Fall 2006

Wk 1:

Mon 9/4  First Class. Course management details, syllabus, student  questionnaire. Outline of topics for the semester. Review of key concepts of differential and integral calculus. Mathematica: Plotting approximations. For Wed class, do review sheet with basics of differential and integral calculus.

Math Connections, Torus video.

 

                  Wed 9/6:   Groups create master worksheet. Exponential functions. (S. 7.2)

Wk 2:

                  Mon 9/ 11:  Graphing techniques using translations, symmetry. Integration: Fundamental Theorem; u-du substitution. Integral of exponential function (S. 7.2). Inverse of exponential function (S. 7.3): logarithm. Worksheet.

                  Wed 9/18:   Derivative of logarithm function (S. 7.4).

Wk 3:

                  Mon 9/18:  Approximating an integral via boxes worksheet, Mathematica program. Riemann sum (S. 5.2).  

                  Wed 9/20  Finding volumes by taking limits of Riemann sums (Sect 6.2). Review of curve sketching.

 

Wk 4: 

Monday 9/25:  Review of trig functions, inverse functions and their derivatives (S. 7.5)

Wed 9/27:  What makes a good answer? (Review for midterm). Improper integrals worksheet. (S. 8.8 )

 

Wk 5:

                  Monday 10/2: ), Further discussion of improper integrals (S. 8.8), which functions grow faster (S. 7. 7) – L’Hopitals Rule. Integration by parts (S. 8.1).

Wed 10/4:   Midterm.

Wk 6:

                  Monday 10/9:  More on integration by parts (S. 8.1); integral tables (S. 8.6), convergence/divergence of improper integrals via comparison test worksheet, instructions for test rewrite and class survey.

                  Wed 10/11:   Comparison tests for improper integrals using worksheet from Monday; informal comparative test. Relation of f(x) function to the area under the curve function (hw sheet); discussion of increasing function either increasing without bound (ie diverging to infinite) or having a bound and then converging.

 

Fall Break: 10/16 – 10/20

Wk 7:

                  Monday 10/23:  Review of L’Hospital rule. Integral tables.  Review length of curve worksheet. Discovery Project assignment and list of who does what problem.

                  Wed 10/25:   Methods of numerical integration (Sect 8.7): midpoint, trapezoid, Simpson’s. Worksheet (individual, group), Mathematica programs for numerical integration.

Wk 8:

                  Monday 10/30:   Simpson’s Method (sect 8.7); More on comparison test (sect 8.8); Discovery Project: rubric, peer assessement, reflection sheet; Introduction to Differential Equations.

Wednesday 11/1:   Peer discussion for Discovery Project. Introductory to differential equations and modeling.

Wk 9:

Monday 11/6:  Differential equations and modeling (Sect 10.1): exponential model for population growth (Sect 10.4); logistic model (Sect 10.5).

Wed 11/8:  Presentations of Discovery Projects to group. Discussion of what makes a good presentation. Doubling time for exponential growth is independent of starting time. Radioactive decay; half life. Solving differential equation via separation of variables. List of topics for midterm 2.

 

 Wk 10:

                  Monday 11/13: 

Wed 11/15:  Review for test. Sect 12.10. Introduction to Taylor Polynomials (approximating a function by a polynomial). Using Mathematica to find how good the approximations are.

Friday 11/17: Pick up take home midterm from Prof. Donnay’s office.

Wk 11:

Monday 11/20:   Midterm 2 – take home test- is due today. Sect 12.10. General formula for Taylor Polynomials.

Wed  11/22:   NO CLASS due to Thanksgiving.

Wk 12:

                  Monday 11/ 27:  Taylor Series (Sect 12.10); Series = sum of infinitely many terms. Series worksheet.

Wed  11/29:    Absolute/Relative rate of change; error (table). Group work on series worksheet using Mathematica. Discussion of sequences (Sect 12.1) monotone increasing sequence; if such a sequence is bounded then it will converge. Geometric series (Sect 12.2).

Wk 13:

                  Monday 12/4:  Discussion of sequences (Sect 12.1); Convergence or divergence of harmonic series? Use comparison with integral of 1/x (Sect 12.3). Rubric for final project.

                  Wed 12/6:   Review of geometric series (Sect. 12.2), Integral test (Sect. 12.3).

                  Thur 12/7: Summary of series rules: integral test (Sect 12.3), comparison test (12.4). Improper integrals of 2nd type (Sect. 8.8).

Wk 14:

                  Monday 12/11: Quadratic approximation based at critical point determines if function has local max/min. Power series; radius of convergence (Sect 12. 8), Taylor Series (Sect 12.9).

                  Wed 12/13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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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).

Thur 9/ 18: Parametric equation of circle, graphing using slices. Group makes a surface together. Worksheet to review derivatives for next class.

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

Thur 9/25: Make saddle shaped surface with pipe cleaners. Partial derivative as slope of slices. Tangent plane. Parametric equations, tangent vectors, tangent lines (worksheet) ; Mathematica notebook.

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.

Thur 10/2: Review for test. Please send questions, requests to Prof Donnay

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

Thur 10/9: Chain Rule (15. 5), worksheet

Fall Break

Wk 7: Tues 10,/21 Taking 2nd 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.

Thur 10/23: Directional derivative , worksheet; weather map with pressure contours.

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 2nd Derivative Test worksheet.

Thur 10/30: More 2nd Derivative Test worksheet.

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

Thur 11/6:. Polar (worksheet, answer key), cylindrical, spherical coordinates (13.7). 

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

Thur 11/13: Integration (16): partial integrals (worksheet), double integrals over rectangular regions (worksheet),

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

 

Thur 11/20: Review for midterm. Polar Coordinate integrals. (worksheet, answer key).

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

Thanksgiving

Wk 13: Tues 12/2: Triple Integrals (16.7), Spherical Coordinates (16.8), Triple Integral worksheet, answer key.

Thur 12/4: Line Integrals (17.2) (worksheet, answer key),

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

Thur 12/11: Green's Theorem (17.5) Worksheet on Green's Theorem, Stokes Theorem (17.8), Divergence Theorem (17.9)

 

 

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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, converting between y=f(x) and parametric equations, lines. Tangent vector, velocity vector, acceleration. Unit tangent vector.

 

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

Thur 9/ 19: Spherical Geometry, great circles = "straight lines", sum of angles in triangle > 180! (see Problem 64, p. 865). 14.2 (derivative of vector valued function, tangent vector, integration), 14.4 (velocity vector, speed, acceleration)

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

Thur 9/26: 15.1 (Different ways to interpret f(x,y), 15.3 (partial derivatives)

 

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 Derivatives 15.3

Thur 10/10: Partial Differential Equations 15.3, Linear Approximations 15.4,

 

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

Thur 10/24: Differentials (15.4), Chain Rule (15. 5)

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

Thur 11/1: Div, Grad, Curl (17.6), Local Max-Min (15.7)

 

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

Thur 11/7: Global Max/ Min (15.7), worksheet, answer key to worksheet.

 

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

Thur 11/14: Review for midterm. Start integration 16.1, 16.2

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

Thur 11/21: Double integrals via polar coordinates (16.4),

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.

Thur 12/5: The Fundamental Theorem of Line Integrals (17.3)

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

Thur 12/12: Not on final exam: Surface Area (16.6), Stokes Theorem (17.8), Divergence Theorem (17.9)