MATH 5720: Vector
Calculus&Complex Variables
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 9.5
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 by E.Kreyszig. Publisher: John
Wiley&Sons, 2006
Supplemental text: Schaum's
Outlines of Theory and Problems of Advanced Calculus by R.Wrede and
M.Spiegel.
Publisher: McGrow-Hill, 2002 (good source of problems and solution
manual)
Office
Hours: at Everett Tower 5527, see detailed schedule here. Math 5720meets
on Monday, Wednesday from 4:00 pm to 5:40 am at Rood
Hall
2211.
Week 14: December 04 - December 08
Topics for
reading
- Chapter
16.Applications to Potential Theory: Electrostatic Fields.
- Section 16.3 Heat Problems.
- Section 16.4 Fluid Flow
- Section 16.5 Poisson's Integral Formula
Week
13: November 27 - December 01
Topics for
reading
- Section 16.2 Singularities and zeroes of functions
- Section 16.3 Residue Integration Method
- Section 16.4 Evaluation
of
Real Integrals
- Section 18.1 Applications to Potential Theory: Electrostatic Fields
- Section 18.2 Use of conformal mappings
- Section 18.3 Heat Problems.
Week
12: November 20 - November 24
Topics for
reading
- Chapter 15. Laurent Series, Residue Integration: Laurent
Series.
Singularities and Zeros.
- Chapter 15. Residue Integration Method. Evaluation
of
Real Integrals
2nd mid-term exam on Monday, November 20:
problems from Chapters 13 and 14 and Sections 15.1, 15.2, 15.3 and 15.4.
No classes on Wednesday, November 22 :
Thanksgiving.
Week
11: November 13 - November 17
Topics for
reading
- 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
midtermexam
on Wednesday, November 15, includes all topics from Chapters 13, 14 and
Sections
15.1 - 15.2.
Week
10: November 06 - November 10
Topics for
reading
- Section 14.3 Cauchy's Integral Formula.
- Section 14.4 Derivatives of
Analytic
Functions.
- Section 14.4 Derivatives of
Analytic
Functions.
- Section 15.1 Series, Comvergence
Tests
Quiz
on Wednesday: Sections 14.1-14.4
Week
9: October 30 - November 03
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.
- Section 14.4 Derivatives of
Analytic
Functions.
Quiz on
Wednesday, November 1:
Sections 13.4 -13.7, 14.1.
Week
8: October 23 - October 27
Topics for
reading
- Section 13.2 Powers and Roots.
- 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
Wednesday,
problems from Sections 13.1 - 13.3.
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. Cauchy-Riemann
Equations.
First
midterm exam on October 18.
Week
6: October 09 - October 13
Topics for
reading
- 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
will be on Wednesday, October 11: Sections 10.5
- 10.7. First
midterm exam on October 18.
Week 5: October 02 -
October 06
Topics for
reading
- 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 on
Wednesday,
Sections 10.2-10.4.
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 Wednesday, September 27 : Sections 9.8, 9.9 and 10.1.
Week 3: September 18 -
September 22
Topics for study and reading
(Sections
8.9-8.11, 9.1-9.3 ):
- 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.
Quiz on Wednsday will
cover
Sections 9.5 - 9.7
Week 2:
September 11 - September 15
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.
Quiz on Wednesday:
problems from section 9.1-9.3.
Week 1:
September 5 - September 8
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)
Note that problems marked with
*
are extra.
<>Section 9.1
(p.370):
2, 4, 5, 10, 16, 18, 20, 24, 29, 31, 32, 36, 38 (a), (b), (e)*,
(f)
Section 9.2 (p.376): 2, 4, 6, 20, 22, 24, 25,
27,
28, 32, , 36, 42 (a), (b), (f)
Section 9.3 (p.383): 2, 4, 6, 12, 20, 22, 24
(12) (13), 26,
28,
31, 32, 36, 38
Section 9.4 (p.389): 1, 2, 5, 10, 11, 21, 23
Section 9.5 (p.398): 1, 2, 4, 5, 7, 20,
24, 25, 27, 32, 34
Section 9.6 (p.403): 3, 4, 8, 9, 10
Section 9.7 (p.409): 3, 4, 10, 14, 20, 32, 37, 42
Section 9.8 (p.413): 1, 2, 5,, 8, 13 b,c,d, 15, 18
Section 9.9 (p.416): 1, 2, 3, 5, 7, 11, 16
a,b,c,e.
Section 10.1 (p.425 ): 1, 5, 7, 10, 11, 14
a,17, 19 b
Section 10.2 (p.432 ): 1, 2, 4, 10 a,b,
12, 14, 15, 19
Section 10.3 (p.438): 3, 6, 7, 9, 12
Section 10.4 (p.444 ): 1, 2,3, 6, 7, 11
, 18
Section 10. 5 (p.495 ): 1, 3, 5, 7, 10,
13,
14, 16, 18,
19 24,
Section 10.6 (p.456): 1, 2, 3, 5,
10, 12
Section 10.7 (p.463): 1, 2, 5, 17,
19, 20
Section 10.8 (p.468): 3, 4, 7, 9, 10
Section 10.9 (p.473 ): 1,2, 3, 5, 7, 8
Section 13.1(p.606): 3, 5, 7, 8, 9, 13
, 17
Section 13.2(p.611): 1, 3, 6, 11, 12,
13, 16, 21,
24,
27, 28
Section 13.3(p.617): 1, 2, 5, 6, 7, 8, 10, 13,
20,
21, 26
e
Section 13.4(p.623): 2, 3, 5, 6, 7, 9,
13, 15, 22
Section 13.5(p.626): 1, 3, 4, 6, 10, 16,
18, 20
Section 13.6 (p. 629): 1, 2, 3, 4,
8, 11, 13, 14,
17, 21
Section 13.7 (p.633): 1, 2, 3, 4, 10,
11, 15 , 18, 22, 24, 30(a), (c)
Section 14.1 (p.645) 1, 2, 4, 5, 22, 24, 26
Section 14.2(p.653) 1,2, 3, 4, 5, 12, 15
Section 14.3 (p.657) 1, 4, 5, 6, 7, 8, 9, 10, 15, 16
Section 14.4 (p.661) 1, 3, 4, 5, 9, 11, 12,
Section 15.1 (p.672) 1, 2, 3,4, 8, 9, 16, 20,
17, 19, 21, 20, 22 , 24
Section 15.2 (p.677) , 3, 4, 5, 6, 9,
10,
16, 17, 18
Section 15.3 (p.682) 1, 2, 3, 4, 8, 12,
17
Section 15.4 (p.690) 1, 2, 3, , 4, 9, 10, 11, 13,
14, 17
Section 16.1 (p.707) 1, 3, 5, 8,
12,
13
Section 16.2 (p.711) 3, 5, 8, 10
Section
16.3 2, 4, 10
Section 16.4 1, 4,
9
Maple 10.0 worksheets
(click
on the title to download worksheet):
Exams
- First mid-term exam : October 18
- Second mid-term exam: November 20
- Final exam (comprehensive) :
Monday,
December 11 at 5 - 7 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 policiesinclude 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 November 22 2006.
Schedule for Week 13. 