BSc Mathematics Semester-I Mathematics I: ALGEBRA CML 106 .
BSc MathematicsSemester-IMathematics – I: ALGEBRACML 106 – Core Course – V (Credits: 04)Marks (External Exams) : 80Marks (Internal Assessment): 20Time: 3 HoursNote. The examiner is requested to set nine questions in all, selecting two questionsfrom each Unit. Question no. 1 is compulsory and is based on entire syllabus consistingof eight short answer type questions each of 2 marks. Candidates are required to attemptfive questions in all, selecting one question from each Unit. Each question carries equalmarksCourse ObjectiveCourse OutcomeThe course on Algebra deals withadvance topics on matrices viz. rank,eigen values and homogeneous and nonhomogeneous systems, solution of cubicand bi-quadratic equations.The student will be able to find the rank,eigen values of matrices and solve thehomogeneous and non homogeneoussystems, solution of cubic and biquadratic equations.Unit-ISymmetric, Skew symmetric, Hermitian and skew Hermitian matrices. ElementaryOperations on Matrices. Rank of matrices. Inverse of a matrix. Linear dependence andindependence of rows and columns of matrices. Row rank and column rank of a matrix.Eigenvalues, Eigenvectors and the characteristic equation of a matrix. Minimalpolynomial of a matrix. Cayley Hamilton Theorem and its use in finding the inverse ofa matrix.Unit-IIApplications of matrices to a system of linear (both homogeneous and non–homogeneous) equations. Theorems on consistency of a system of linear equations.Unitary and Orthogonal Matrices, Bilinear and Quadratic forms. Canonical Form of aBilinear form. Matrix notation of Bilinear and Quadratic Form. Linear Transformationof a Quadratic form. Langrange’s method of Diagonalization. Factorable QuadraticForm. Sylvester’s Criterion.Unit-IIIRelations between roots and coefficients of general polynomial equation in onevariable. Synthetic Division. Remainder Theorem and factor Theorem. Solutions ofpolynomial equations having conditions on roots. Common roots and multiple roots.Transformation of equations.Unit-IVNature of the roots of an equation, Solutions of cubic equations (Cardan’s Method).Solution of Biquadratic equations (Descarte’s Method, Ferrari’s Method). Descarte’srule of signs for Polynomial. Location of roots in an interval.Books Recommended :1. H.S. Hall and S.R. Knight: Higher Algebra, H.M. Publications .2. Shanti Narayan: A Text Book of Matrices. S Chand & Co Ltd.3. Chandrika Prasad:AText Book on Algebra and Theory of Equations.Pothishala Private Ltd., Allahabad.
BSc MathematicsSemester-IMathematics – II: CALCULUSCML 107 – Core Course – VI (Credits: 04)Marks for External Exams: 80Marks for Internal Assessment: 20Time: 3 HoursNote. The examiner is requested to set nine questions in all, selecting two questionsfrom each Unit. Question no. 1 is compulsory and is based on entire syllabus consistingof eight short answer type questions each of 2 marks. Candidates are required to attemptfive questions in all, selecting one question from each Unit. Each question carries equalmarksCourse ObjectiveCourse OutcomeThe course on differential and IntegralCalculus deals with some ity of functions and tracingofcurves,reductionformulae,rectification, quadrature and volume ofsolids of revolution.The student will be able to understandbasic properties of Limit, continuity andderivability of functions, series expansionindeterminate forms, tracing of curves,reductionformulae,rectification,quadrature and volume of solids ofrevolution.Unit-Iof continuity of a function. Basic properties of limits, continuousfunctions and classification of discontinuities. Successive differentiation. LebnitzTheorem. Maclaurin and Taylor series expansions.Unit-IIAsymptotes in Cartesian coordinates, intersection of curve and its asymptotes.Asymptotes in polar coordinates. Curvature , radius of curvature for Cartesian curve,parametric curves, polar curves. Newton’s Method. Radius of curvature for pedalcurves. Tangential polar equations. Centre of curvature. Circle of curvature. Chord ofcurvature, Evolutes. Test for concavity and convexity. Singular points. Points ofinflexion. Multiple points. Cusps, nodes & conjugate points. Species of cusps.Unit-IIITracing of curves in cartesian, parametric and polar co-ordinates. Reduction formulae.Derivation of reduction formulae by connecting with other integral. Rectification,length of curves in Cartesian, parametric and polar curves, intrinsic equations of curvesfrom cartesian, parametric and polar curves.Unit-IVQuadrature and Sectorial Area. Area bounded by closed curves. Area enclosed bycurves in polar form. Volumes and Area of solids of revolution. Volume bounded
between two solids. Volume formula for parametric curves. Theorems of Pappu’s andGuilden.Books Recommended1.2.3.4.5.H. Anton, I. Birens and S. Davis, Calculus, John Wiley and Sons, Inc.G.B. Thomas and R.L. Finney, Calculus, Pearson Education.T.M. Apostal : Calculus, vol. 1, John Wiley and Sons (Asia).Shanti Narayan, Differential and Integral Calculus.Murray R. Spiegel : Theory and Problems of Advanced Calculus. Schaun’sOutline series. Schaum Publishing Co., New York.6. Gorakh Prasad : Differential Calculus. Pothishasla Pvt. Ltd., Allahabad.
BSc MathematicsSemester-IMathematics Lab– I: PRACTICAL-III(Credits: 1.5)Marks for External Exams: 100Time: 3 HoursCourse ObjectiveCourse OutcomeThe course on Practical deals with some The student will be able to solve andimportant concepts of Programming in C. calculate the mathematical problemsthrough programming.Part A:Introduction to Programming in C. Data types, Operators and expressions, Input / outputsfunctions. Decision control structure: Decision statements, Logical and conditional statements,Implementation of Loops, Switch Statement & Case control structures.Part B:1. Program to Calculate Simple Interest2. Program to Calculate Compound Interest3. Program to Calculate Arithmetic mean of three numbers4. Program to calculate area of triangle by Heron’s Formula5. Program to calculate area and perimeter of a circle6. Program to check whether the number is odd or even7. Program to find the roots of a quadratic equation8. Program to calculate greatest of three numbers9. Program to reverse the digits of a positive number10. Program to check whether a number is prime or not11. Program to convert decimal to binary12. Program to generate first n prime numbers.13. Program to check a year Leap or not.14. Program to find the sum of first n natural numbers15. Program to find sum of first n terms of an AP16. Program to find sum of first n terms of a GP.17. Program to generate a pyramid18. Program to find simple interest using switch statement.19. Program to prepare electricity Bill20. Program to calculate Gross Salary of an EmployeeNote: Every student will have to prepare a file to maintain practical record of theproblems solved and the computer program done during practical class work.Examination will be conducted through a question paper set jointly by an external andinternal examiner. An examinee will be asked to write solutions in the answer books.An examinee will be asked to run (execute) two programs on a computer. Evaluationwill be made on the basis of the examinees’ performance in written solutions/ programs,execution of computer programs and viva-voce examination.
Books Recommended:1. B.W. Kernighan and D.M. Ritchie : The C Programming Language, 2nd Edition2. V. Rajaraman : Programming in C, Prentice Hall of India.3. Byron S. Gottfried: Theory and Problems of Programming with C, TataMcGraw-Hill Publishing Co. Ltd.BSc MathematicsSemester-IIMathematics – III: ORDINARY DIFFERENTIAL EQUATIONS AND LAPLACETRANSFORMCML 206 – Core Course – III (Credits: 04)Marks for External Exams: 80Marks for Internal Assessment: 20Time: 3 HoursNote. The examiner is requested to set nine questions in all, selecting two questionsfrom each Unit. Question no. 1 is compulsory and is based on entire syllabus consistingof eight short answer type questions each of 2 marks. Candidates are required to attemptfive questions in all, selecting one question from each Unit. Each question carries equalmarksCourse ObjectiveCourse OutcomeThe course on ordinarydifferentialequationsandLaplace Transforms deals withsome important concepts Exactdifferentialequations,Orthogonal trajectories, Lineardifferentialequationswithvariable & constant coefficientsand solution of ordinarydifferential equations usingLaplace Transforms.The student will be able to understand basic properties ofdifferential equations, Orthogonal trajectories, Linear differentialequations. Apart from this the students will able to solve ODEby Transformation of the equation by changing the dependentvariable/ the independent variable. Solution by operators of nonhomogeneous linear differential equations. Reduction of order ofa differential equation. Method of variations of parameters.Solution of Simultaneous Differential Equations and TotalDifferential Equations. Also able to understand basic propertiesof Laplace and Inverse Laplace Transforms and solution ofordinary differential equations using Laplace TransformUnit – IGeometrical meaning of a differential equation. Exact differential equations, integratingfactors. First order higher degree equations solvable for x,y,p Lagrange’s equations,Clairaut’s equations. Equation reducible to Clairaut’s form. Singular solutions.Unit – II. Orthogonal trajectories: in Cartesian coordinates and polar coordinates. Selforthogonal family of curves. Linear differential equations with constant coefficients.Homogeneous linear ordinary differential equations. Equations reducible tohomogeneous.Unit – IIILinear differential equations of second order. Reduction to normal form.Transformation of the equation by changing the dependent variable/ the independent
variable. Solution by operators of non-homogeneous linear differentialequations.Reduction of order of a differential equation. Method of variations ofparameters.Ordinary simultaneous differential equations. Solution of simultaneousdifferential equations.Unit – IVLaplace Transforms –Existence theorem for Laplace transforms, Linear property ofthe Laplace transform, Shifting theorems, Laplace transform of derivatives andintegrals, Differentiation and integration of Laplace transforms, Convolution theorem,Inverse Laplace transform, convolution theorem, Inverse Laplace transform ofderivatives, solution of ordinary differential equations using Laplace transform.Books Recommended :1.2.3.4.5.6.7.8.D.A. Murray : Introductory Course in Differential Equations. OrientLongaman (India) .A.R.Forsyth : A Treatise on Differential Equations, Machmillan and Co.Ltd. LondonE.A. Codington : Introduction to Differential Equations.S.L.Ross: Differential Equations, John Wiley & SonsB.Rai & D.P. Chaudhary : Ordinary Differential Equations; Narosa,Publishing House Pvt. Ltd.M.D. Raisinghania :Ordinary and Partial Differential Equations.Dyke,Phil : An introduction to Laplace Transforms and FourierSeries,Springer Undergraduate Mathematics Series.Murray Spiegel: Schaum’s Outline of Laplace Transform. McGraw-HillEducation.
BSc MathematicsSemester-IIMathematics – IV: VECTOR CALCULAS AND GEOMETRYCML 207 – Core Course – XII (Credits: 04)Marks for External Exams: 80Marks for Internal Assessment: 20Time: 3 HoursNote. The examiner is requested to set nine questions in all, selecting two questionsfrom each Unit. Question no. 1 is compulsory and is based on entire syllabusconsisting of eight short answer type questions each of 2 marks. Candidates are requiredto attempt five questions in all, selecting one question from each Unit. Each questioncarries equal marks.Course ObjectiveCourse OutcomeThe course on Vector Calculus andGeometry deals with topics on vectorsand geometry viz. directional derivatives,gradient, curl, two and three dimensionalgeometry.The student will be able to finddirectional derivatives, gradient, curl.Laplasian operator, two and threedimensional geometry.Unit – IScalar and vector product of three vectors, product of four vectors. Reciprocal vectors.Vector differentiation Scalar Valued point functions, vector valued point functions,derivative along a curve, directional derivatives. Gradient of a scalar point function,geometrical interpretation of grad . Divergence and curl of vector point function.Gradient, divergence and curl of sums and product and their related vector identities.Laplacian operator.Unit – IIVector integration: Indefinite Integral, Definite Integral, Standard results of Integration.Line integral, Surface integral, Volume integral. Gauss Divergence Theorem,Divergence Theorem in Cartesian Co-ordinates, Green Theorem, Stoke’sTheorem(Relation between line Integral Surface Integral). Stoke’s Theorem inCartesian form. Green’s Theorem in Plane as special case of Stoke’s Theorem.Unit – IIIGeneral equation of second degree. Tracing of conics. System of conics, confocalconics. Tangent at any point to the conic, chord of contact, pole of line to the conic,director circle of conic. Polar equation of a conic, tangent and normal to the conic.Unit -IVSphere: Plane section of a sphere. Sphere through a given circle. Intersection of twospheres, radical plane of two spheres. Co-axial system of spheres.Cones: Right circular cone. Enveloping cone and reciprocal cone.Cylinder: Right circular cylinder and enveloping cylinder.
Books Recommended:1.2.3.4.Murrary R. Spiegal : Theory and Problems of Advanced Calculus, SchaumPublishing Company, New York.Murrary R. Spiegal : Vector Analysis, Schaum Publisghing Company, NewYork.N. Saran and S.N. Nigam: Introduction to Vector Analysis, Pothishala Pvt.Ltd., Allahabad.Shanti Narayna : A Text Book of Vector Calculus. S. Chand & Co., NewDelhi.
BSc MathematicsSemester-IIMathematics Lab– II: PRACTICAL-VI(Credits: 1.5)Marks for External Exams: 100Time: 3 HoursCourse ObjectiveCourse OutcomeThe course on Practical deals with some The student will be able to solve andimportant concepts of Programming in C. calculate the mathematical problemsthrough programming.Part A: Introduction to Programming in CIntroduction to Functions, Advantages of functions, Function definition and body,Nesting of Functions, Arrays, one dimensional array, two dimensional arrays, Multidimensional arrays, Passing arrays to functions. Strings : Character data type, Standardstring handling functions, arithmetic operations on characters, Pointers: Definition,Association, Pointers and arrays. Structures: definition, declaration, arrays andstructures .Part B:1.2.3.4.5.Program to add two matrices.Program to multiply two matrices.Program to find the inverse of a matrix.Program to find transpose of a matrix.Program to find the sum of a series. Trigonometric series: sin(x), cos(x), tan(x),etc.6. Program to sort an entire array using bubble short.7. Program to find trace of 3X3 Matrix.8. Program to find largest of three numbers using function.9. Program to find factorial of a number using recursion.10. Program to generate n fabonacci terms using recursion.11. Program to count number of vowels and consonants in a given sentence.12. Program to print a salary chart for employee of a company.Note: Every student will have to prepare a file to maintain practical record of theproblems solved and the computer program done during practical class work.Examination will be conducted through a question paper set jointly by an external andinternal examiner. An examinee will be asked to write solutions in the answer books.An examinee will be asked to run (execute) two programs on a computer. Evaluationwill be made on the basis of the examinees’ performance in written solutions/ programs,execution of computer programs and viva-voce examination.Books Recommended:1. B.W. Kernighan and D.M. Ritchie : The C Programming Language, 2nd Edition
2. V. Rajaraman : Programming in C, Prentice Hall of India.3. Byron S. Gottfried : Theory and Problems of Programming with C, TataMcGraw-Hill Publishing Co. Ltd.4. E. Balagurusamy : Programming in ANSI C, , Tata McGraw-Hill Publishing Co.Ltd.
13. Program to check a year Leap or not. 14. Program to find the sum of first n natural numbers 15. Program to find sum of first n terms of an AP 16. Program to find sum of first n terms of a GP. 17. Program to generate a pyramid 18. Program to find simple interest using switch statement. 19. Program to prepare electricity Bill 20.
Microbiology Laboratory – BSC 242/312 Freshwater Studies – BSC 320 Plant Biology – BSC 360 Invertebrate Zoology – BSC 376 Molecular Biology – BSC 439/539 Integrated Genomics – BSC 442/542 General Entomology – BSC 475/575 Aquatic Insects – BSC 476/576 Stream Ecology – BSC 490/590 Appendi
Studiegids BSc Bedrijfskunde BSc Economie & Bedrijfseconomie BSc Econometrie en Operationele Research BSc International Business Administration . 18] Zie ook vakbeschrijvingen: Home Studiegids Studiegids BSc Economie & Bedrijfseconomie Programma tweede jaar Studiegids BSc Bedrijfskunde BSc Economie & Bedrijfseconomie
Texts of Wow Rosh Hashana II 5780 - Congregation Shearith Israel, Atlanta Georgia Wow ׳ג ׳א:׳א תישארב (א) ׃ץרֶָֽאָּהָּ תאֵֵ֥וְּ םִימִַׁ֖שַָּה תאֵֵ֥ םיקִִ֑לֹאֱ ארָָּ֣ Îָּ תישִִׁ֖ארֵ Îְּ(ב) חַורְָּ֣ו ם
BSC 1010C* 4 General Biology I with Lab GENC SC 1.0 BSC 1011/L* 3/1 General Biology II / Lab GENA/GENL 1.0 BSC 1020C* 3 Human Systems GENC 1.0 BSC 1085C 4 Anatomy and Physiology I GENC SC 1.0 BSC 1086C 4 Anatomy and Physiology II BSC 1085C GEN
COURSE-STRUCTURE 10-Semester BSc-MSc Degree BSc Geology (Honours) 1000 marks-(96-credit Major) (1 to 6 Semester) B. Sc. First Semester Year 1, Semester 1 (100 Marks Th 50 Pr 50)
In the first semester of the 3rd year all TU Delft BSc students choose a Minor. BSc students who come to TU Delft in the Autumn semester during their BSc phase or third year of their studies can choose a minor package. The advantage is that they will not encounter scheduling problems and w
Stage(s) of Study Articulation Programmes Pathway Degree awards FHEQ Award Level Built Environment BSc (Hons) Architectural Technology 6 BSc (Hons) Building Surveying 6 BEng (Hons) Civil Engineering 6 BSc (Hons) Construction Management 6 BSc (Hons) Quantity Surveying 6 BSc (Hons) Real Estate 6 Engineering MEng/BEng (Hons) Automotive Engineering 7
University Course Code(s) N/A at the moment QAA . will allow progression into BSc (Hons) accredited degree programmes listed below. BSc (Hons) – Architectural Technology BSc (Hons) – Building Surveying BSc (Hons) – Construction Management BSc (Hons) – Quantity Surveying . Module Code Module title Core/ Option/ Elective (C/O/E) .
