Projected Weekly Syllabus

I will add specific information to this syllabus periodically.  You need Mathematica or Mathematica Reader to read this file.

(The brackets on the right side of the page indicate closed Mathematica cells that contain information.)

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:  Position vectors, vector sums as tips-to-tails, displacement vectors, scalar multiples

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

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.

Wed Lect:  Angles & projection

Sect 2.5 Ex 1, 3(b), 4, 5, 6(b), 10(a)

Thu Disc:

Fri Lect: Cross products

Sect 2.6 Ex 2, 3, 5 Sect 2.7 Ex 2

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

Mon Lect: The Geometric-Algebraic Lexicon

Sect. 2.8 Ex.1, 2, 4

Tues Disc:

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

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

Sect 3.3 Ex 1, 2(b), 3(b)

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

Mon Lect: Partial Derivative Computations: Drill & Practice Sect 3.4

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

Three uses for ∇f: the tangent plane equation, directional derivative, and approximation
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: Numerical Approximation with Differentials, Second Partials, & More

Sect 3.3 Ex.3; Sect 3.7 Ex.1; Sect. 6.1 Ex.1

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

Mon Lect: Contour Graphs of Linear Functions

Sect.4.1, Ex. 1(b), (c), 2, 3, 4

Tue Disc: Computer Lab 1245 SC -Contour Tangents

Submit to Bb6 in the form "JonesSLab3.nb"

Wed Lect: The Nonlinear Gradient: Graphs and Measurements

Sect. 4.2, Ex. 1(c), 2(c), 3, 4

Thu Disc:

Fri Lect: The Analytical Gradient

Sect. 4.2, Ex. 5(a), (b), (c), 6, 7

Week #6: Max - min  & Exam #1  23 - 27 Feb
Exam #1 Thurs 26 Feb 7:00 pm - room to be announced
eExam#1 is in the Exercise set of Sect.3.6 on CD and at www.engineering.uiowa.edu/~engmath2/

Mon: Critical points and ∇f = 0

Sect. 7.2, Ex. 1, 2, 3, 4, 5

Tues Disc:

Work homework, discuss Exercise 5.2.8 in class. (more examples in closed cell)

Wed Lect: Review for Exam#1

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

Thu Disc: Review for Exam #1 7:00 pm tonight

Fri Lect: eExam#1 due today - submit to Bb6 in the form JonesSeEx1.nb

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

Tue Disc:

Wed Lect: Integrals over rectangular regions

Sect. 8.2, Ex. 2, 3, 4, 5

Thu Disc:

Fri Lect: Iterated integrals over non-rectangular regions

Sect. 8.3, Ex. 1, 3, 4;

Week #8: More Multiple Integrals 8 - 12 Mar

Mon Lect: Interchanging order of integration

Sect. 8.3, Ex.5, 7;

Tues Disc

Wed Lect: Polar coordinates

Sect. 13.2 Ex. 1, 2, 3, 4, 5

Thu Disc

Fri Lect: Finish Polar coordinates

Enjoy the break

Spring Break

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

Mon Lect: Parametric lines & circles 2D

Sect. 9.1, Ex.1, 2, 3 Sect 9.2, Ex. 1, 5

Tues Disc

Wed Lect: Curves in 3D

Sect. 9.4, Ex. 1, 2, 3, 4

Thu Disc:

Fri Lect: Parametric tangents

Sect. 9.6, Ex. 1, 2, 3, 7

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

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

The lab on plotting parametric curves with Mathematica is due on Blackboard

Wed Lect: Arclength, Curvature & Product Rules

Sect. 9.7, Ex. 1, 2, 4, 5(d)

Thu Disc:

Fri Lect: Velocity, Acceleration, eExam#2

Sect. 10.1, Ex. 1, 2, 3(d), 4(a), 5

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

Mon Lect: Sketching basic fields

Sect 11.1 Ex. 1

Tues Disc

Wed Lect: Flow around and across boundaries

Sect 11.4 Ex. 1, 2, 3

Thu Disc

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

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

Tues Disc

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

Sect. 12.3 Ex.1, 2, 3, 4, 5

Thu Disc

Fri Lect: Applications of divergence and Swirl

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:  eExam#2 due today - submit to Bb6 in the form JonesSeEx2.nb

Wed Lect: Review for Exam#2

Thu Disc: Review for Exam#2  Exam#2 7:00 pm rm ***

Fri Lect: Geometric Series

Sect. 22.1 Ex. 1, 2, 3

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)
Sect. 22.3 Ex. 1, 2, 3, 4

Tues Disc

Wed Lect:  Convergence tests (radius of convergence)

Assign. Sect. 22.4 Ex. 1, 2, 3

Thu Disc

Fri Lect: Differentiation & Integration of Series

Assign. Sect. 22.5 Ex. 1, 2

Week #15: Power Series 3 - 7 May

Mon Lect: Taylor series in general

Ex. 22.5 Ex. 3

Tues Disc: :  eExam#3 Weierstrass' Wild Wiggles due today - submit to Bb6 in the form JonesSeEx3.nb

Wed Lect: Review

Thu Disc: Review

Fri Lect: Review

Final Exam - 9:45 am Mon 10 May 04 - rooms to be announced

NOTE: The University is very strict about the Final Exam schedule.  
I cannot change this time without the permission of the Dean.