Algebra Unit 1 0. Historical Background .... i-xvi 1. Linear Dependence and Independence of Row and Column Matrices and Rank of Matrix .... 1-58 2. Characteristic Equation of a Matrix, Eigen Values and Eigen Vectors .... 59-86 Unit 2 3. Cayley-Hamilton Theorem .... 87-97 4. Application of Matrices to a System of Linear Equation .... 98-125 Vector Analysis Unit 3 5. Product of Four Vectors and Reciprocal Vectors .... 126-155 6. Vector Differentiation .... 156-174 7. Gradient, Divergence and Curl .... 175-237 Unit 4 8. Vector Integration .... 238-250 9. Theorem of Gauss, Theorem of Green and Stoke’s Theorem (Without Proof); and Problems Based on them .... 251-300 10. Application to Geometry .... 301-356 Geometry Unit 5 11. General Equation of Second Degree and Tracing of Conics .... 357-407 12. System of Conics .... 408-432 13. Cone .... 433-485 14. Cylinder and its Properties .... 486-504
Unit-I 0. Historical Background .... 1-4 1. Groups and Their Basic Properties .... 1-65 2. Subgroups .... 66-80 3. Cyclic Groups .... 81-93 4. Coset Decomposition, Lagrange’s and Fermat’s Theorem .... 94-113 5. Normal Subgroups .... 114-125 6. Quotient Groups .... 126-131 Unit-II 7. Homomorphism and Isomorphism of Groups, Fundamental Theorem of Homomorphism .... 132-151 8. Transformation and Permutation Group Sn (n < 5), Cayley’s Theorem .... 152-186 9. Group Automorphism, Inner Automorphism, Group of Automorphisms .... 187-206 Unit-III 10. Definition and Basic Properties of Rings, Subrings .... 207-232 11. Ring Homomorphism, Ideals, Quotient Ring .... 233-259 12. Polynomial Ringh .... 260-296 13. Integral Domain .... 297-310 14. Field .... 311-330 Unit-IV 15. Definition and Examples of Vector Space, Subspaces, Sum and Direct sum of Subspaces, Linear Span, Linear Dependence, Linear Independence and Their basic Properties .... 331-360 16. Basis, Finite Dimensional Vector Space and Dimension (Existence Theorem, Extension Theorem, Inoriance of the number of Elements), DImension of sum of Subspaces, Quonient Space and It Dimension .... 361-380 Unit-V 17. Linear Transformation and Its Representation as a Matrix .... 381-403 18. Algebra of Linear transformations, Rank-Nullity Theorem, Change of basis, Dual Space, Bi-dual Space and Natural Isomorphism Adjoint of a Linear Transformation .... 404-438 19. Eigen-Values and Eigen-Vectors of a Linear Transformation, Diagonalization .... 439-472
Unit-I 0. Historical Background .... i-iii 1. Field Structure and Ordered Structure of R, Intervals, Bounded and unbounded sets, Supremum and infimum, Completeness in R, Absolute value of a real Number .... 1-33 2. Sequence of Real Numbers, Limit of a Sequence, Bounded and Monotonic Sequences, Cauchy’s General Principle of Convergence, Algebra of Sequence and Some Important Theorems .... 34-80 Unit-II 3. Series of non-negative terms, Convergence of positive term series .... 81-146 4. Alternating Series and Leibrintr’s test, Absolute and conditional convergence of Series of real Terms .... 147-163 5. Uniform Continuity .... 164-185 6. Chain Rule of Differentiability .... 186-202 7. Mean Value Theorems and Their Geometrical Interpretations .... 203-228 Unit-III 8. Limit and continuity of functions of two variables .... 229-256 9. Change of Variables .... 257-280 10. Euler’s Theorem on Homogeneous Functions .... 281-294 11. Taylor’s Theorem For functions of two Variables .... 295-307 12. Jacobians .... 308-337 13. Maxima and Minima of Functions of Two Variables .... 338-354 14. Lagrange’s Multipliers Method .... 355-367 15. Beta and Gamma Functions .... 368-395 Unit-IV 16. Partial Differential Equations of The first order .... 396-415 17. Lagrange’s Solution .... 416-440 18. Some Special types of equations which can be solved easily by methods other than the general method .... 441-462 19. Charpit’s General Method .... 463-474 20. Partial Differential Equation of Second and Higher Order .... 475-485 Unit-V 21. Classification of Partial Differential Equations of Second Order .... 486-494 22. Homogeneous and Non-homogeneous Partial Differential Equations of Constant coefficients .... 495-541 23. Partial Differential Equations Reducible to Equtions with Constant Coefficients .... 542-551
Algebra Unit 1 0. Historical Background .... i-xvi 1. Linear Dependence and Independence of Row and Column Matrices and Rank of Matrix .... 1-58 2. Characteristic Equation of a Matrix, Eigen Values and Eigen Vectors .... 59-86 Unit 2 3. Cayley-Hamilton Theorem .... 87-97 4. Application of Matrices to a System of Linear Equation .... 98-125 Vector Analysis Unit 3 5. Product of Four Vectors and Reciprocal Vectors .... 126-155 6. Vector Differentiation .... 156-174 7. Gradient, Divergence and Curl .... 175-237 Unit 4 8. Vector Integration .... 238-250 9. Theorem of Gauss, Theorem of Green and Stoke’s Theorem (Without Proof); and Problems Based on them .... 251-300 10. Application to Geometry .... 301-356 Geometry Unit 5 11. General Equation of Second Degree and Tracing of Conics .... 357-407 12. System of Conics .... 408-432 13. Cone .... 433-485 14. Cylinder and its Properties .... 486-504
The Salmophasia fishes are included under the order – cypriniformes and belong to the family – Cyprinidae (Day, 1958). Most of the Salmophasia species are inhabitants of the tropical and subtropical waters. Man made reservoirs and lakes provide unique habitats for the fishery wealth of Karnataka. Reservoir ecosystems have been recognized for their great potential for fish production. At the present level of management, the average fish yield of Indian reservoirs is only between 10-16 kg/ha/year (Jhingran, 1991). The small reservoirs have the potential to yield more than 100-200 kg/ha. Siltation in the rivers and reservoirs, apart from diminishing the quantum of water flow results in the destruction of breeding grounds of fishes, migration of fishes and overall productivity of the reservoir. Siltation also affects the benthic population and the natural recruitment of fishes in the impounded waters. Reservoirs, like rivers are inevitably being affected by industrialization and urbanisation.
Motilal Nehru and Jawaharlal Nehru are both prominent Indian men in their own right. Motilal is known as a widely successful civil lawyer and a popular political figure, while Jawaharlal made his mark as a firm nationalist leader and possible heir of the Mahatma. This book serves as a discussion of Motilal’s life and achievements, and looks into the first four decades of Jawaharlal’s life. It shows that while the father–son tandem played different roles in the nationalist struggle of India, their close emotional bonds helped them influence each other. Their story can be combined with that of the Indian freedom movement. The book covers a number of important events in the lives of the Nehrus—from Motilal’s childhood in Agra, Jawaharlal’s acceptance into Trinity College, and Jawaharlal’s entry into the political arena, to the father–son conflict over the changing political atmosphere in India. This book also takes a look at several notable individuals who play important roles in Motilal and Jawaharlal’s lives. These include Annie Besant, the leader of the Home Rule movement, and Mahatma Gandhi, the fierce fighter for India’s independence.
One of twentieth-century India’s great polymaths, statesmen, and militant philosophers of equality, B. R. Ambedkar spent his life battling Untouchability and instigating the end of the caste system. In his 1948 book The Untouchables, he sought to trace the origin of the Dalit caste. Beef, Brahmins, and Broken Men is an annotated selection from this work, just as relevant now, when the oppression of and discrimination against Dalits remains pervasive. Ambedkar offers a deductive, and at times a speculative, history to propose a genealogy of Untouchability. He contends that modern-day Dalits are descendants of those Buddhists who were fenced out of caste society and rendered Untouchable by a resurgent Brahminism since the fourth century BCE. The Brahmins, whose Vedic cult originally involved the sacrifice of cows, adapted Buddhist ahimsa and vegetarianism to stigmatize outcaste Buddhists who were consumers of beef. The outcastes were soon relegated to the lowliest of occupations and prohibited from participation in civic life. To unearth this lost history, Ambedkar undertakes a forensic examination of a wide range of Brahminic literature. Heavily annotated with an emphasis on putting Ambedkar and recent scholarship into conversation, Beef, Brahmins, and Broken Men assumes urgency as India witnesses unprecedented violence against Dalits and Muslims in the name of cow protection.
This comprehensive and well known textbook deals with the characteristics, classification and life cycle of different species of fungi. While it provides a detailed account of bacteria, viruses, mycoplasma and lichens, it also discusses elementary plant pathology.
Clinical Diagnosis of Congenital Heart Disease is the latest edition of this comprehensive, highly illustrated guide to the diagnosis of congenital heart disease. Divided into 31 sections, each chapter discusses a different aspect of congenital heart disease, clearly explaining history, assessment, imaging, clinical diagnosis and management techniques. This third edition has been fully revised to provide the latest advances in the field, with in depth discussion on new diagnostic modalities. Each topic concludes with a summary of key points, and includes schematic diagrams depicting abnormal anatomy and its pathophysiological consequences. Key Points Highly illustrated guide to diagnosis of congenital heart disease Fully revised, third edition with in depth discussion on new diagnostic modalities Each topic features a summary of key points and schematic diagrams of abnormal anatomy Previous edition (9789351529125) published in 2015
The Rigveda mentions the use of herbal medicines. The use of herbal medicines has been neglected due to advent of western system of medicine. The peoples are turning to cheaper and easily available medicines which has less side effects.Karnataka is rich treasure of herbal medicines. In the last two decades there has been a remarkable interest in the use of herbal medicines. In India about 80%% of the drugs contain plant ingredients. India also has long history of herbal medicines. A large number of plants are used for preparation of herbal medicines ,are in the verge of extinction.Due to biotic pressure and modernization, the herbal medicines are depleting. Therefore, it is the need of the hour to establish gene banks, setting up of botanical gardens at species level, in-Vitro conservation and conservation in natural habitat.
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