University of Madras - Syllabus of Bachelor of Science (BSc) Mathematics - Semester II - Paper II - Calculus and Coordinate Geometry of 2 Dimensions

UNIVERSITY OF MADRAS

B.Sc. DEGREE COURSE IN MATHEMATICS

SEMESTER SYSTEM WITH CREDITS

(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester II - Paper II - Calculus and Coordinate Geometry of 2 Dimensions

Duration of Examination: 3 hrs

Maximum Marks: 100

Credits: 4

Differential Calculus :-

n^{th} derivative; Leibnitz's theorem (without proof) and its applications; Partial differentiations. Total differentials; Jacobians; Maxima and Minima of functions of 2 and 3 independent variables - necessary and sufficient conditions (without proof); Lagrange's method (without proof) - simple problems on these concepts.

Integral Calculus :-

Methods of integration; Properties of definite integrals; Reduction formulae - Simple problems.

Coordinate Geometry :-

Conics - Parabola, ellipse, hyperbola and rectangular hyperbola - pole, polar, co-normal points, con-cyclic points, conjugate diameters, asymptotes and conjugate hyperbola.

Reference Books :-

1. Analytical Geometry: T. K. Manickavachagam Pillai and others (S. Viswanathan Publications)

2. Analytical Geometry of 2 dimensions: P. Duraipandian

3. Coordinate Geometry: Dr. P. Balasubramanian and others (McGraw Hill publishers)

4. Calculus: S. Narayanan and others (S. Viswanathan Publications)

5. Integral Calculus: Shanti Narayanan (S. Chand and Co.)

6. Integral Calculus and Differential Equations: Dipak Chatterji (TATA McGraw Hill publishing company)

7. Calculus: Dr. S. Sudha (Emerald Publishers).