Continuity. Closeness, Approximations.?] Implicit Differentiation Chain Rule(2-2-1) What is continuity? What does differentiable mean? Definition of limit. Review of continuity and differentiability. Gradient and level curve/surfaces. 8 Exam #1 Self Scheduled Wed. 3/11 3/9 Begin Directional derivatives and the gradient. Geometry of the gradient. (Review for exam #1) More Gradient and level surfaces Tangent planes from gradients. More on Tangent Planes. Testing for extremes. 3/14 to 3/22 No Classes. Spring Break 9Summary #3 Due 3/27 3/23 . 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 POW #3 Submit Friday 4/3 3/30 Start Integration over rectangles 3/31 No Class CC Day. More on Integration and iterated integrals Fubini's Theorem. Beginning- 11 What about 4 variables: 1-3, 3-1, 2-2 ?  5 variables? 2-3, 3-2? 4/6 Integration over compact regions. Basic properties.applications volumes. The area problem.11.2(?) More Integration over compact regions Examples for changing order of Integration- factors in integration [e^(-y^2)] Properties of integration in the plane. Average Value 12Summary #4 Due 4/13 POW #4 Due April 17 5:00 pm. 4/13 More Change of Order- example. Begin Integration with Polar Coordinates. Polar coordinates review assigned. More integration with Polar Coordinates. The integral of exp(-x2). Quadric Surfaces 13.6? 13 Exam #2 Self Scheduled Wed. April 22 4/20 Cross Product More Integration in the plane. Cross products Begin Integration in 3D. Cartesian coordinates More on cross products, planes and normal vectors More on Integration in 3D Compact Domains bounded by Surfaces. . 14 POW # 5 Due May 1 5:00 pm. 4/27 . Finish Cross Product. More on Integration in 3D Compact Domains bounded by Surfaces. A first look at other integration with one or two controlling variables. Parametrized curves and surfaces. Integration of functions over curves. Cylindrical coordinates. Integration of functions over curves. Vector fields and line integrals FT of calculus for line integrals. Integration in Cylindrical and spherical coordinates Applications of integration in the plane and space to mass, probability and means? 15Summary #5 Due 5/5 5/4 ?More work on integration and spherical coordinates. Applications?  Curvature Formulae 13.3 Applications of integration in the plane and space to mass, probability and means? Surface Integrals.I 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 11, 12:40 -14:30 Wednesday May 13, 10:20-12:10 Thursday May 14 10:20-12:10 Thursday May 14 3:00-4:50 Friday May 15 10:20-12:10