Actual Weekly Syllabus

I will add specific information to this syllabus as we proceed.

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(The brackets on the right side of the page indicate closed Mathematica cells.  To open and read these cells, double-click on the bracket.)

Week #1: Graphs of  z = f[x, y]  20 - 23 Jan

Mon: U Holiday - no class

Assignment: Buy the text at Zephyr Copies

Tues Disc: Explicit, implicit and parametric  specifications of graphs

Text cells after discussion days contain suggestions for that class, not assigned homework.
Work in class on Section 1.1 Exercises 1(b), 2(b), 3(b); 
Section 1.2 Exercises 1(b), 2(b), 3(b);  Section 1.3 Exercises 1(b), 2(b)

Wed Lect: More on explicit, implicit and parametric specifications of graphs, and TANGENT LINES.

The ASSIGNED homework appears in the text cell following a Lecture.  Due after one discussion section

Section 1.4 Exercises 1 (b), (d), (f); 2(b), (d), (f); 3(b), (d), (i);  (ASSIGNMENT DUE Tues. Jan 27 )

Thu Disc:  Practice with tangent lines to implicitly specified graphs, and discuss  section 1.4

Fri Lect: Contour graphs of simple functions & plots with Mathematica

Homework for Thurs, Jan 29:
A:  Do the three exercises under NOTE 3 in Professor Goodman's Notes on Chapter 1 (available on his course web page).
B:  Section 1.6 Ex., 2(b), 3 (a), (b)  4 (g)

Week #2: Basic Vector Geometry 26 - 30 Jan

Mon  Lect:  Finish material on 3D plots of  functions z = f[x, y].   Numerical and geometric vectors, vector addition and multiplication by scalars.   Length of vectors.  (Sections 2.1-2.4)

No new homework

Tue Disc: Meet in Computer Lab 1245 SC -  3D Plots

In Computer Lab: Work step-by-step the Mathematica Primer, 00MathPrimer.nb  eHomework: Work through the Lab NoteBook 01Math3DPlot.nb (same as text section 1.7). Nothing to eSubmit this time.

It is also useful to work through the first several of Professor Goodman's Mathematica tutorials, available on the course web page.

Wed Lect:   Dot product, angles, and projections (section 2.5)
Homework due Tuesday, Feb. 3:  
Sect. 2.1 Ex. 1(vect B), 2(vect B), 3(b); Sect. 2.2 Ex. 1(A+B), 2(A+B);
Sect. 2.3 Ex. 1(AtoB), 2(AtoB), 3; Sect. 2.4 Ex. 1, 2, 3(vects A & B from1&2), 4
Sect 2.5 Ex 1, 3(b), 4, 5, 6(b), 10(a)

Thu Disc:

Fri Lect:  Dot products, angles, and projections.   Cross products

Week #3: Limits & Partial Derivatives  2 - 6 Feb

Mon Lect: The Geometric-Algebraic Lexicon

Due Tuesday, Feb. 10:  Sect. 2.8 Ex.1, 2, 4

Tues Disc:

Weds Lect: Explicit Linear Functions, Graphs & Axis-slopes

Due Tuesday, Feb. 10:  Sect 3.1 Ex 1, 2, 3, 6, 8

Thu Disc

T.A.s: Review finding tangent lines in 1 variable, see the closed eTopic in Sect 3.3:
Slope of  y = f[x]  at  x = (Subscript[x, 0]), microscopic tangency in one variable

Fri Lect: Local Linear Approximation, Partial and Total Differentiation

Due Thursday Feb. 12:  Sect 3.3 Ex 1, 2(b), 3(b)

Week #4: Total Derivatives and Tangent Planes, Directional Derivatives  9 - 13 Feb

Mon Lect:  Review of the idea of linear approximation of curves and surfaces.  The rate of change of a linear function of two variables.  The tangent plane to the graph of a non-linear function of two variables and the tangent plane approximation.

Section 3.4 Exercises will not be collected, but we will have skill quizzes in discussion sections.
You can use Mathematica to check your differentiation skills.

Tue Disc: Computer Lab 1245 SC -Tangents & D[z,x], D[z,y]

Sally Jones should eSubmit a NoteBook to BalckBoard6 named "JonesSLab2.nb"
Make sure you submit to the course "Digital Dropbox" (not your personal one.)

Wed Lect: Directional Derivatives.  The famous watermelon demonstration, and the definition of directional derivatives.  Computation of directional derivatives via the formula (Subscript[D, U]) f((Subscript[x, 0]), 
            (Subscript[y, 0])) = ∇f((Subscript[x, 0]), (Subscript[y, 0])) · U.    Computation of partial derivatives using rules for differentiation:  product rule, chain rule, etc.

Due Tuesday, Feb. 17:  Assignment: Sect 3.5 Ex 1(b), 2(b), 3(b), 4, 5(b)

Thu Disc:

Work partial differentiations carefully step-by-step for the homework problems.  Carefully explain use of the product rule and chain rule.  Write them out carefully.  See Section 3.4.

Fri Lect:  Summary of the week and examples:  Three uses for ∇f: the tangent plane equation, directional derivative, and approximation.

Due Thursday, Feb. 19:  Sect 3.3 Ex.3; Sect 3.7 Ex.1

Week #5: Gradients & Level Sets in 2D  16 - 20 Feb

Mon Lect: Example of tangent plane, directional derivative, and approximate change along the tangent plane.  Error propogation.  Contour Graphs of Linear Functions.   Start on contour graphs of non-linear functions

Sect.4.1, Ex. 1(b), (c), 2, 3, 4  Due Tuesday, Feb. 24.

Tue Disc: Computer Lab 1245 SC -Contour Tangents

Submit to Bb6 in the form "JonesSLab3.nb"

Wed Lect:  Contour graphs and level curves of non-linear functions.  The role of the gradient.

Sect. 4.2, Ex. 1(c), 2(c), 3, 4.   Due Thursday, Feb. 26

Thu Disc:  emphasize various meanings and uses of the gradient.

Fri Lect:  Implicit function theorems.   Smoothness of functions of several variables.  Implicit function theorem in 3 variables:  implicitly defined smooth surfaces and their tangent planes.

Sect. 4.2, Ex. 5(a), (b), (c), 6, 7  Sect. 4.5, Ex. 1, 2.  Due Thursday, Feb. 26

Week #7: Multiple Integrals in Cartesian Coordinates 1 - 5 Mar

Mon Lect:  Riemann sums over 2D regions,

Sect. 8.1 Ex.1, Sect. 8.2 Ex.1 ; Due on Thursday, March 4

Tue Disc:   Max-Min exercises.   Review of techniques of integration (finding anti-derivatives).

Wed Lect: Integrals over rectangular regions and non-rectangular regions

Thu Disc:  Double and iterated integrals.

Fri Lect: More examples of iterated integrals over non-rectangular regions

Sect. 8.2, Ex. 2, 3, 4, 5;   Sect. 8.3, Ex. 1, 3, 4  Due Thursday, March 11.

Week #8: More Multiple Integrals 8 - 12 Mar

Mon Lect: Interchanging order of integration

Sect. 8.3, Ex.5, 7;  Due Thursday after spring break.

Tues Disc

Wed Lect: Polar coordinates; CM of a semi-circular wedge.

Sect. 13.2 Ex. 1, 2, 3, 4, 5,  Due Thursday after spring break.

Thu Disc

Fri Lect: Finish Polar coordinates.

Enjoy the break next week.

Week #9: Parametric Curves in Space and Triple integrals  22 - 26 Mar

Mon Lect: Parametric lines & circles 2D and Curves in 3D

Sect. 9.1, Ex.1, 2, 3 Sect 9.2, Ex. 1, 5, Sect. 9.4, Ex. 1, 2, 3, 4; Due Tuesday, March 30.

Tues Disc; Work on parametric curves.

Wed Lect: Parametric tangents

Sect. 9.6, Ex. 1, 2, 3, 7; Due Thursday,  April 1

Thu Disc:

Fri Lect:  Triple integrals

Week #10: Motion on Curves, Tangential and Normal Acceleration 29 Mar - 2 Apr

Mon Lect: The Chain Rule & Parametrization

Sect. 9.6 Ex. 4, 5, 6, Due Tuesday April 6.

Tue Disc: Meet in Computer Lab 1245 SC -  3D Motion

The lab on plotting parametric curves with Mathematica is due on Blackboard,  due Tuesday, April 6.

Wed Lect: Arclength, Curvature & Product Rules

Sect. 9.7, Ex. 1, 2, 4, 5(d), Due Thursday, April 8.

Thu Disc:

Fri Lect: Velocity, Acceleration;  tangential acceleration and normal acceleration.

Sect. 10.1, Ex. 1, 2, 3(d), 4(a), 5,  Due Thursday, April 8.
eExam#2,  Due Thursday, April 15.

Week #11: Vector Fields in 2D 5 - 9 Apr

Mon Lect:  Finish section 9.7 and Introduction to vector fields.

Sect 11.1 Ex. 1; Due Thursday April 15.

Tues Disc

Wed Lect: Gradient vector fields;   Flow around and across boundaries

Sect 11.4 Ex. 1, 2, 3; Due Thursday April 15.

Thu Disc  Work on path integrals of vector fields of two types.

Discuss Ex. 11.4.3, work some parametric path integrals.

Fri Lect: The chain rule, potential functions & independence of path

Sect 11.5 Ex. 1, 2, 3, 4;  Due Thursday April 15.

Week #12: Green's theorem 12 - 16 Apr

Mon Lect: Green's Theorems for Flow around and across

Sect 12.1 Ex. 1, 2, 3, 4  Due Tuesday, April 20

Tues Disc  Examples of Green's theorems.

Wed Lect: The "curl" test for a conservative vector field

Sect. 12.3 Ex.1, 2, 3, 4, 5  Due Tuesday, April 20

Thu Disc  Examples of "swirl" test.

Fri Lect: Applications of divergence and curl.  
Dubya   is not conservative.

Week #13: Exam #2 & Geometric  Series 19 - 22 Apr
Exam #2 Thu 22 Apr  7:00 pm

Mon Lect: Review for Exam#2

Review exams are on your CD and at www.engineering.uiowa.edu/~engmath2/

Tue Disc:

Wed Lect: Review for Exam#2

Thu Disc: Review for Exam#2  Exam#2 7:00 pm room 100 PH

Fri Lect: Geometric Series

Sect. 22.1 Ex. 1, 2, 3  Due Thursday April 29.

Week #14:  Series Approximation 26 - 30 Apr

Mon Lect: Weierstrass' test & the classic series (Exp, Sin, Cos, Log, ArcTan)

eExam#3 = 
Sect. 22.2 Ex. 3 Zooming on Weierstrass Wild Wiggles, (due electronically on Blackboard by Thursday May 6).

Sect. 22.3 Ex. 1, 2, 3, 4 due Thursday May 6

Tues Disc

Wed Lect:  Convergence tests (radius of convergence)

Assign. Sect. 22.4 Ex. 1, 2, 3 due Thursday May 6

Thu Disc

Fri Lect: Differentiation & Integration of Series

Assign. Sect. 22.5 Ex. 1, 2  due Thursday May 6