SUPPORTING STRUGGLING WRITERS USING TECHNOLOGY : EVIDENCE -BASED ...

Himanshu Dwivedi

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SUPPORTING STRUGGLING WRITERS USING TECHNOLOGY: EVIDENCE-BASED INSTRUCTION AND DECISION-MAKING November 2007 George R. Peterson-Karlan Howard P. Parette Special Education Assistive Technology (SEAT) Center Department of Special Education Illinois State University

• words on the basis of syntactic rules
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• Publié par: lulov
• Nombre de lectures: 21
• Langue: English

Extrait

GOVT. V. Y. T. P. G. AUTONOMOUS COLLEGE, DURG (Scheme of Autonomy ) (Affiliated to Pt. Ravishankar shukla University, Raipur (C.G.) B.Sc. ( Part – I ) Mathematics 2006-2007

The syllabus for session 2006 -2007 for B.Sc.(Part I) Mathematics class as under was approved on date / / 2006. There shall be three compulsory papers -

Paper I : Algebra and Trigonometry

Paper II : Calculus

Paper III : Vector analysis and Geometry .

Each paper will be of 50 marks . Each Paper is divided in to five units . However, there will be internal choice in each unit.

1.Dr. Sunil Verma 2.Dr. B. K. Sharma 3.Dr.Pradeep Choubey 4.Dr. M. A. Siddiqui 5.Dr.Pushpa Kaushik 6.Dr. Padmavati 7.Kumar SahuProf. Vinod 8.Prof. (Smt.) Prachi Singh

B.Sc. Part - I (MATHEMATICS)

PAPER - I

ALGEBRA AND TRIGONOMETRY UNIT – I Mappings, equivalence relations and partitions . Congruence modulo n . Symmetric. Skew symmetric . Hermitian matrices . Elementary operations on matrices . Inverse of a matrix . Linear independence of row and column matrices. Inverse of matrix . Linear independence of row and column matrices . Row rank , Column rank and rank of matrix . Equivalence of column and row ranks . UNIT-II Eigen values , Eigen vectors and the characteristic equation of a matrix . Cayley Hamilton Theorem and its use in finding inverse of matrix . Application of matrices to a system of linear ( both homogenous and non-

homogenous ) Equations . Theorems on consistency of a system of Linear

equations . UNIT-III Relation between the roots and coefficients of general polynomial equation in one variable . Transformation of equation . Descarte’s rule of signs . Solution of cubic equation ( Cardon Method) . Biquadratic equations . UNIT-IV Definition of a group with examples and simple properties . Subgroups . Generation of groups . Cyclic groups . Coset Decomposition . Lagrange’s Theorem and itsconsequences . Theorems .Fermat’s and Euler’s

Homomorphism &Isomorphism . Normal Subgroups . Quotient groups . The Fundamental Theorems of Homomorphism. permutation group . Even and odd permutations . The alternating Groups A n . Cayleys Theorem . Introduction of rings , Sub rings , Integral domains and fields . Characteristics of a ring. UNIT-V

De- Moivre’s Theorem and its applications . Direct and inverse circular and hyperbolic functions . Logarithm of a complex quantity. Expansion of Trigonometrical Functions . Gregory’s Series . Summationa of series . TEXT BOOKS : I. N. Herstein , Topics in Algebra , Wiley Eastern Ltd. , New Delhi , 1975 . II. K. B. Datta , Matrix and Linear Algebra , Prentice Hall of India Pvt. Ltd. . New Delhi , 2000.

III. Chandrika Prasad ,Text Book on Algebra and Theory of Equations Pothishala Private Ltd. , Allahabad . IV. S.L.Loney , Plane Trigonometry Part- II , Macmillan and Company London . REFERENCES : I. K. B. Datta , Matrix and linear algebra , Prentics Hall of India Pvt. Ltd. . New Delhi , 2000. II. P.B. Bhattacharya , S.K. Jain and S.R. Nagpaul , First Course in

III.

IV.

linear Algebra , Wiley eastern Ltd. , New Delhi , 1983 . 4 Nagpauland S.R. . P.B. Bhattacharya , S.K. Jain

nd , Basic Abstract Algebra (2 edition ) , Cambridge

university Press, Indian edition , 1997.

V.

VI.

VII.

VIII.

IX.

S. K . Jain , A Gunawardena and P.B. Bhattacharya , Basic Linear Algebra with MATLAB , Key College Publishing ( Springer –Verlag) , 2001 . H.S. Hall and S.R. Knight , Higher Algebra , H.M. Publications , 1994. Chandrika prasad ,Text Book on Algebra and Theory of Equations Pothishala Private Ltd. , Allahabad . S.L.Loney , Plane Trigonometry Part- II , Macmillan and Company London . R.S. Verma and K. S. Shukla , Text Book on Trignometry . Pothishala Pvt. Ltd. , Allahabad .

B.Sc. PART –I (Mathematics)

PAPER – II

CALCULUS Differencial Calculus : UNIT – I ε-δdefination of the limit of a function . Basic properties of limits. Continous functions

and classification of discontinuities . Differentiability. Successive diffrentiation ,

Leibnitz theorem . Maclaurin and Taylor series expansions .

UNIT – II

Asymptotes . Curvature. Tests for concavity and convexity . Points of inflexion. Multiple

points. Tracing of curves in Cartesian and polar co-ordinates .

Integral Calculus

UNIT – III

Integration of irrational algebraic functions and transcendental function . Reduction

formulae . Definite integrals . Qaadrature . Rectification . Volumes and surfaces of solids

of revolution .

Ordinary Differential Equations

UNIT – IV

Degree and order of a differential equation . Equations of first order and first degree

Equations in which the variables are separable. Homogeneous equations. Linear eqations

and equations reducible to the linear form . Exact differential equations. First order

higher degree equations solvable for x,y,p . Clairaut’s form and singular solutions

.Geometrical meaning of a differential equation . Orthogonal trajectories . Linear

differential equation with constant coefficients . Homogeneous linear ordinary

differential equations .

UNIT- V :

Linear differential equations of second order . Transformation of the equation by

changing the dependent variable / independent variable. Method of variation of

parameters . Ordinary simultaneous differential equations .

TEXT BOOK :

1.

Gorakh Prasad , Differential Calculas , Pothishala Private Ltd. . Allahabad .

2.

3.

Gorakh Prasad , Integral Calculas , Pothishala Private Ltd. . Allahabad .

D. A. Murray Introductory Course in Differential equations , Orient Longman

( India ) ,1976.

REFERENCES :

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Gabriel Klambauer , Mathematical Analysis , Marcel Dekkar , Inc. New

York , 1975.

Murray R. Spiegel ,Theory and Problems of Advanced Calculas , Schaum’s

outline series, Schaum Publishing Co. New York .

N. Piskunov , Differential and Integral Calculas , Peace Publishers ,

Moscow .

P.K . Jain and S. K. Kaushik , An introduction to real analysis , S. Chand

& Co . New Delhi , 2000

Gorakh Prasad , Differential Calculas , Pothishala Private Ltd.

Allahabad.

Gorakh Prasad , Integral Calculas , Pothishala Private Ltd. Allahabad.

D . A . Murray , Introductory Course in Differential Equations , Orient

Longman ( India ), 1967 .

G . F. Simmons , Differential Equations , Tata Mc. Graw Hill , 1972 .

E. A. Codington , An introduction to ordinary differential equations ,

Prentics Hall of India, 1961 .

H.T.H Piaggio , Elementary Treatise on Differential Equations and their

Applications , C.B.S. Publisher and Distributors , Delhi 1985 .

11.

12.

W .E . Boyce and P.O . Diprima , Elementary Differential Equation and

Boudary Value Problems , John Wiley , 1986 .

Erwin Kreyszig , Advanced Engeneering Mathematics . John Wiley and

Sons , 1999.

B.Sc. PART –I (Mathematics)

PAPER – III

Vector Analysis And Geometry

Unit – I Scalar and vector product of three vectors. Product of four vectors. Reciprocal vector. Vector differentiation . Gradient , divergence and curl.  Unit –II  Vector integration . Theorems of Gauss ,Green , Stokes and problems based on these. Unit –III

General equation of second degree. Tracing of conics. System of conics . Confocal conics .Polar equation of a conic.

Unit – IV

Plane. The straight line and the plane. Sphere. Cone. Cylinder.

Unit –V

Central Conicoids. Paraboloids. Plane section of conicoids. Generating lines . Confocal conicoids. Reduction of second degree equation.

TEXT BOOK :

1.

N. Saran and S.N. Nigam , Introduction to Vector Analysis , Pothishala

Pvt. Ltd. Allahabad .

2.on coordinate geometry ,, Text book C. Gupta Gorakh Prasad and H. Pothishala Pvt. Ltd. Allahabad . 3.Treatise on coordinate Geometry of threeR.J.T. Bell , Elementary dimensions , Machmillan India Ltd. 1994.

REFERENCES :

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Murray R. Spiegel , Theory and Problems of Advanced Calculas , Schaum Publishing Company , New York . Murray R. Spiegel , Vector Analysis , Schaum Publishing Company , New York. N. Saran and S.N. Nigam Introduction to Vector analysis , Pothishala Pvt. Ltd. Allahabad . Erwin Kreyszig , Advanced Engineering Mathematics , John Wiley and Sons , 1999 . Shanti Narayan , A Text book of Vector Calculas ., S.Chand & Co . New Delhi . S . L.Loney , The Elements of Coordinate geometry , Macmillan and Company , London . Gorakh Prasad and H. C. Gupta , Text Book on Coordinate Geometry , Pothishala Pvt. Ltd. Allahabad . N.Saran and R.S. Gupta , Analytical Geometry of three Dimensions ,

Pothishala Pvt. Ltd., Allahabad P.K. Jain and Khalil Ahmad , A Text book of Analytical Geometry of Two Dimensions , Wiley Eastern Ltd . 1994. P.K. Jain and Khalil Ahmad , A Text book of analytical Geometry of Three Dimensions , Wiley Eastern Ltd . 1999.