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B.Sc IInd Year (III - semester)
MATHEMATICS
FOR SESSION (2013 - 2014 only)
Paper-I: Advanced Calculus
Maximum Marks: 50 University Exam: 40
Minimum Pass Mark : 35 % Internal Assessment: 10
Time allowed: 3 Hrs.
Lectures to be delivered: 5 periods (of 45 minutes duration) per week
Instructions for paper-setters
The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from the respective sections of the syllabus and Section C will consist of one compulsory question having ten short answer type questions covering the entire syllabus uniformly. All questions will carry equal marks.
Instructions for the candidates
Candidates are required to attempt five questions in all selecting two questions from each section A and B and compulsory question of Section C. All questions will carry equal marks.
SECTION-A
Limit and Continuity of Functions of several variables. Differentiability of real-valued functions of two variables. Partial differentiation, Jacobians and their properties, Schwarz’s & Young’s theorems. Euler’s theorem on homogenous functions. Taylor’s theorem for functions two variables and error estimation. Maxima and Minima, Lagrange’s multiplier method.
SECTION-B
Scalar and vector fields, differentiation of vectors, velocity and acceleration. Vector differential operators: Del, Gradient, Divergence and Curl, their physical interpretations. Formulae involving Del applied to point functions and their products. Line, surface and volume integrals, Greens Theorem in the Plane Parameterized Surface, Stokes Theorem and the Divergence Theorem. Applications of Green’s, Stoke’s and Divergence theorem.
.Recommended books:
1. Mathematical Analysis by Malik and Arora.
2. Mathematical Analysis by Shanti Narayan
B.Sc IInd Year (III - semester)
MATHEMATICS
FOR SESSION (2013 - 2014
MATHEMATICS
FOR SESSION (2013 - 2014 only)
Paper-I: Advanced Calculus
Maximum Marks: 50 University Exam: 40
Minimum Pass Mark : 35 % Internal Assessment: 10
Time allowed: 3 Hrs.
Lectures to be delivered: 5 periods (of 45 minutes duration) per week
Instructions for paper-setters
The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from the respective sections of the syllabus and Section C will consist of one compulsory question having ten short answer type questions covering the entire syllabus uniformly. All questions will carry equal marks.
Instructions for the candidates
Candidates are required to attempt five questions in all selecting two questions from each section A and B and compulsory question of Section C. All questions will carry equal marks.
SECTION-A
Limit and Continuity of Functions of several variables. Differentiability of real-valued functions of two variables. Partial differentiation, Jacobians and their properties, Schwarz’s & Young’s theorems. Euler’s theorem on homogenous functions. Taylor’s theorem for functions two variables and error estimation. Maxima and Minima, Lagrange’s multiplier method.
SECTION-B
Scalar and vector fields, differentiation of vectors, velocity and acceleration. Vector differential operators: Del, Gradient, Divergence and Curl, their physical interpretations. Formulae involving Del applied to point functions and their products. Line, surface and volume integrals, Greens Theorem in the Plane Parameterized Surface, Stokes Theorem and the Divergence Theorem. Applications of Green’s, Stoke’s and Divergence theorem.
.Recommended books:
1. Mathematical Analysis by Malik and Arora.
2. Mathematical Analysis by Shanti Narayan
B.Sc IInd Year (III - semester)
MATHEMATICS
FOR SESSION (2013 - 2014
References: 1. T. M. Apostol, Mathematical Analysis, Norosa Publishing House, New Delhi, 1985. 2. R. R. Goldberg, Real Analysis, Oxford & IBH Publishing Co., New Delhi, 1970. 3. Shanti Narayan 4. R.V. Churchill & J.W. Brown, Complex Variables and Applications, 5th Edition, McGraw Hill, New York, 1990. MATHEMATICS FOR SESSION (2013 - 2014 only)