syllabus spring 2012 - Knowledge

BACHELOR EAI
SYLLABUS SPRING 2012
CODE DU COURS
NOM DU COURS / COURSE NAME
CALCULUS III
MTH2001
Crédits / Credits
EAI Credits 4 / ECTS Credits 8
Face à face / Contact Hours
Travail individuel et/ou de groupe /
Personal &/or Team Work
Evaluation / Evaluation
52.5h
225h
7.5h
Charge de travail / Student workload
Langue d’enseignement / Teaching
Language
English
Pré-requis / Prerequisite
CALCULUS II
Période d’enseignement / Teaching
period
Responsable du cours / Course
Coordinator
Spring 2012 - Wednesday 8:30 am - 11:30 am and Friday 1:00 pm-2:30 pm
Audrey DALMASSO, PhD.
[email protected]
Intervenant(s) / Instructor(s)
Bruno Chastaingt, PhD.
Evaluateur(s) / Evaluator(s)
Bruno Chastaingt
Description du cours / Course
description
This multivariate Calculus course is the last of the Calculus series. This sophomore course is required in
almost all engineering and science majors. It covers cylindrical and spherical coordinates, vectors, functions
of several variables, partial derivatives, multiple integrals and vector integral calculus.
[email protected]
•Connaissances / Knowledge and Understanding (subject specific)
Résultats d’apprentissage / Learning
Outcomes
Three dimensional space; vectors
Vectors, dot products, cross product
Lines, planes, quadric surfaces
Cylindrical and spherical coordinates
Vector valued functions
Motion along a curve, tangent and normal vectors, curvature
Multivariable functions, limits, continuity
Partial derivatives, tangent planes, differentials
Chain rules, directional derivatives, gradients
Maxima and minima, Lagrange multipliers
Double integrals in Cartesian and polar coordinates
Parametric surfaces and surface areas
Triple integrals (Cartesian, cylindrical, spherical coordinates)
Mass, center of gravity, theorem of Papus
Change of variables in multiple integrals, Jacobians
Line integrals, independence of path, Green’s theorem
Cours inscrit dans le process
Assurance of Learning AACSB
No
• Devoir surveillé (DS) / Written examination
Evaluation des étudiants / Student
Assessment
%
45% (3 x 15%)
3 midterm tests
Final exam
30%
• Contrôle continu
Quizzes
15%
BACHELOR EAI
SYLLABUS SPRING 2012
Homeworks
06/01/12
11/01/12
13/01/12
18/01/12
Plan de cours / Course plan
20/01/12
25/01/12
27/01/12
01/02/12
03/02/12
08/02/12
10/02/12
15/02/12
17/02/12
22/02/12
10%
1h30
3h
1h30
3h
1h30
3h
12.1: Rectangular coordinates in 3_space, spheres, cylindrical
surface, 12.2: Vectors. 12.3: Dot product, projections.
12.4: Cross product
12.5: Parametric equations of lines. 12.6: Planes in 3_space.
12.7: Quadric surfaces.
12.8: Cylindrical and spherical coordinates.
13.1: Introduction to vector valued functions.
13.2: Calculus of vector valued functions.
13.2: Calculus of vector valued functions.
13.3: Change of parameter; arc length.
13.4: Unit tangent, normal and binormal vectors.
13.5: Curvature.
1h30
3h
1h30
3h
1h30
3h
1h30
3h
Midterm n°1
13.5: Curvature. 13.6: Motion along a curve.
13.7: Kepler’s law of planetary motion.
14.1: Functions of two or more variables.
14.2: Limits and continuity.
14.3: Partial derivatives.
14.4: Differentiability, differentials and local linearity.
14.5: The chain rule.
14.6: Directional derivatives and gradients.
14.7: Tangent planes and normal vectors.
14.8: Maxima and minima of functions of two variables.
24/02/12
1h30
Midterm n°2
29/02/12
02/03/12
3h
1h30
No Course
No Course
07/03/12
3h
09/03/12
14/03/12
16/03/12
21/03/12
14.9: Lagrange multipliers. 15.1: Double integrals.
1h30
15.2: Double integrals over nonrectangular regions.
3h
15.2: Double integrals over nonrectangular regions.
15.3: Double integrals in polar coordinates.
15.4: Parametric surface, surface area.
15.5: Triple integrals.
15.6: Centroid, center of gravity, theorem of Papus.
1h30
3h
23/03/12
1h30
28/03/12
3h
15.8: Change of variables in multiple integrals, Jacobians.
15.7: Triple integrals in cylindrical and spherical coordinates.
16.1: Vectors fields. 16.2: Line integrals.
16.3: Independence of path; conservative vector fields.
BACHELOR EAI
SYLLABUS SPRING 2012
30/03/012
04/04/12
Midterm n°3
1h30
3h
06/04/012
1h30
16.4: Green’s theorem. 16.5: Surface integrals.
16.6: Applications of surface integrals , flux.
16.7: The divergence theorem. 16.8: Stokes’ theorem.
11/04/012
1h30
16.8: Stokes’ theorem.
Final Exam
Obligatoire pour le module /
Required for the course
Bibliographie / References
Site(s) web / Web sites
Thomas’ Calculus (12th Ed.), George B.
Thomas, Maurice D. Weir, Joel R. Hass
None
None
CAMPUS
SOPHIA
Nombre et
durée des CM
52.5h
Nombre et
durée des TD
Modalités de délivrance du cours
(Par campus si différent)
Optionnelle pour le module /
Recommended references
Autres
(ex : coaching
projets,
distance
learning, etc.)
weekly
Préciser les
spécificités de
programmation
(TD en journée
complète,
cadencement
spécifique des
séances)
CAMPUS
LILLE
CAMPUS
PARIS
CAMPUS
CHINE
CAMPUS US