# Mathematics for Degree Students B. Sc. 1St Yr, 2/e Authors : P K Mittal

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P K Mittal :- M.Sc., Ph.D., Head of Mathematics Deptt. Govt. Post Graduate College, RISHIKESH

•; As per the UGC Model Curriculum including *Algebra and Trignometry *Differential & Integral Calculus *Ordinary Differential Equations *Vector Analysis and Geometry.

•; Illustrative Solved Examples and Up-to-date Questions added of different important Indian Universities.

•; Objective Type Questions given as per the requirement of the topic.

#### Contents

BMH 101 (A & B) Algebraand Trigonometry:Algebra, 1. Functions and Relations, 2. Congruence of Integers, 3. Some Special Types of Matrices, 4. Elementary Operations and Inverse of a Matrix , 5. Linear Dependence of Vectors, 6. Rank of a Matrix, 7. Linear Equations, 8. Characteristic Roots and Vectors, 9. Theory of Equations,10. Group, 11. Permutations, 12. Homomorphism and Isomorphism, 13. Normal Sub-Groups, 14. Rings and Subrings, 15. Integral Domain and Field, Trigonometry: 1. De Moivre's Theorem and Deductions, 2. Hyperbolic Functions, 3. Inverse Hyperbolic Functions, 4. Logarithms, of Complex Quantities, 5. Gregory's Series, 6. Trigonometrical Expansions, 7. Summation of Series, BMH 102 (A & B) Calculus: Differential Calculus: 1. Limits and Continuity, 2. Differentiability, 3. Successive Differentiation, 4. Expansion of Functions, 5. Asymptotes, 6. Curvature, 7. Concavity, Convexity and Singular Points, 8. Curve Tracing, Integral Calculus: 1. Integration of Irrational Algebraic Functions, 2. Integration of anscendental Functions, 3. Reduction Formulae, 4. Definite Integrals, 5. Area of Curves (Quadrature), 6. Lengths of Curves (Rectification), 7. Volume and Surface of Solid and Revolution, Ordinary Differential Equations: 1. Differential Equations: An Introduction, 2. Differential Equations of First Order and First Degree, 3. Differential Equations of First Order but not of First Degree, 4. Geometrical Interpretation and Orthogonal Trajections, 5. Linear Differential Equations with Constant Coefficients, 6. Homogeneous Linear Differential Equations, 7. Linear Differential Equations of Second Order with Variable Coefficients, 8. Simultaneous Ordinary Differential Equations, BMH 103 (A & B) Vector Analysis and Geometry: Vector Analysis: 1. Multiple Products, 2. Differential of Vectors, 3. Differential Operators, 4. Integration of 1Vectors, 5. Gauss's Green's and Stoke's Theorem, Geometry: [(a) Two-Dimensional]: 1. General Equation of Second Degree and Tracing of Conics, 2. System of Conics: Confocal Conics, 3. Polar Equations, [(b) Three- Dimensional], 1. Systems of Coordinates, 2. The Plane, 3. The Straight Line, 4. The Sphere, 5. Cones, Cylinders, 6. Coincide, 7. Plane Section of Conicoids, 8. Generating Lines of Conicoids, 9. General Equation of the Second Degree, 10. Confocal Conicoids