MATH 5720: Vector
Calculus&Complex Variables
Schedule for Week 14. Quiz
on Thursday, December 7 includes topics and problems from
Sections 16.3, 16.4.
Course Info

Weekly Schedules





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, midterm 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: on Monday, Tuesday and Friday
from 11 pm to 11:50 am , on Thursday from 1 pm to
1:50 pm in Everett Tower 5527, see
detailed schedule here.
Math 5720 meets on Monday, Tuesday,Thursday and Friday
from 9:00 am to 9:50 am at 2202
Dunbar Hall .
Week 15: December 11 
December 15
Week 14: December 4 
December 8
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 7. Problems from Sections
16.3,16.4.
Week 13: November 27  December 1
Topics for
reading
 Section 16.1 Laurent series
 Section 16.2 Singularities
and zeroes of functions
 Section 16.3 Residue Integration Method
 Section 16.4 Evaluation of Real Integrals
Quiz on Friday, : Sections
16.1, 16.2, 16.3.
Week 12: November 20  November 24
Topics
for reading
 Section 15.3 Functions given by power series
 Section 15.4 Taylor and Maclaurin series
 Section 16.1 Laurent series
 Section 16.2 Singularities and zeroes of functions
No classes from Thursday, November 23 to Friday,
November 24 : Thanksgiving.
Week 11: November 13  November 17
Topics for
reading
 Section 15.2 Power Series: Radius of
convergence Tests, properties of power series
 Section 15.3 Functions given by power series
 Section 15.4 Taylor and Maclaurin series
2nd midterm exam on Thursday, November 16 includes all
topics from Chapters 13, 14 and Sections 15.1, 15.2.
Week 10: November 6  November 10
Topics for
reading
 Section 14.3 Cauchy's Integral Formula.
 Section 14.4 Derivatives of Analytic
Functions.
 Section 15.1 Series, Convergence
Tests
 Section 15.2 Power Series, Taylor Series:
Sequences, Series, Convergence Tests.
Quiz on Thursday: Sections 14.314.4,
15.1.
Week 9: October 30 November 3
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 on Friday,
November 3  problems from Sections 13.7 and 14.1, 14.2.
Week 8: October 23  October
27
Topics for
reading
 Section 13.313.4 Derivative. Analytic Function.
CauchyRiemann 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
27: problems from Sections 13.3  13.6.
Week 7: October 16  October 20
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. CauchyRiemann
Equations.
First midterm exam
on Monday, October 16 : Chapters 910. Quiz on Friday, October 20,
Sections 13.1 and 13.2.
Week 6: October 9 October 13
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.
Quiz on Monday, October 9: Sections 10.210.4, quiz on
Thursday, October 12: Sections 10.510.8
Week 5: October 2 
October 6
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 6:
Sections 10.210.5.
Week 4: September 25  September 29
 Sections 10.1 Line Integrals.
 Section 10.2 Line
Integrals
Independent of Path.
 Sections 10.3  10.4 Double Integrals.
Quiz on Friday: Sections 9.8 9.9, 10.1.
Week 3: September
18  September 22
Topics for study and reading:
 Sections
9.5 Curves in mechanics. Velocity and Acceleration.
 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 22 will cover Sections 9.5, 9.7  9.9
Week 2:
September 11  September 15
Topics for study and reading
(Sections 9.29.5) :
 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.
Quiz on Monday, September 11: problems from Sect.9.19.2.
Second quiz on Friday: problems from Sections 9.39.4.
Week 1:
September 5  September 8
Topics for study and reading
:
 Sections 9.1 Vector Algebra on plane and in space.
 Sections 9.293 Inner
product. Vector Product (Cross Product).
Triple
scalar product)
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
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.) 6, 10, 12, 16
Section 15.3 (p.682 9th edit.) 1, 2,
3, 4, 8, 12, 17
Section 15.3 (p.689 10th edit.) 5, 6, 7, 12. 15
Section 15.4 (p.690 9th edit.) 1, 2,
3, , 4, 9, 10, 11, 13, 14, 17
Section 15.4 (p.697 10th edit.) 3, 4, 6, 7, 9 14, 19, 20
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 18 worksheets
(click on the title to download worksheet):
Exams
 First midterm exam : Monday, October
16
 Second midterm exam: Thursday,
November 16
 Final exam (comprehensive) :
Tuesday, December 12, 10:15 a.m. to 12:15 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 welldocumented reason
then arrangements may be made on an individual basis.
Academic Integrity
Students are
responsible for making themselves aware of and understanding the
University policies and procedures that pertain to Academic
Honesty. These policies include cheating, fabrication,
falsification and forgery, multiple submission, plagiarism,
complicity and computer misuse. The academic policies addressing
Student Rights and Responsibilities can be found in the
Undergraduate Catalog at http://catalog.wmich.edu/content.php?catoid=24&navoid=974 and
the Graduate Catalog athttp://catalog.wmich.edu/content.php?catoid=25&navoid=1030. 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) and if you believe you are not responsible, you will
have the opportunity for a hearing. You should consult with your
instructor 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 November 24, 2017.