BSC Mathematic Syllabus || SEMESTER 2 || OFFICIAL SYLLABUS BASED ON [Under Choice Based Credit System]

CBCS PATTERN SYLLABUS
 Semester II 
Mat/ Sem II/ C 3 – Analysis I

 Instruction: - 

Ten questions will be set. Candidates will be required to answer Seven Questions.

 Question no. 1 will be Compulsory consisting of 10 short answer type covering entire syllabus uniformly. Each question will be of 2 marks. Out of remaining 9 questions candidates will be required to answer 6 questions selecting at least one from each group. Each question will be of 10 marks.

 GROUP - A 

Analysis I 

The axiom of least upper bound and greatest lower bound in R. The completeness property of R, Archimedean property, density of rational and irrational numbers in R. Neighbourhoods and limit point of a set, open and closed sets, isolated points, Bolzano – Weierstrass theorem for sets (Statement only). Sequences, bounded sequence, convergent sequence, monotonic sequence, subsequence, Cauchy sequence and Cauchy’s general principle of convergence.                                        5 Questions

 GROUP - B 

Infinite series, Convergence and divergence of infinite series of real numbers, Pringsheim’s theorem, Comparison test, Cauchy’s root test, D’Alembert’s ratio test, Raabe’s test, De-Morgan’s and Bertrand’s test, Gauss’s ratio test, Cauchy’s condensation test, Integral test, Alternating Series, Leibnitz test, Absolute and conditional convergence.         

                                                            4 Questions 

Books Recommended: 

1. Elements of Real Analysis – Shanti Narayan & M D Raisinghania.

 2. Higher Algebra – S Bernard & J M Child

CBCS PATTERN SYLLABUS

 Semester II 
Mat/ Sem II/ C 4 – Integral Calculus and Analytic Geometry 3D

 Instruction: -

 Ten questions will be set. Candidates will be required to answer Seven Questions. 

Question no. 1 will be Compulsory consisting of 10 short answer type covering entire syllabus uniformly. Each question will be of 2 marks. Out of remaining 9 questions candidates will be required to answer 6 questions selecting at least one from each group. Each question will be of          10 marks.

 GROUP - A

 Integral Calculus – Integration of rational and irrational functions. Evaluation of definite integrals, Special integrals, differentiation and integration under the sign of integration (Beta and Gamma functions are excluded), Reduction formula. Point of inflexion, double point, curve tracing. Length of plane curve and area bounded by plane curves. Volume and surface area of solid of revolution.                                                                                                                                                       5 Questions

 GROUP - B

 3D – Rectangular, spherical-polar and cylindrical co-ordinates, Direction cosines. Angle between straight lines, equation of planes and straight lines, shortest distance between the lines. Sphere.                                                                                                                                                4 Questions

 Books Recommended: 

1. Calculus – G B Thomas & R L Finney.

 2. Integral Calculus – Das & Mukherjee.

 3. Integral Calculus – Lalji Prasad.

 4. Coordinate Geometry of 3D – J T Bell

 5. Analytical Geometry of 3D – Lalji Prasad.

 CBCS PATTERN SYLLABUS 
Mat/ Sem II/ GE 2 – MATHEMATICS – II

 Instruction for Generic Elective: -

 Eleven Questions will be set. Candidates will be required to answer Eight Questions.

 Question no. 1 will be Compulsory consisting of 10 short answer type covering entire syllabus uniformly. Each question will be of 3 marks. Out of remaining 10 questions will be required to answer 7 questions selecting at least one from each group. Each question will be of 10 marks.

 GROUP - A

 Differential Calculus II 

Partial Differentiation, Curvature, Asymptotes, Maxima and Minima of functions of two variables.                                                                                                                                    2 Questions 

Integral Calculus II

 Evaluation of definite integrals, reduction formulae, curve tracing, length and area, Surface area and volume of solids of revolution.                                                                                   2 Questions 

GROUP - B 

Vector II 

Gradient, Divergence and curl and second order vector differential operators in Cartesian coordinates systems.                                                                                                         2 Questions

 Co- ordinate geometry of two dimensions II

 Reduction of the general equation of second degree to the standard forms, Chord of Contact, Polar and pair of tangents in reference to general equation of conic, Polar equation.                            2 Questions 

Real Analysis II 

Series: Definition, Convergent Series, Divergent Series, Pringsheim’s theorem, Comparison tests, Cauchy,s root test , D’Alembert’s ratio test, Alternating series and Leibnitz test, Absolutely convergent series.                                                                                                           2 Questions

SEMESTER 3 (SYLLABUS)