Multivariable Calculus for Engineering or Physics
Carleton
University, Mathematics 2004
Updated December 14, 2023
TEXTBOOK: The ABC’s of Calculus, Volume 2, by
Angelo Mingarelli, Nolan Company.
For the 2021 Digital edition of The
ABC’s of Calculus with active
hyperlinks, go to books.mingarelli.com , select
the MULTI
VARIABLE option and order it for 150
continuous days for $95. VISA and Cryptocurrency supported.
Softcover copies are NOW AVAILABLE in HP 4380 for $100
(net/tax in); cash or e-transfer only to thenolanco@gmail.com, no credit cards.
Solutions Manual to go with the above text
can be found at 2021-2022
Solutions Manual
In the following table 1 week represents 2
lectures @1.5 hours, and NOT a full week, as usual.
Week 1
Vectors:
Dot Product, Cross Product, Triple Product; Direction Cosines, Geometry of cross products
Sections 1.1-2-3-4-5-6-7-8-9-10
Suggested
Homework Problems from Exercise Set 1 through Set 9
Week 2
Lines and Planes, Rotations of axes and translations in the plane
Sections
2.1-2-3-4-5-6
Planar curves and their parametric representations;
Conic sections; Sketching parametric curves
Sections 2.7-8
Suggested Homework Problems from Exercise Set
10 all the way to Set
18 (incl.)
Week 3
Applications to Area and Length of curves
Sections 2.9-10
Polar coordinates, Curve sketching in
polar coordinates, Applications
Sections
2.11-12-13-14
Suggested Homework Problems from Exercise Set 19 all
the way to Set 25 (Skip Set 26)
Week 4
Limits, Continuity, Partial Derivatives (Read
over 3.4, p. 184 on Differentiability for information.)
Sections 3.1-2-3
Directional derivatives; Gradients
(Read over MVT in 3.5.2, p. 199 for
information)
Sections
3.5 -
3.5.1
Suggested Homework Problems from Exercise Set 27, Set 29, Set
30
(Skip Set 28)
Week 5 -- Assignment 1
The Chain Rule, Implicit differentiation, Tangent
planes and normal lines
Section
3.6
Conservative fields, Divergence, and Curl.
Section 3.8
Suggested Homework Problems from Exercise Set 31 all the way to Set 36
Week 6 – Test 1
Line Integrals
Sections 4.1-2-3
Double Integral, Iterated integrals
Sections
5.1-2
Suggested Homework Problems from Exercise Set 37 all the way to Set 39
Week 7 (Winter Break NO CLASSES!)
Week 8—Assignment 2
Applications to Volume under a surface,
Section 5.3
Change of variables in double integrals
Section 5.4
Suggested Homework Problems from Exercise Set 40
Week 9
|
Three dimensional
plots and quadric surfaces |
Section
5.5
Parametric equations of a surface
Section
5.6
Suggested Homework Problems from Exercise Set 41
Suggested Homework Problems from Exercise Set 42 and Set 43
|
|
Week 10 – Test 2
Surface integrals and some applications
Sections 6.1-2
Green's Theorem
Section
6.3
Suggested Homework Problems from Exercise Set 44 and Set 45
Week 11
Stokes’ Theorem
Section 6.4
Triple integrals; Change of variables in triple
integrals
Sections 6.5-6
Suggested
Homework Problems from Exercise Set 46
Week 12
Describing solids in cylindrical and spherical
coordinates
Section 6.7
The Divergence Theorem
Section 6.8
Suggested Homework Problems from Exercise Set 47 and Se4948
Week 13
Maxima and minima of functions of two variables,
Lagrange multipliers
Sections 7.2-3
(Skip 7.1)
Problems from Exercise Set 49 and Set 50 and Suggested homework sets from those two.
Classes end, Review
(1 lecture)
EVALUATION
Your final grade will be calculated as:
Tutorial attendance: expected but not graded.
2 tests of 50 minutes at a time TBA by your individual instructors: 15%+15%=30%
2 assignments 2 x 15 = 30%
Final: 40%
Missed tests and assignments will be dealt with at a unique predetermined time before the end of term. Ask your instructor for more details.
Accommodations: In place of a doctor’s note or medical certificate, students will be advised to complete the
self-declaration form available on the Registrar’s Office website to request academic accommodation for missed course
work including exams and assignments. Students will also be encouraged to connect directly with their instructors to discuss required accommodations arising from the COVID-19 situation.
Miscellaneous:
It is important to remember that COVID is still present in Ottawa.
The situation can change at any time and the risks of new variants and
outbreaks are very real. There are a number of actions you can take to lower your risk
and the risk you pose to those around you including being vaccinated, wearing a
mask, staying home when you’re sick, washing your hands and maintaining proper
respiratory and cough etiquette.
Students
with disabilities requiring academic accommodations in this course are
encouraged to contact the Paul Menton Center for
Students with Disabilities (500 University Center: Call 613-520-6608 or email
pmc@carleton.ca)
TUTORIAL CENTRE: Herzberg Building, new wing, 3rd floor.
Course Sharing Websites
"Classroom teaching and learning activities,
including lectures, discussions, presentations, etc., by both instructors and
students, are copy protected and remain the intellectual property of their
respective author(s). All course materials, including PowerPoint presentations,
outlines, and other materials, are also protected by copyright and remain the
intellectual property of their respective author(s). Students registered
in the course may take notes and make copies of course materials for their own
educational use only. Students are not permitted to reproduce
or distribute lecture notes and course materials publicly for commercial or
non-commercial purposes without express written consent from the copyright
holder(s).”
At least
100,000
websurfers served since Jan. 5, 1998
HTML 3.2 Checked!