1.Sequence, Convergence and Divergence of Infinite series – and typical examples of convergent and
divergent series.
2.Comparison test (statement only) and related problems
3.Ratio test (statement only) and related problems
4.Cauchy’s root test (statement only) and related problems
5.Alternating series, Leibnitz’s theorem (without proof), absolute convergence and related problems.

Calculus of Functions of One Variable:

Review of limit and continuity and differentiability.
Successive differentiation, Leibnitz’s theorem (without proof but with problems of the type of
recurrence relations in derivatives of different orders and also to find (y_{n})_{0} ):

Rolle’s theorem (statement only); Mean Value Theorems—Lagrange & Cauchy (statement only),
Taylor’s theorem (without proof and problems in respect of direct use and applications of the
theorem only), Expansions of functions by Taylor and Maclaurin series. Maclaurin’s expansion in
infinite series of the functions: log (1+x), e^{x} , sinx, cosx, (a+x)^{n} , n being a negative integer or a
fraction L’Hospital’s Rule (statement only) and related problems.Integration of
m, n are positive integers.

Application: Rectification

Three Dimensional Geometry (Cartesian):

Direction Cosine, Direction Ratio; Equation of a Plane (general form, normal form and intercept
form); Equation of a Straight Line passing through one point and two points; Pair of intersecting
planes representing a straight line.

Elementary ideas of surfaces like sphere, Right Circular Cone and Right Circular Cylinder (through
Geometrical configuration) and equations in standard forms.

Calculus of Functions of Several Variables:

Introduction of Function of several variables and examples.
Knowledge of limit and continuity.

Partial derivative & related problems. Homogeneous Functions and Euler’s Theorem (statement
only) & Problems upto 3 variables.Chain rules and related problems.
Differentiation of implicit functions & related problems.
Total differentials and related problems..

Maxima, minima and saddle points – definition, condition of extrema & problems for two variables.
Lagrange’s multiplier method – problems related to two variables only.

Line Integral, Double Integrals, Triple Integral – Discussion w.r.t. different types of limits and
problems; Moment of Inertia, Centre of Gravity.

Jacobian – Definition and related problems for two variables.
Applications to areas and volumes, surface area of revolution.

Calculus of Functions of Several Variables:

Scalar and Vector fields – Definition and Terminologies; Products: dot, cross, box, vector triple
product.

Statements of
Green’s theorem, Divergence theorem, Stokes’ theorem with applications.

Reference Book

1. G.B.Thomas and R.L. Finney, “Calculus and Analytic Geometry”, 6th edition, Addison Wesley /
Narosa, 1985.
2. Piskunov, “Differential and Integral Calculus”, Vol-I & II, Mir Publishers, Moscow, 1979.
3. B.S. Grewal “Engineering Mathematics”, S. Chand & Co., New Delhi.
4. Integral Calculus, Das & Mukherjee
5. An Introduction to Real Analysis- S.K.Mapa
6. Higher Algebra – Lahiri & Roy
7. Higher Algebra, Ghosh & Chakraborty
8. Higher Algebra, Bernard & Child
9. Differential Calculus, Maity & Ghosh
10. Integral Calculus, Maity & Ghosh
11. Engineering Mathematics, Prof.T.Majumdar
12. An Introduction to Analysis, Mallick & Arora
13. Undergraduate Engg Math- Jana, Vikas
14. Engineering Math Vol 1,2,3- Lakshami, Vikas
15. Calculus of One Vairable – Pandey G.S. (New Age International)
16. Differential Calculus – Dhami H.S. (New Age International)
17. Integral Calculus – Dhami H.S. (New Age International)
18. Numerical Methods for Engineers – Gupta S.K. (New Age International)
19. A Textbook of Engg Maths Vol.1 & Vol.2 – Dutta D. (New Age Inter.)
20. Advanced Engg. Mathematics By D.P. Das, Cyber Tech