GOUR MOHAN SACHIN MANDAL MAHAVIDYALAYA

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1 1 2 GOUR MOHAN SACHIN MANDAL MAHAVIDYALAYA Department : MathematicsYear: 1 st year Session: Teacher Name : alaram Paria Analytical Geometry I-Module II Transformation of Rectangular axes. General July 06 of 2D equation of second degree. Pair of straight lines. Analytical Geometry of 2D I-Module II Pair of straight lines. Polar equation. August 06 Analytical Geometry of 2D I-Module II Conic Sections. Pair of tangents. Poles and Polars. September 06 Analytical Geometry of 2D I-Module II Tutorial / Revision September 05 Analytical Geometry of 2D I-Module II Rectangular Cartesian Co-ordinates in 3D Space. November 10 Equation of Planes. Analytical Geometry of 2D I-Module II Straight lines in 3D Space. December 10 Vector Algebra I-Module II Addition, Multiplication by Scalar. Vector Product. January 10 Application of Vector Algebra. Vector Equations. Vector Algebra I-Module II Tutorial/ Revision February 10 3 Teacher Name : Chanchal Mondal 4 Analysis I Real Numbers System July 10 Analysis I Sets in Real Numbers August 10 Analysis I Sequence of real numbers September 10 Evaluation of Integrals Evaluation of integrals November 10 Analysis I Countability of sets December 08 Analysis I Analysis I 5 Continuity of real valued functions of a real variable, January 10 Tutorial. Uniform continuity February 10 Teacher Name : Subhasis Kundu Linear Algebra I-Module IV Inner Product of Vector Space. July 08 Linear Algebra I-ModuleIIV Determinants August 08 Linear Algebra I- Matrices of real & complex numbers. Elementary Operations on Matrices Statement and applications. September 08

2 Linear Algebra Linear Algebra Vector Calculus I Vector Calculus I 6 ModuleIIVGroup- A I-Module VI I-Module IV I-Module IV I-Module IV Echelon matrix. Rank of a matrix. Vector space definitions and examples, subspace and their union, intersection and linear sum. Linear combination independence and dependence. November 10 linear span, basis, Replacement theorem,extension theorem, Dimension of vector space,extration of basis, Linear homogeneous system of equation and their solutions. Eigen vector of matrices. Clay Hamilton Theorem and examples. Congruence of matrices December 05 Vector differentiation with respect to a scalar variable, velocity, acceleration, direction derivative, Divergence, Curl, Gradiant, Laplacian and their physical significance. January 10 Tutorial/Revision February 5 Teacher Name : alaram Paria Classical Algebra I-Module I Complex numbers, Inequalities, Polynomials with real July 10 coefficient. Classical Algebra I-Module I Polynomial equations August 05 Classical Algebra I-Module I Statement of well ordering principle, prime intergers, Euclid s First Theorem. September 08 Classical Algebra 7 I-Module I Ecluid s Second Theorem, Chinees remainder Theorem, Fermat s Theorem, Phi n. January 08 Teacher Name : Subhsis Kundu Modern Algebra I-Module I Set, Mapping,Algebric Structure July 10 Modern Algebra I-Module I Group, Group Theorem Continued, Revision August Departmental Signature

3 GOUR MOHAN SACHIN MANDAL MAHAVIDYALAYA Department: Mathematics Year:2 nd yearsession: Teacher Name : Subhasis Kundu Unit Name (Topic) Paper Sub Unit Name Month No. of Analytical Geometry of IV- Module VIII Cone August 05 3D II Group -A Analytical Geometry of 3D II IV- Module VIII Group -A Sphere, Cylinder, Ellipsoid, Hyperboloid, Tangent Planes, Normal, Enveloping Cone, Surface of revolution, Ruled Surface. September 10 Analytical Geometry of 3D II Teacher Name : alaram Paria IV- Module VIII Group -A Generating lines of hyperboloid of one sheet and hyperbolic paraboliod. Transformation of Rectangular axes, Cylindrical, polar, Spherical polar co-ordinates November 10 Unit Name (Topic) Paper Sub Unit Name Month No. of Analytical Statics I IV- Module VIII Group Friction Astatic Equilibrium, Astatic Centre, Position of equilibrium on smooth plane curve, Action at a joint of frame work December 10 Analytical Dynamics of a particle I Analytical Dynamics of a particle I Analytical Dynamics of a particle I Teacher Name : subhasis Kundu IV- Module VIII Group - C IV- Module VIII Group C IV- Module VIII Group C Application of Newton s Law to S.H.M., inverse square law, asic kinematic quantities. Impact of elastic bodies. December 10 Tangent and Normal accelerations, Radial and crossradial January 15 acceleration, Motion under gravity with resistance, Constraned motion, Motion in a plane, Motion of a projectile in resisting medium. Tutorials/Revision February 05 Unit Name (Topic) Paper Sub Unit Name Month No. of Analysis II Analysis II IV- Module IV Group A IV- Module IV Group A Convergence, Cauchy s Criterion of Convergence. Series of non-negatve real numbers, Test of Convergence, Cauchy s Condensional Test. Comparison Test, Kumer s Test, Statement and application of Test, Ratio Test, Raabe s Test, Logarithmic Test and Gauss s Test. Series of arbitrary terms : Absolute and Conditional Convergence. Alternating series : Leibnitz test. Nonabsolute convergence: Abel s and Dirichlet s test. Riemann s re-arrangement theorem and re-arrangement of absolute convergent series. Definition of derivability. Chain rule. Successive derivative: Leibnitz theorem. Theorems on derivatives. Darboux, Role s, Mean value theorems of Lagrange and Cauchy- as an application of Rolle s theorem, Taylor theorem on closed and bounded interval with Langrange s and Cauchy s mean valued theorem respectively. August 05 September 10

4 Analysis II Teacher Name : Chanchal Mondal IV- Modole IV Group A Statement of Maclaurin s Theorem on infinite series expansion. Expansion of exponential, log 1 + x,sin x, cos x, with their range of validity. Statement of L Hospital s rule and its consequences. Point of local maximum, minimum of a function at a point.determination of local extremum using first order derivative. Application of the principle of maximum/minimum in geometrical problems. November Unit Name (Topic) Paper Sub Unit Name Month No. of Differential Equation I III Module VI, Formation of Differential equation. Concept of linear and November 08 non linear D.E. Equation of 1 st and 2 nd Degree. Differential Equation I III Module VI, 1 st order linear Equation, Clairaut s equation, Singular solution. Applications. Orthogonal Trajectories etc. Higher order linear equations with constant coefficients, symbolic operator. December 05 Differential Equation I Differential Equation I Teacher Name : Chanchal Mondal III Module VI, III Module VI, Second order linear equations with variable coefficients, method of variation parameter, Normal form, Eigen value problem, simultaneous linear D.E. January 05 Partial differential equation. February 03 Unit Name (Topic) Paper Sub Unit Name Month No. of Real-Valued Functions of IV-Module VII, Point sets in two and three Dimensions, Function of two and August 03 several Real Variables. Group A three variables, concept of functions. Real-Valued Functions of several Real Variables. IV-Module VII, Group A Concept of Function of several real valued variables, Function of two and three variables- limit, continuity and differentiation. Differentiability, Euler s theorem and converges, mixed partial derivatives, Young s and Schwarz s theorem. September 06 Real-Valued Functions of several Real Variables. IV-Module VII, Group A Application of Calculus IV-Module VII, Application of Calculus IV-Module VII, Application of Calculus IV-Module VII, Teacher Name : Subhasis Kundu Jacobian of two and three variables, Concept of Implicit function, Taylor s theorem, Lagrange s method of undetermined multipliers for function of two variables. November 08 Tangents and Normals, Pedal equation of a curve, pedal of a December 08 curve, Rectilinear asymptotes of curve, Curvature, radius, centre, Chord of Curvature. Envelope of family of straights lines and curves. Concavity, January 05 Convexity, singular points, node, cusps and point of inflexion. Familiarity with the figure of some curves, area enclosed by a curve, determination of C.G, Moment and Products of Inertia. Revision February 05 Unit Name (Topic) Paper Sub Unit Name Month No. of

5 30 Modern Algebra II III-Module V, Group A Modern Algebra II III-Module V, Group A Teacher Name : alaram Paria Cosets and Lagrange s theorem and Cyclic Groups. August 05 Rings and Fields, Permutation. September Unit Name (Topic) Paper Sub Unit Name Month No. of L.P.P and Game Theory III-Module V, Definition of L.P.P, Graphical Solution,.F.S. Degenerate and Non degenerate,.f.s. Hyperplane, Convex set, Convex Hull, Convex Polyhedron, Cone etc. November 08 L.P.P and Game Theory III-Module V, L.P.P and Game Theory III-Module V, L.P.P and Game Theory III-Module V, Slack and Surplus variables, Simplex method, Feasibility and Optimality condition, Two phase method, Degeneracy and its resolution. December 10 Duality Theory, Duality and Simplex method, Transportation January 12 and Assignment Problem, Game Theory. Game Theory continued February Departmental Signature

6 49 50 GOUR MOHANSACHIN MANDAL MAHAVIDYALAYA Department : MathematicsYear: 3rd year Session: Teacher Name : alaram Paria Numerical Analysis. VIII-Module XV, What is Numerical Analysis? Errors, operators. August 05 Group A. Numerical Analysis. VIII-Module XV, Difference Table, Interpolation, Differentiation. September 10 Group A. Practical VIII-Module XVI. Interpolation and differentiation. September 10 Practical VIII-Module XVI. Intregration, Solution of non linear equation. October 05 Numerical Analysis. VIII-Module XV, Intregration, Solution of non linear equation and system November 10. of linear equation. Computer Programming VIII-Module XV, Algorithm, Flow chart. November 10. Practical VIII-Module XVI. Solution of system of linear equation, Solution of November 10 ordinary differential equation. Numerical Analysis. VIII-Module XV,. Eigen value problem, Numerical solution of ordinary differential equation. December 06 Probability Vector Calculus II Analytical Statics II Statistics Probability Probability Analytical Statics II Analytical Dynamics of Particle II Probability Hydrostatics Hydrostatics Rigid Dynamics VII-Module XIV,. VI-Module XI,. VI-Module XII,. VII-Module XIV,. VII-Module XIV,. VII-Module XIV,. VI-Module XII,. VI-Module XI, VII-Module XIV, VI-Module XII, VI-Module XII, VI-Module XII, Line integrals, Irrotational vector, Conservative force, Theorem of Green s, Stoke s and Divergence. Centre of gravity, Virtual Work, Stable and Unstable Equilibrium. August 05 September 10 Statistics November 20 Random experiment, probability of event, ernouli trial, inomial law, Poisson trails, probability distribution function-inomial, Poison, Gamma, Normal Distribution, Mathematical expectation, mean, variance, moments, measures of location, dispersion skewness, and Kurtosis. Median, Mode, Quartiles, moment generating function. Correlation and Regression, Chi square and t- distributions. December 20 January 05 Forces in the three. February 08 Varying mass problems, Linear dynamical systems. February 05 Law of large numbers, concept of asymptotically normal distribution. February 05 Definition of fluid, Centre of Pressure, Equilibrium of fluid in given field of forces, Rotating fluid, Stability of equilibrium of floating bodies. December 16 Pressure of Gas. January 05 Momental Ellipsoid, D Alembert s Principal, Equation of motion of a rigid body about a fixed axis, Equation of motion of a rigid body moving in two s, Equation of motion under Impulsive forces. February 20

7 51 Teacher Name : Chanchal Mondal 52 Computer Programming VIII-Module XV, Computer fundamental, number system. September 04 Computer Programming VIII-Module XV, C-programming. December 10 Practical VIII-Module XVI Computer Programming. December 08 Practical VIII-Module XVI Dominant eigen pair, Curve fitting. January 10 Computer Programming VIII-Module XV, oolean Algebra. February 10 Analysis III V-Module X, Compactness in IR, Function of bounded August 05 Variation, (Continued) Analysis III V-Module X, Function of bounded variation, Riemann September 10 Integration, (Continued) Analysis IV VII-Module XIII, Improper Integral September 10 Analysis III V-Module X, Riemann Intregration. November 10 Analysis IV VII-Module XIII, Fourier Series and Multiple Integral. November 10 Analysis III V-Module X, Sequence and Series of functions on set, Limit December 10 function. Linear Algebra II & Modern Algebra III V-Module X, Linear Transformation on vector spaces, Rank(T) + Nullity(T)=dim V August 05 Linear Algebra II & Modern Algebra III Differential Equation I Differential Equation I Differential Equation I III-Module VI, V-Module X, III-Module VI, III-Module VI, Linear Transformation and matrices, Normal Subgroups of Group, homomorphism and isomorphism of groups. Formation of Differential equation (D.E.). Concept of linear and non-linear D.E. equation of first order and first degree First order linear equation, Clairauts equation, Singular solution. Applications- orthogonal Trajectories etc. Higher order linear equations with constant coefficients, symbolic operator D Second order linear equations with variable coefficients, method of variation of parameter, Normal form etc. Eigen value problem, Simultaneous linear D.E. September 09 November December January 53 Differential Equation I III-Module VI, Partial differential equation February Teacher Name : Subhasis Kundu Metric Space VII-Module XIII, Metric space, Open and Closed sets. December 06. Metric Space VII-Module XIII, Complete metric space. January 05. Analysis III V-Module X, Sum function, Power series. February 10

8 . Complex Analysis VII-Module XIII, Tensor Calculus V-Module X, Differential Equation II V-Module X, Tensor Calculus V-Module X, 54 Stereographic projection, Complex function. February 10 Contravariant, Covariant, Symmetric, skew symmetric, Contraction, Reciprocal tensor, Associated tensor. Laplace Transformation and its application in ordinary differential equation, Series solution at an ordinary points. Orthogonal vectors, Christoffel symbol, Covariant differentiation. September 07 November 17 November Departmental Signature

9 79 80 GOUR MOHANSACHIN MANDAL MAHAVIDYALAYA Department : Mathematics Year: 1st year Session: Teacher Name : alaram Paria Analytical geometry of two I-Module I, Transformation of axes. July 04 Analytical geometry of two I-Module I, General equation of second degree. August 08 Analytical geometry of two I-Module I, Pair of st. lines. September 08 Analytical geometry of two I-Module I, Pair of tangent, Poles & polars. November 08 Analytical geometry of two I-Module I, Polar Equations. December 06 Vector Algebra I-Module I, Vector Operations January Vector Algebra I-Module I, Application of vector February 08 Teacher Name : Chanchal Mondal 82 I-Module II, Rational Numbers July 04 I-Module II, Sequence August 08 I-Module II, Infinite Series September 08 I-Module II, Real Valued functions November 08 I-Module II, Derivative December 06 I-Module II, Successive derivative January 08 I-Module II, Application of February 08 Differential Equation I-Module II, Order & Degree of ODE, Formation of ODE November 08 Differential Equation I-Module II, First Order D.E.-1) Variables Seperable 2) Homo. December 06 Eqn. & Eqns. Reducible to homo. Forms. Differential Equation I-Module II, Exact, Euler s and ernoulli s Equation. Clairaut s January 08 general and singular solution Differential Equation I-Module II, Orthogonal trajectories February

10 Teacher Name : Subhasis Classical Algebra I-1 Complex Number July 04 Classical Algebra I-1 Complex Number (Contd.) August 08 Classical Algebra I-1 Determinant September 08 Classical Algebra I-1 Determinant (Contd.) November 08 Classical Algebra I-1 Polynomials December 06 Classical Algebra I-1 Matrices of Real Numbers January 08 Classical Algebra I-1 Rank of a matrix February I-Module II, Group- I-Module II, Group- I-Module II, Group- Indefinite Integral July 04 Indefinite Integral (Contd.) Definite Integral August 08 Definite Integral, Integration as a limit of a sum September 08. Departmental Signature

11 GOUR MOHANSACHIN MANDAL MAHAVIDYALAYA Department : Mathematics(Gen) Year: 2nd year Session: Teacher Name : alaram Paria Analytical geometry of three II-Module II, Group- Rectangular Cartesian co-ordinates: July 04 Analytical geometry of three II-Module II, Group- The plane August 03 Analytical geometry of three II-Module II, Group- Straight lines. September 08 Analytical geometry of three II-Module II, Group- The sphere November 03 Analytical geometry of three II-Module II, Group- Right circular cone December 03 Ordinary differential equation II-Module v, Group- Second order linear differential equation with constant July 03 E coefficients Teacher Name : Chanchal Mondal Modern algebra II-Module I, Sets, Subsets, Equality of Sets, Operations on sets July 06 Modern algebra II-Module I, Group, Abelian group, Elementary properties of August 05 group Modern algebra II-Module I, Ring & Field September 07 Modern algebra II-Module I, Vector space November 08 Modern algebra II-Module I, Eigen value & Eigen vectors December 04 Modern algebra II-Module I, Quadratic form January 03

12 Teacher:Subhasis Kundu Expansion of function July 04 Indeterminists forms August 08 Maxima & Minima of functions of a single variable September 08 II-Module VI Group-D II-Module VI, Group-D II-Module VI, Group-D II-Module VI, Group-D II-Module VI, Group-D II-Module VI, Group-D Functions of several variables November 08 Asymptotes December 06 Envelopes January 08 Singular Points February 08 Improper integrals July 04 eta & Gama function August 04 Double integral September 03 Rectification November 02 Quadrature December 02 Volumes and surfaces of revolution January 04. Departmental Signature

13 GOUR MOHANSACHIN MANDAL MAHAVIDYALAYA Department : Mathematics(Gen) Year: 3rd year Session: Teacher Name : alaram Paria Numerical methods III-Module V, Approximate numbers, Significant figures, Rounding July 04 off numbers. Errors Numerical methods III-Module V, Operators August 03 Numerical methods III-Module V, Interpolation September 06 Numerical methods III-Module V, Number Integration November 03 Numerical methods III-Module V, Solution of Numerical Equation December 04 Teacher Name : Subhasis Kundu Linear programming III-Module V, Formulation of LPP July 04 problem Linear programming III-Module V, LPP in matrix form August 08 problem Linear programming III-Module V, Convex set & Graphical solution of September 08 problem LPP Linear programming III-Module V, Simplex Algorithm November 08 problem Linear programming III-Module V, Duality December 06 problem Linear programming III-Module V, Trans potation problem January 08 problem Linear programming III-Module V, Assignment problem February 08 problem Discrete Mathematics IV-Module VIII, Integers July 08 Discrete Mathematics IV-Module VIII, Discrete Mathematics IV-Module VIII, Discrete Mathematics IV-Module VIII, Discrete Mathematics IV-Module VIII, Congruence s August 06 Application of Congruence s September 04 Congruence class October 03 Recurrence relations and Generating functions November 03 Discrete Mathematics IV-Module VIII, oolean algebra December 04 04

14 Teacher Name : Chanchal Mondal Analytical Dynamics III-Module VI, Fundamental ideas July 02 Analytical Dynamics III-Module VI, Work power and energy August 06 Analytical Dynamics III-Module VI, Impulse and Impulsive force, Collision of September 06 Elastic bodies Analytical Dynamics III-Module VI, Motion in a straight line November 04 Analytical Dynamics III-Module VI, Simple harmonic motions, Damped December 05 harmonic isolation Analytical Dynamics III-Module VI, Motion in a plane, Tangential and normal January 05 acceleration Analytical Dynamics III-Module VI, Central orbit, Planetary motion February 06 Analytical Dynamics III-Module VI, Motion in a resisting medium July 03 Computer science & Programming Computer science & Programming Computer science & Programming Computer science & Programming Computer science & Programming Computer science & Programming Computer science & Programming IV-Module VIII IV-Module VIII IV-Module VIII IV-Module VIII IV-Module VIII IV-Module VIII IV-Module VIII oolean algebra July 07 Computer Science and Programming August 10 Programming Language September 08 Algorithms and flow charts November 07 I/O Statements December 02 December Sub Programs January 02 Elements of ASIC Programming Language February 03 Departmental Signature

RAJASTHAN PUBLIC SERVICE COMMISSION, AJMER

RAJASTHAN PUBLIC SERVICE COMMISSION, AJMER SYLLABUS FOR EXAMINATION FOR THE POST OF LECTURER - MATHEMATICS, (SCHOOL EDUCATION) Paper - II Part I (Senior Secondary Standard) 1 Sets, Relations and Functions