MATH 5720: Vector
Calculus&Complex Variables
Schedule for Week
14.
Quiz
on
Thursday, December 8. Problems from Sections 16.3,16.4, 18.1,
18.2.
Course
Info
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Weekly Schedules
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Course
description: This course includes most of the
standard material
for vector calculus and complex analysis. We'll use a
computer algebra
system Maple 13 in this course for some
computer
projects. You can find a list of topics here.
It is expected that you will work most of the basic
exercises at the
end of each section. A list of additional problems to work
will be
placed at the course webpage (see homework
problems).
It
is recommended to write down solutions of these
problems and
keep your homework to use in preparation for quizzes,
mid-term
and final exams. Every week we'll have a quiz containing two
or three
problems analogous to ones solved in class and from
homework. If you
have any questions about problems, please ask them in class
or
during office hours.
Textbook:
Advanced Engineering Mathematics (10th edition)
by
E.Kreyszig. Publisher: John Wiley&Sons, 2011
Supplemental text: Schaum’s
outline
of theory and problems of vector analysis and Schaum's
Outline
of
Complex Variables, 2ed by M.Spiegel.
(good source of problems and solution manual). I
Office
Hours: Monday,Tuesday and
Friday 10:30-11:30:50 a.m., Thursday: 10:00-10:50 at Everett Tower 5527, see
detailed schedule here. Math 5720
meets on Monday, Tuesday,
Thursday and Friday from 12:00 p.m. to 12:50
p.m. at
03217 Sangren Hall .
Week 15: December 12 -
December 16
Week 14: December 5 -
December
9
Topics for
reading
- Chapter
18.Applications to Potential Theory: Electrostatic Fields.
- Section 18.2 Use of
conformal mappings
- Section 18.3 Heat Problems.
- Section 18.4 Fluid Flow
- Section 18.5 Poisson's Integral Formula
Quiz
on
Thursday, December 8. Problems from Sections 16.3,16.4, 18.1,
18.2.
Week
13:
November 28 - December 2
Topics for
reading
- Section 16.2 Singularities and zeroes of functions
- Section 16.3 Residue Integration Method
- Section 16.4 Evaluation of Real Integrals
Quiz on Tuesday,
November 29: Sections 15.3, 15.4. Quiz on Friday, December
2: problems
from Sections 16.1, 16.2, 16.3 and 16.4.
Week
12:
November 21 - November 25
Topics for
reading
- Chapter 15. Laurent Series, Residue Integration: Laurent
Series. Singularities and Zeros.
- Chapter 15. Residue Integration Method.
Evaluation
of Real Integrals
No classes ofrom Wednesday, November 23 to Friday,
November 25 : Thanksgiving.
Week
11:
November 14 - November 18
Topics for
reading
- Section 15.1 Series, Comvergence
Tests
- Section 15.2 Power Series, Taylor Series:
Sequences, Series, Convergence Tests.
- Section 15.3 Functions given by power series
- Section 15.4 Taylor and Maclaurin series
- Section 16.1 Laurent series
2nd
midterm
exam on Thursday, November 17, includes all topics from
Chapters 13, 14 and Section 15.1.
Week
10:
November 7 - November 11
Topics for
reading
- Section 14.3 Cauchy's Integral Formula.
- Section 14.4 Derivatives of Analytic
Functions.
- Section 15.1 Series, Comvergence
Tests
Quiz
on
Friday: Sections 14.3-14.4, 15.1.
Week
9:
October 31 - November 4
Topics for
reading
- Section 14.1 Complex Integration: Line Integral in the
Complex Plane.
- Section 14.2 Cauchy's Integral Theorem
- Section 14.3 Cauchy's Integral Formula.
Quiz on Friday,
November 4 - problems from Sections 13.7 and 14.1, 14.2.
Week
8: October 24 - October 28
Topics for
reading
- Section 13.3-13.4 Derivative. Analytic Function.
Cauchy-Riemann
Equations. Laplace's Equation.
- Section 13.5 Exponential Function.
- Section 13.6 Trigonometric Functions, Hyperbolic
Functions.
- Section 13.7 Logarithm. General Power.
Quiz on
Friday,
October 28: problems from Sections 13.3 - 13.6.
Week
7:
October 17 - October 21
Topics for
reading
- Section 13.1 Complex Numbers. Complex Plane. Polar
Form of
Complex numbers.
- Section 13.2 Powers and Roots. Derivative.
- Section 13.3 Analytic Functions. Cauchy-Riemann
Equations.
Quiz
on
Friday , October 21, Sections 13.1 and 13.2.
Week
6:
October 10 - October 14
Topics for
reading
- Sections 10.5 - 10.6 Surface Integrals.
- Section 10.7 Triple Integrals. Divergence
Theorem
of Gauss.
- Section 10.8 Applications of the Divergence
Theorem.
- Section 10.9 Stokes
theorem.
This
Monday,
October 10, we'll meet in Computer Lab (Large
PC
Lab, 3396 Rood Hall) for Maple
computer project.
First
midterm exam on Thursday, October 13 :
Chapters
9-10. .
No
quiz
on Friday.
Week 5: October 3 -
October 7
Topics for
reading
- Section 10.4 Green's Theorem in the Plane.
- Sections 10.5 - 10.6 Surfaces for Surface Integrals.
Surface Integrals.
- Section 10.7 Triple Integrals. Divergence Theorem of
Gauss.
Quiz will be on Friday, October 7:
Sections 10.3
-
10.6.
Week 4: September 26 - September 30
- Sections 10.1 Line Integrals.
- Section 10.2 Line
Integrals
Independent of Path.
- Sections 10.3 - 10.4 Double Integrals.
Quiz
on
Friday, September 30 : Sections 10.1, 10.2 and
10.3.
Week 3: September
19 -
September 23
Topics for study and reading:
- Section 9.7 Gradient of a
Scalar
Field. Directional Derivative.
- Section 9.8 Divergence
of
a
Vector
Field.
- Section 9.9 Curl
of
Vector
Field.
- Sections 10.1 Line Integrals.
Quiz on Friday,
September 23 will cover Sections 9.7 - 9.9
Week 2:
September 12 - September 16
Topics for study and reading
(Sections 9.2-9.5) :
- Sections 9. 2 - 9.3
Inner (Dot) Product and Vector (Cross) Product.
- Section 9.4 Vector and
Scalar
Functions and Fields. Derivatives. Curves. Tangents. Arc
Length.
- Sections 9.5 Curves in
mechanics.
Velocity and Acceleration.
- Section 9.7 Gradient of a
Scalar
Field. Directional Derivative.
Quiz on Friday,
September
16: problems from Sect.9.3-9.6.
Week 1:
September 6 - September 9
Topics for study and reading
:
- Sections 9.1 Vector Algebra on plane and in space.
- Sections 9.2-93 Inner
produact. Vector Product (Cross Product).
Triple
scalar product)
Quiz on Friday, September 9: problems from Sect.9.1-9.3.
Note that problems marked with
* are extra.
Section 9.1 (p.370 9th edit., p.360 10th edit.):
2,
4, 5, 7, 14, 16, 18, 24, 25, 28, 31, 34, 36, 38 (a),
(b),
(e)*, (f)
Section 9.2 (p.376 9th edit., p.367 10th edit.):
2, 4,
6, 20, 25, 27, 28, 30, 32, , 34, 36, 42 (a), (b),
(f)
Section 9.3 (p.383 9th edit.): 2, 4, 6, 12, 20,
22, 24
(12) (13), 26, 28, 31, 32, 36, 38
Section 9.3
(p.374 10th edit.): 4, 11, 13, 16, 24 (13), 25, 27,
29,
32
Section 9.4 (p.389 9th edit.):
1,
2, 5, 10, 11, 21, 23
Section 9.4 (p.380 10th edit.):
1, 2, 5, 9, 11, 22,23
Section 9.5 (p.398 9th edit.):
1,
2, 4, 5, 7, 20, 24, 25, 27,
32, 34
Section 9.5 (p.390 10th edit.):
2,
5, , 11, 12, 13, 16, 25, 28, 35, 36
Section 9.6 (p.403 9th edit.):
3,
4, 8, 9, 10
Section 9.7 (p.409 9th edit.):
3,
4, 10, 14, 20, 32, 37, 42
Section 9.7 (p.402 10th edit.):
2,
3, 7, 8, 9, 13, 15, 24
Section 9.8 (p.413 9th edit.):
1,
2, 5, 8, 13 b,c,d, 15, 18
Section 9.8 (p.405 10th edit.):
1,
2, 3, 5, 9, 17
Section 9.9 (p.416 9th edit.):
1,
2, 3, 5, 7, 11, 16 a,b,c,e.
Section 9.9 (p.408 10th edit.):
4,
8, 9, 13, 14, 17
Section 10.1 (p.425 9th edit.
):
1, 5, 7, 10, 11, 14 a,17, 19 b
Section 10.1 (p.418 10th edit.):
2, 4, 5, 12(b), 13, 15
Section 10.2 (p.432 9th edit.
):
1, 2, 4, 10 a,b, 12, 14, 15, 19
Section
10.2
(p.425 10th edit.):
3, 4, 6, 10 (a),(b), 13, 18
Section 10.3 (p.438 9th edit.):
3,
6, 7, 9, 12
Section 10.3 (p.432 10th edit.):
3,
4, 8. 9
Section 10.4 (p.444 9th edit.): 1, 2, 3, 6, 7, 11 ,
18
Section 10.4 (p.438 10th edit.):
1,
3, 5, 6, 9, 18
Section 10. 5 (p.495 9th edit.): 1, 3, 5, 7, 10, 13, 14, 16,
18, 19 24
Section 10.5 (p.442 10th edit.):
1, 3, 5, 7, 14, 15, 19
Section 10.6 (p.456 9th edit.): 1, 2, 3, 5, 10, 12
Section 10.6 (p.450 10th edit.):
1, 2, 4, 6, 10
Section 10.7 (p.463 9th edit.): 1, 2, 5, 17, 19, 20
Section 10.7 (p.457 10th edit.):
1, 2, 6, 9, 12, 13
Section 10.8 (p.468 9th edit.): 3, 4, 7, 9, 10
Section 10.8 (p.462 10th edit.):
3, 4, 10, 12
Section 10.9 (p.473 9th edit. ): 1,2, 3, 5, 7, 8
Section 10.9 (p.468 10th edit.):
1, 2, 4, 6, 8
Section 13.1(p.606 9th edit.):
3,
5, 7, 8, 9, 13 , 17
Section 13.1(p.612 10th edit.):
1, 3, 4, 5, 7, 8, 14
Section 13.2(p.611 9th edit.):
1,
3, 6, 11, 12, 13, 16, 21, 24, 27, 28
Section 13.2(p.618 10th edit.):
1, 2, 3, 5, 7, 12, 13, 16, 22, 27, 29, 34
Section 13.3(p.617 9th edit.):
1,
2, 5, 6, 7, 8, 10, 13, 20, 21, 26 e
Section 13.3(p.624 10th edit.):
1, 3, 4, 6, 14, 16, 21, 24
Section 13.4(p.623 9th edit.):
2,
3, 5, 6, 7, 9, 13,
15,
22
Section 13.4(p.629 10th edit.):
2, 3, 6, 12, 15, 23, 29
Section 13.5(p.626 9th edit.):
1,
3, 4, 6, 10, 16, 18, 20
Section 13.5(p.632 10th edit.): 2
, 6, 8, 9, 15, 18 (a),
22
Section 13.6 (p. 629 9th edit.):
1,
2, 3, 4, 8, 11, 13, 14, 17, 21
Section 13.6(p.636 10th edit.):
1, 2, 6, 8, 12, 16, 18, 19
Section 13.7 (p.633 9th edit.):
1,
2, 3, 4, 10, 11, 15 , 18, 22, 24, 30(a), (c)
Section 13.7(p.640 10th edit.):
3,
5, 6, 8, 13, 14, 15, 18, 22, 23, 30(a), (d)
Section 14.1 (p.645 9th edit.) 1, 2, 4, 5, 22, 24, 26
Section 14.1 (p.651 10th edit.) :
2, 3, 6, 8, 13, 14, 21, 23, 24, 26
Section 14.2(p.653 9th edit.) 1,2, 3, 4, 5, 12, 15
Section 14.2 (p.659 10th edit.) :
9, 12, 15, 21, 22, 23
Section 14.3 (p.657 9th edit.) 1, 4, 5, 6, 7, 8, 9, 10, 15, 16
Section 14.3(p.663 10th edit.) :
1, 4, 12, 13, 16, 17, 18
Section 14.4 (p.661 9th edit.) 1, 3, 4, 5, 9, 11, 12,
Section 14.4 (p.667 10th edit.) :
1, 2, 4, 7, 10, 11, 17
Section 15.1
(p.672 9th edit.)
1,
2, 3,4, 8, 9, 16, 20, 17, 19, 21, 20, 22 , 24
Section 15.1 (p.679 10th edit.)
, 2, 3, 4, 8, 16,
18,
19, 21, 22, 24
Section 15.2 (p.677 9th edit.)
,
3, 4, 5, 6, 9, 10, 16, 17, 18
Section 15.2 (p.684 10th edit.)
Section 15.3 (p.682 9th edit.)
1,
2, 3, 4, 8, 12, 17
Section 15.3 (p.689 10th edit.)
Section 15.4 (p.690 9th edit.)
1,
2, 3, , 4, 9, 10, 11, 13, 14, 17
Section 15.4 (p.697 10th edit.)
Section 16.1 (p.707 9th edit.)
1, 3, 5, 8, 12, 13
Section 16.1 (p.714 10th edit.)
1, 3, 5, 9, 12, 20, 22
Section 16.2 (p.711 9th edit.)
3, 5, 8, 10
Section 16.2 (p.719 10th edit.)
1, 4, 3, 14, 19
Section
16.3 (
9th edit) 2, 4, 10
Section 16.3 (p.725 10th edit.)
4, 5, 9, 14, 17, 20
Section 16.4 ( 9th edit) 1, 4,
9
Section 16.4 (p.697 10th edit.)
1, 3, 5, 10, 14, 18, 22
Maple 15.0
worksheets
(click on the title to download worksheet):
Exams
- First mid-term exam : Friday, October
14
- Second mid-term exam: Thursday,
November
17
- Final exam (comprehensive) :
Tuesday, December 13 at 2:45 p.m. - 4:45 p.m.
Grades and
Makeup
Policy
Grades will be assigned using a
sliding
scale. The usual passing level "C" is between 65% and 68%. Someone
with
88% may get "A". After each test we'll get an approximate passing
level. Do not panic if your grade seems low, come and talk with
me about your perfomance.Various numbers below
determine the relative weights of exams' and quizzes'
grades: Total number of points 500. The final exam - 200 points.
Each
midterm exam - 100 points, quizzes grade - 100.
In general, there will be NO
makeups
for exams. If you miss an exam for a valid well-documented
reason then
arrangements may be made on an individual basis.
Academic Integrity
You are
responsible for making yourself aware of and understanding the
policies
and procedures in the Graduate Catalog (pp. 26-28) that pertain to
Academic Integrity. These policies include cheating, fabrication,
falsification and forgery, multiple submission, plagiarism,
complicity
and computer misuse. If there is reason to believe you have been
involved in academic dishonesty, you will be referred to the
Office of
Student Conduct. You will be given the opportunity to review the
charge(s). If you believe you are not responsible, you will have
the
opportunity for a hearing. You should consult with me if you are
uncertain about an issue of academic honesty prior to the
submission of
an assignment or test.
Comments,
questions, problems to ledyaev@wmich.edu
.
Last modified December 2, 2011.
