Fall 2003

Wk 1: Tues9/2 : First Class. Course management details, syllabus. Outline of topics for the semester. Math and the World, Torus Movie, Sect 13. 1 (Coordinates)

Thur 9/4: 13.1 (Distance in R³, spheres), 13.2 ( Vectors), 

Wk 2: Tues 9/9: 13.3 (Dot Product), 13.5 (Equation of Plane using Normal Group Worksheet Vector Multiplication and Applications.

Thur 9/11: ), 13.4 (Cross Product, finding normal to plane generated by two vectors), Sect. 13.3 (Projections and Work), 13.5 (parametric equation of lines) ,

Wk 3: Tues 9/16 13.5 Parametric equations of lines (worksheet), 17.1 Vector Fields (worksheet), Functions of 2 variables (15.1).

Wk 4: Tues 9/23 Group review of derivatives (worksheet), Partial Derivatives (worksheet), Making surface from pipecleaners (worksheet).

Wk 5: Tues 9/30: Review of various interpretations for partial derivatives including contour plot application (worksheet). Answer Key p1, p2, p3, p4. Tangent line to parametric curve; spiral curve on surface of cylinder.

Wk 6: Tues 10/7 : Differentials (15.4), Contour lines (15.1), worksheet

Fall Break

Wk 7: Tues 10,/21 Taking 2^nd partial derivatives using the chain rule (15.5), Directional Derivatives and the Gradient Vector. For class on Thur, take the derivative dT/ dt, where T(x,y) = x² + y² and x(t) and y(t) are given by the formulas in class.

Wk 8: Tue 10/28: Del, grad, div, curl (17.6), global vs local max/min worksheet, answer key 1,2, 3(15.7) , Intro 2^nd Derivative Test worksheet.

Wk 9: Tue 11/ 4: Criltical points, Quadratic approximation and 2^nd derivative test; worksheet.

Wk 10: Tue 11/11: L Lagrange Multipliers (15.8). Globlal maximum/ min.

Wk 11: Tues 11/18: non rectangular regions (worksheet, answer key ).

Wk 12: Tues 11/25: Change of coordinates: double integrals via polor coordinates (Sect. 16.4), Surface Area (16.4)

Wk 14: Tues 12/9: Conservative Vector Field worksheet.,(17.4), answer key

Fall 2002

Wk 1: Tues9/5 : First Class. Course management details, syllabus. Outline of topics for the semester. Math and the World, Torus Movie, Sect 13. 1 (Coordinates)

Thur 9/7: 13.1 (Distance in R³, spheres), 13.2 ( Vectors), 

Wk 2: Tues 9/10: 13.3 (Dot Product), 13.5 (Equation of Plane using Normal 13.4 (Cross Product, finding normal to plane generated by two vectors),. Group Worksheet Vector Multiplication and Applications.

Thur 9/12: Sect. 13.3 (Projections and Work), 13.5 (Equations of planes and parametric equation of lines. Angles between planes) ,Parametric equations in 2 and 3 dimensions (Sect 14.1, see also 11.1), circles, ellipses, onverting between y=f(x) and parametric equations, lines. Tangent vector, velocity vector, acceleration. Unit tangent vector.

Wk 3: Tues 9/17 11.4 (Polor Coordinates), 13. 7 (Spherical Coordinates), 14.1 (Parametric Curves ).

Wk 4: Tues 9/24 14.3 (Arc Length), computer program for arc length.

Wk 5: Tues 10/1: 15.1 Sketching the graph of z = f(x,y) and constructing via pipe cleaners. 15.3: Partial derivatives gives slope of tangent line to the graph along x or y direction.

List of topics for mid-term.

  Thur 10/3: 15.1 Sketching z = x², partial derivatives via table - finite difference quotient, linear functions z = z₀ + a (x - x₀) + b(y-y₀), Tangent planes (15.4). Review for exam.

Wk 6: Tues 10/8 : Review for exam. Higher Order Deriatives 15.3

Wk 7: Tues 10,/22: Contour plots 15.1

Wk 8: Tue 10/29: Directional Derivatives (15.6) and Gradient, Vector Fields (17.1).

Wk 9: Tue 11/ 5: 2^nd Deriviative Test, Quadratic Approximations (15.7)

Wk 10: Tue 11/12: Lagrange Multipliers (15.8).

Wk 11: Tues 11/19: Partial integral and worksheet, Double integrals over rectangles (16.2) and worksheet, general regions (16.3)

Wk 12: Tues 11/26: Triple Integrals (16.7), Spherical Coordinates (16.8), Triple Integral worksheet.

Wk 13: Tues 12/3: Line integrals (17. 2). Group worksheet.

Wk 14: Tues 12/10: Green's Theorm (17.4).