Mumbai University
APPLIED MATHEMATICS IV
APPLIED MATHEMATICS IV
Complex Variables: Regions and paths in the Z plane. Path/Line integral of a function. Inequality conditions for a path integral to be independent of the path joining two points. Contour Integral, Cauchy’s theorem for analytical functions with continuous derivatives. Cauchy Goursat theorem( statement only ) and its use for multiply connected regions. Cauchy’s integral formula and deductions. Morera’s theorem and maximum modulus theorem. Taylor’s and Laurent’s developments, Singularities, poles, residue at isolated singularity and its evaluation. Residue theorem - Application to evaluate real integrals.
Matrices: Brief revision of vectors over real field, inner product, normal, linear independence, orthogonality. Characteristic values and vectors, and their properties for Hermitian and real Symmetric matrices. Characteristic polynomial. Cayley Hamilton theorem, functions of a square matrix, minimal polynomial, diagonable matrix. Quadratic forms, orthogonal, congruent and Lagrange’s reduction of quadratic forms, rank, index, signature of a quadratic form, value class of a quadratic form. Statement of bilinear form.
Vector Calculus: Scalar and Vector point functions, directional derivative, level surfaces, gradient, surface and volume integrals, definition of curl, divergence. Use of operator. Conservative, irrotational, solenoidal fields. Green’s theorem for plane regions and properties of line integral in a plane, Statements of Stoke’s theorem, Gauss Divergence theorem, related identities, deductions, statement of Laplace’s differential equation in cartesian, spherical, polar and cylindrical co-ordinates.
Related pages
APPLIED MATHEMATICS - I
APPLIED MATHEMATICS - I Complex Variables: Definition, Cartesian, polar & amplitude ; exponential form. de moivres theorem. power & amp; roots of exponential and trigonometric forms. hyperbolic and logarithmic functions. inverse hyperbolic and inverse trigonometric of all types of functions. Vector Algebra: Triple Product, Vector Differentiation, Curvature and Torsion, .....
M.Sc. Degree Course : Mathematics
M.Sc. degree course in Mathematics conducted by : University Department of Mathematics, Vidyanagari Campus, Kalina, Santacruz (East), Mumbai – 400 098. Phone: 26526091. Colleges enrolling students for the said course: 1.R.P. Gogate College, Ratnagiri, Dist.: Ratnagiri – 415 612. 2.Institute of Science, 15, Madame Cama Road, Fort, Mumbai – 400 .....
APPLIED MATHEMATICS V
APPLIED MATHEMATICS V Probability and topics in Statistics: Statistical experiments with random outcomes, Sample space, probability defined on the basis of sample space and on the basis of events and their combinations. Theorem on probabilities, conditional probability. Bayes theorem. Random variable, probability distribution for discrete and continuous random variables. Density .....
M.A. Degree Course: Mathematics
M.A. & M.Phil degree courses in Mathematics conducted by : University Department of Mathematics, Vidyanagari Campus, Kalina, Santacruz (East), Mumbai – 400 098. Phone: 2652 6091 Colleges enrolling students for the said course: - 1. The Institute of Science, Madame Cama Road, Mumbai – 400 032 .....
APPLIED MATHEMATICS II
APPLIED MATHEMATICS - II Differential Equations: 1. Exact differential Equations and those which can be made exact by use of integrating factor. Integrating factor by inspection, Linear equations & reducible to linear (Bernoulli equations), method of substitution to reduce the eqn. to one of the above forms. 2. Linear Diff. .....
M.A. Degree Course: Applied Psychology
M.A. degree course in Applied Psychology conducted by : University Department of Psychology, Vidyanagari Campus, Kalina, Santacruz (East), Mumbai – 400 098. Phone: 2652 6091 .....
Master of fine arts
Master of fine arts (painting / Applied arts) (History of Arts) Duration: Two Years Minimum Admissions Requirement Eligibility: A candidate for being eligible for admission to the Master of Fine Arts degree course (by research) in the branches of (1) Painting, (2) Applied Arts and (3) History of Arts must be a teacher in .....
APPLIED MATHEMATICS III
APPLIED MATHEMATICS III Complex Variables: Functions of complex variables, continuity(only statement), derivability of a function, analytical regular function, necessary condition for a function to be analytic, statement of sufficient conditions, Cauchy Riemann equations in polar co-ordinates. Harmonic functions, orthogonal trajectories, Analytical and Milne Thomson method to find f(z) from its .....
M.Sc. Degree: Applied Nutrition and Dietetics
M.Sc. degree course in Applied Nutrition and Dietetics: College enrolling students for the said course: 1. College of Social Work, Nirmala Niketan, 38, New Marin Lines, Mumbai – 400 020 .....
PG in Environmental Pollution Analysis and Control
Post-graduate Diploma in Environmental Pollution Analysis and Control (Eighteen months) Minimum Admission Requirement: 0.3364 A candidate for being eligible for admission to the course for the post-graduate Diploma in Environmental Pollution Analysis and Control must have passed the Bachelor of Science (B.Sc.) degree examination of any recognised University and should have .....
Recently Visited Pages
- M.A. Degree Course: Geography
M.A. degree course in Geography conducted by : University Department of Geography, Vidyanagari Campus, Kalina, Santacruz (East), Mumbai – 400 098. Phone: 2652 6091 (.....) - M.A. Degree Course
Name & Address: M.A. Degree Course : Marathi M.A. & M.Phil. degree courses in Marathi conducted by : University Department of Marathi, Vidyanagari (.....) - Human Resource Management
Introduction, personnel role today, characteristics of today's work force, job design analysis and evaluation, personnel planing, recruitment, induction, job appraisal, training and development, job rotation (.....) - Advanced Diploma Course in Russian
Advanced Diploma Course in Russian Duration: One year (part-time) Minimum Admission Requirement: 0.2679 Eligibility: A candidate for being eligible for admission to the Advanced Diploma Course in (.....) - Certificate course in Yoga
Certificate course in Yoga (conducted by department of philosophy Duration: One year (Part-time) Minimum Admission Requirement A candidate for being eligible for admission to the course for the Certificate (.....) - PHILOSOPHY
Courses Available: 1. M.A.(Pt.I) 2.M.A.(Pt.II) 3. M.Phil. 4. Ph.D. 5. Certificate in Jainology 6. Diploma in Jainology 7.P.G. Diploma in Jainology 8. Certificate in Yoga (.....) - Diploma in Public Health
Information about this course is coming soon. (.....) - Diploma in Virology
Information about this course is coming soon. (.....) - Export-Import procedures and documentation
National economic self-reliance, practices and problems of international marketing, regulations for international trade, export in world markets, import substitutions, export promotion, difficulties in foreign trade, (.....) - M.A. Degree Course -English
M.A. & M.Phil. degree courses in English conducted by : University Department of English,Vidyanagari Campus, Kalina, Santacruz (East), Mumbai – 400 098. Phone : (.....) - Elements of Logistics Management
Overview of logistics function, strategy and planning, logistics system fundamentals, transport system, logistics planning process, facilities location decisions, inventory policy, purchasing and product scheduling decisions, (.....) - Master of Dental Surgery
(.....) - M.Sc.(Home Science)
Master of Science (Home Science) M.Sc. (Home Science) Minimum Admission Requirement: 0.3540 The Bachelor of Science (Home Science) degree examination of this University or an examination (.....) - Bachelor of Fine Arts
Bachelor of Fine Arts Duration: Five years Minimum Admission Requirement The Secondary school Certificate examination held at the end of the Xth Standard conducted by the Maharashtra (.....) - M.A. Degree Course: Statistics
M.A. degree course in Statistics conducted by : University Department of Statistics, Vidyanagari Campus, Kalina, Santacruz (East), Mumbai – 400 098. Phone: 2652 6091 (.....)