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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