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7/29/2019 MATH_C191
1/2
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI
INSTRUCTION DIVISION
II SEMESTER 2010-2011
Course Handout (Part II)
Date: 07/01/2011In addition to part-I (General Handout for all courses appended to the time table) this portion gives
further specific details regarding the course.
Course No. : MATH C191
Course Title : Mathematics-I
Instructor-in-charge : DEVENDRA KUMAR
1. Course Description: The course is intended as a basic course in calculus of several variablesand vector analysis. The objective is to give a perspective into the geometry of two and three
dimensions using the knowledge of differentiation and integration. It includes polar coordinates,
convergence of sequences and series, Maclaurin and Taylor series, partial derivatives, vector calculus,
vector analysis, theorems of Green, Gauss and Stokes.
2. Scope and Objective of the Course: Calculus is needed in every branch of science &engineering, as all dynamics is modeled though differential & integral equations. Functions of several
variables appear more frequently in science than functions of single variable. Their derivatives are more
interesting because of the different ways in which the variables can interact. Their integrals occur in
several places as probability, fluid dynamics, electricity, just to name a few. All lead in a natural way to
functions of several variables. Study of these functions is one of finest achievements of Mathematics.
3. Text Book:
M. D. Weir, J. Hass and F. R. Giordano: Thomas Calculus, 11th edition, Pearson
educations, 2008.
4. Course Plan:
Lec. No. Learning Objectives Topics to be Covered Ref. to textBook:Chap/Sec.
1,2,3 The curvilinear coordinate systems like
polar coordinates can be more natural
than Cartesian coordinates many a times.
Polar coordinates, graphing, polar
equations of conic sections,
Integration using polar coordinates.
10.5 to 10.8
4 Review of real valued functions of one
variable.
Properties of limits, infinity as a limit,
continuity.
2.3 to 2.6
5,6,7 Study of vector valued functions of one
variable, motion and its path in space.
Limit continuity & differentiability of
vector function, arc length, velocity
unit tangent vector.
13.1, 13.3
8,9,10 The relation between the dynamics and
geometry of motion.
Curvature, normal vector, torsion and
TNB frame, tangential and normalcomponents of velocity and
acceleration.
13.4, 13.5
11 Motions in other coordinate systems. Polar and cylindrical coordinates. 13.6, p. 964
12,13 Limits and continuity of functions of
several variables is more intricate.
Functions of several variables, level
curves, limits, continuity.
14.1, 14.2
14,15,16 Difference between derivative and
partial derivative.
Partial derivatives, differentiability,
chain rule.
14.3,14.4
17,18 Generalizations of partial derivatives and Directional derivatives, gradient 14.5, 14.6
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their applications. vectors, tangent planes & normal
lines, linearization
19,20 How to optimize (maximize or
minimize) functions of several variables
locally as well as globally.
Maximum, minimum & saddle points
of functions of two or three variables,
Lagrange multipliers.
14.7, 14.8
21,22, 23 Evaluation of area of planar regions and
volumes using iterated integrals.
Double integrals, area, change of
integrals to polar coordinates.
15.1, 15.3
24,25,26 Volumes of solids in space using
suitable curvilinear coordinate system.
Triple integrals, integral in cylindrical
and spherical coordinates, substitution
in integrals.
15.4, 15.6,
15.7
27,28,29,
30
Different integrals of vector fields on
objects in space; applications to flow,
flux, work etc.; their mutual relationship
via Greens theorem generalizing the
fundamental theorem of integral
calculus.
Line integrals, work, circulation,
flux, path independence, potential
function, conservative field, Greens
theorem in plane
16.1,16.2,16.3,
16.4
31-35 Divergence theorem and Stokes
theorem further generalize Greens
theorem.
Surface area & surface integral,
Gauss divergence theorem, Stokes
theorem.
16.5,16.7,16.8
36-40 Differentiate clearly between three typesof series convergence with examples &
counter examples.
Convergence of sequences and seriesof real numbers, different tests of
convergence, series of non negative
terms, absolute & conditional
convergence, alternating series
11.1 to 11.611.1 is for self
study
41-43 Approximating functions with
polynomials.
Power series, Maclaurin series, Taylor
series of functions
11.7, 11.8
5. Evaluation Scheme:EC
No.
Evaluation
Component
Duration Marks Date Time Nature of
Component
1. Test I 50 min 40 3/3 8:00 - 8:50 AM CB
2. Test II 50 min 40 7/4 8:00 - 8:50 AM OB
3. Quiz/assignment 10 min 40 CB
4. Compre. Exam. 3 hrs 80 4/5 AN CB
6. Make-up Policy: Make-up will be given only for very genuine cases and prior permissionhas to be obtained from I/C.
7. Chamber consultation hour: To be announced in the class.
8. Notices: The notices concerning this course will be displayed on the Notice Board of FDIII only.
Instructor-in-charge
MATH C191