ENGINEERING MATHEMATENGINEERING MATHEMATENGINEERING MATHEMATENGINEERING MATHEMATICSICSICSICS----I [BSI [BSI [BSI [BS----111]111]111]111]

L T P

3 1 0 [35 Lectures + 10 Tutorials = Approx. 45 hours duration]

1. ALGEBRA (Infinite Series) Convergence and divergence of infinite series, Geometric series test, Positive term series, p-series test, [Comparison test, DAlemberts ratio test, Cauchys root test (Radical test), Integral test, Raabes test, Logarithmic test, Gausss test] (without proofs), Alternating series and Leibnitzs rule, Power series, Radius and interval of convergence. [07 Lectures] 2. DIFFERENTIAL CALCULUS Introduction to limits and Indeterminate forms, Partial Differentiation and its geometrical interpretation, Homogeneous functions, Eulers theorem and its extension, Total differentials, Composite function, Jacobian, Errors and increments, Taylors and Maclaurins infinite series, Curve tracing (Cissiod, Astroid, Cycloid, Folium of Descartes, Cardiod and Equiangular spiral), Maxima and minima of functions of two variables, Method of undetermined multipliers. [09 Lectures] 3. INTEGRAL CALCULUS Quadrature, Rectification, Surface and Volume of revolution for simple curves, Double integrals and their applications, Change of order of integration, Triple integrals and their applications, Change of variables. [08 Lectures] 4. VECTOR CALCULUS Differentiation of vectors, Curves in space, Velocity and acceleration, Relative velocity and acceleration, Scalar and vector point functions, Vector operator del, gradient, divergence and curl with their physical interpretations, Formulae involving gradient, divergence and curl, Line, surface and volume integrals, Theorems of Green, Stokes and Gauss (without proofs) and their verifications and applications, Irrotational and Solenoidal fields. [11 Lectures]

TEXT BOOKS: 1. Advanced Engineering Mathematics: by Erwin Kreyszig. John Wiley and Sons, NC, New York. 2. Advanced Engineering Mathematics: by R. K. Jain & S. R. K Iyengar, Narosa Pub. House.

REFERENCE BOOKS: 1. Advanced Engineering Mathematics: by C. R. Wylie & L. C. Barrett, McGraw Hill 2. Differential & Integral Calculus: by N. Piskunov , MIR Publications.

Next page: Course plan of Engineering Mathematics-I (BS-111)

Course Plan Course Plan Course Plan Course Plan

of of of of

Engineering MathematicsEngineering MathematicsEngineering MathematicsEngineering Mathematics----I I I I

[BS[BS[BS[BS----111]111]111]111] Lecture Number

1. Algebra [Infinite Series]:

1. Introduction Definition of Infinite series, Convergence and divergence of infinite series, Geometric series test (with proof), Definition of positive term series.

2. nth term test, Comparison test and p-series test (with proof). 3. DAlemberts ratio test.

4. Cauchys root test (Radical test) and Cauchys Integral test. 5. Raabes test, Logarithmic test, Gausss test] (without proofs). 6. Definition of Alternating series, Leibnitzs rule (with proof), Absolutely

convergent series, Conditionally convergent series. 7. Power series, Radius and interval of convergence, Convergence of

logarithmic, exponential and Binomial series. 2. Differential Calculus: 8. Partial Differentiation and Partial Differential Coefficient,

Homogeneous Functions, Eulers Theorem and its extension. 9. Total Differentials and Total Differential Coefficient,

Composite Function, Jacobian. 10. Taylors and Maclaurins Infinite Series 11. Errors and approximations 12. Indeterminate forms-I,

Indeterminate forms-II,

13. Indeterminate forms-III

14. Maxima and minima of functions of two variables

15. Lagranges Method of undertermined multipliers

16. Curve tracing (Cissiod, Astroid, Cycloid, Folium of Descartes, Cardiod and Equiangular spiral)

3. Integral Calculus: 17. Single Integral:

Applications: Quadrature for simple curves 18. Applications: Rectification, Surface and Volume of revolution for simple

curves

19. Double Integrals: Where limits are given, Where limits are not given, but region of integration is given.

20. Change of order of integration 21. Evaluation of double integrals in polar co-ordinates

Change of variables (cartesian to polar co-ordinates) 22. Applications:

Area enclosed by plane curves by double integrals Volume by double integrals Volume of solid of revolution (in Cartesian and polar co-ordinates)

23. Triple Integrals: Where limits are given Where limits are not given, but region of integration is given

24. Change of variables (rectangular to spherical polar and cylindrical co-ordinates) Applications: Volume by triple integrals

4. Vector Calculus: 25. Differentiation of vectors, Curves in space 26. Velocity and acceleration, Relative velocity and acceleration 27. Scalar and vector point functions, Vector operator del, gradient, Physical

interpretation of gradient, Directional derivative 28. Del applied to vector function, Divergence and curl, Physical interpretation

of divergence and curl, Irrotational motion, 29. Del applied twice to point function, Del applied to products of point

functions

30. Integration of vectors, Tangential line integral, Circulation, Work 31. Surface Integral, Flux across a surface, Solenoidal vector point function 32. Greens theorem in the plane 33. Stokes theorem 34. Volume integral, Gausss Divergence theorem, Greens theorem and Greens

reciprocal theorem 35. Irrotational fields and Solenoidel fields.

MARKS DISTRIBUTIONMARKS DISTRIBUTIONMARKS DISTRIBUTIONMARKS DISTRIBUTION

1st

Mid-term exam 2nd

Mid-term exam Home assignments,

Class tests, Seminars, Quizzes, Attendance, etc.

End semester exam

Total Marks

15 Marks 15 Marks 20 Marks 50 Marks 100 Marks

TOPICS FOR VARIOUS ETOPICS FOR VARIOUS ETOPICS FOR VARIOUS ETOPICS FOR VARIOUS EXAMINATIONSXAMINATIONSXAMINATIONSXAMINATIONS

1st Mid-term exam 1. Infinite Series 2. Differential Calculus Partial Differentiation Taylors and Maclaurins Infinite Series Errors and approximations

2nd Mid-term exam 3. Differential Calculus Indeterminate forms Maxima and minima Curve tracing 4. Integral Calculus

End semester exam Complete syllabus