BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE-PILANI, HYDERABAD CAMPUSFIRST SEMESTER 2013-2014

INSTRUCTION DIVISIONCOURSE HANDOUT (PART-II)

Date: 01.08.2013In addition to part-I (General Handout for all courses appended to the timetable) this portion gives furtherspecific details regarding the course.Course No. : MATH F111Course Title : MATHEMATICS-IInstructor-in-charge : AKHLAD IQBALName of Instructors : Bivudutta Mishra, DK Satpathi, PK Sahoo, K. Venkata Ratnam, ManishKumar, Jagan Mohan Jonnalagadda, Sumit Kumar Vishwakarma, A.K. Kapoor

1. Course Description: Functions and graphs; limit and continuity; applications of derivative and integral.Conics; polar coordinates; convergence of sequences and series. Maclaurin and Taylor Series. PartialDerivatives. Vector Calculus in Rn; 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 alldynamics is modeled through differential & integral equations. Functions of several variables appear morefrequently in Science than functions of a single variable. Their derivatives are more interesting because of thedifferent ways in which the variables can interact. Their integrals occur in several areas such as probability,fluid dynamics, and electricity, just to name a few. All these lead in a natural way to functions of severalvariables. Mathematics of these functions is one of the finest achievements of modern Mathematics.

3. Text Book:Weir, MD, Hass J, Giordano FR: Thomas’ Calculus, Pearson education 11th Ed, 2007.

4. Reference Books:Erwin Kreyszig - Advanced Engineering. Mathematics, 8th Edition Wiley-India, 2007James Stewart – Calculus, 5e, Cengage learning, 2003.Monty J. Strauss, Gerald L. Bradley, & Karl J. Smith – Calculus 3rd Edition, Pearson 2007.

5. Course Plan:

Lect. No. Learning Objectives Topics to be Covered Ref. To text Book:chap/Sec.

1-5 How equations of certain curve aresimpler in polar coordinates

Polar coordinates, Graphing,polar equations of conicsections, Integration

10.5-10.8

6 One variable elementary calculusdefinitions, function, limit &continuity.

Properties of limits, infinity as alimit, continuity.

Chap 2

7-9 How definitions of one variable realvalued functions are related withdefinitions of vector valued functions

Limit, continuity &differentiability of vectorfunctions; arc length, velocity& unit tangent vector

13.1,13.3

10-12 Appreciate difficult concepts ofcurvature. What is curvature of aplane curve?

Curvature, Normal vector,Torsion and Binormal vector,Tangential and normalcomponents of velocity andacceleration.

13.4, 13.5

13,14 How to prove continuity ordiscontinuity or existence of limits isdifferent in several variables.

Functions of several Variables,level curves, Limits, Continuity

14.1,14.2

15-17 Difference between derivativespartial derivatives

Partial derivatives, chain Rule 14.3, 14.4

18,19 Distinguish between all types ofderivatives

Directional derivative, gradientvectors, Tangent planes &normal line

14.5, 14.6

20,21 Actual definition of a localMaximum & Minimum.

Maximum, Minimum & Saddlepoints of Functions of two orthree variables, ConstrainedMaxima and Minima – Methodof Lagrange multipliers

14.7,14.8

22-24 How formula for area in polarcoordinates can be found throughpolar double integral

Double Integrals, Area, Changeof integrals to PolarCoordinates.

15.1, 15.3

25-28 Try to identify which type of Integralevaluates volume of a solid insimplest way

Triple Integral, Integral inCylindrical and Sphericalcoordinates

15.4,15.6,15.7

29-32 Learn equivalent definitions ofconservative field & how Green’stheorem can simplify evaluation ofline integrals.

Line integral, work,circulation, flux, pathindependence, potentialfunction, conservative fields;Green’s theorem in the plane

16.1,16.2,16.3,16.4

33-36 Is Stokes’ theorem analogue ofGreen’s theorem in plane?

Surface area & Surface Integral;Gauss divergence theorem,Stokes’ theorem.

16.5,16.7,16.8

37-40 Study of convergence of infiniteseries with examples & counterexamples

Sequence of real numbersfrequently occurring limits,infinite series different tests ofConvergence, series of nonnegative terms, absolute &conditional convergence,alternating series

11.1-11.611.1,11.2 is for self

study

41-43 Approximating complex functionswith polynomials

Power series, Maclaurinseries, Taylor series offunctions

11.7,11.8

6. Evaluation Scheme:

SlNo.

EvaluationComponent

Duration Weightage Date, Time Nature ofComponent

1. Test I 1 hr. 30% 27.09.2013 (11.00-12.00 P.M.) CB2. Test II 1 hr. 30% 12.11.2013 (11.00-12.00 P.M.) OB3. Comprehensive

Examination3 hrs. 40% 09.12.2013 ( 9.00-12.00 P.M ) CB

7. Make-up Policy: Make-up will be given only for very genuine cases and prior permissionhas to be obtained from I/C.

8. Chamber consultation hour: To be announced in the class by the respective instructors.

9. Notices: The notices concerning this course will be displayed on the LTC Notice Board only.

Instructor-in-chargeMATH F111