CONTENTS

Preface —Pgs. v

Joint Admission Test for M Sc (JAM) —Pgs. vii

MODULE I

1. Sequences and Series of Real Numbers —Pgs. 3

1.1 Sequence and Series —Pgs. 3

1.2 Bounds of A Sequence —Pgs. 7

1.3 Oscillatory Sequence —Pgs. 9

1.4 Algebra of Sequence —Pgs. 13

1.5 Cauchy Sequence —Pgs. 14

1.6 Infinite Series —Pgs. 16

1.7 Tests for Series —Pgs. 19

Mock Test Module I  —Pgs. 37

MODULE II

2. Functions of One, Two or Three Real Variables I —Pgs.49

2.1 Differentiation —Pgs. 49

2.2 Mean Value Theorem —Pgs. 51

2.3 Indeterminate Forms —Pgs. 56

3. Functions of One, Two or Three Real Variables II —Pgs. 87

3.1 Differential Coefficients —Pgs. 87

3.2 Rules for Differentiation —Pgs. 87

4. Functions of One, Two or Three Real Variables III —Pgs.113

4.1 Applications of Derivatives —Pgs. 113

4.2 Maximum and Minimum —Pgs. 113

4.3 Monotonic Function —Pgs. 114

4.4 Rolle’s and Lagrange’s Theorem —Pgs. 115

Mock Test Module II —Pgs. 151

MODULE III

5. Integration I —Pgs. 167

5.1 Indefinite Integration —Pgs. 167

5.2 Rules and Methods of Integration —Pgs. 167

5.3 Integration of Rational Fractions —Pgs. 169

5.4 Integration of Irrational Fractions —Pgs. 170

6. Integration II —Pgs. 201

6.1 Definite Integration —Pgs. 201

6.2 Definite Integration and Areas —Pgs. 202

6.3 Sketches of Curves —Pgs. 203

6.4 Line Integral —Pgs. 204

6.5 Double Integrals —Pgs. 205

6.6 Triple Integrals —Pgs. 208

6.7 Stoke’s and Gauss Divergence Theorem —Pgs. 210

Mock Test Module III —Pgs. 241

MODULE IV

7. Differential Equations —Pgs. 257

7.1 Differential Equations —Pgs. 257

7.2 Formation of Differential Equation —Pgs. 258

7.3 Solution of Differential Equation —Pgs. 258

7.4 Tangent and Normal —Pgs. 259

7.5 Equation Reducible To A Linear Form —Pgs. 259

7.6 Applications of Differential Equations —Pgs. 265

7.7 Trajectories —Pgs. 266

7.8 Particular Integral —Pgs. 269

7.9 Homogeneous Linear Equation —Pgs. 271

Mock Test Module IV —Pgs. 303

MODULE V

8. Vector Algebra —Pgs. 319

8.1 Vectors and Their Representation —Pgs. 319

8.2 Straight Lines —Pgs. 320

8.3 Plane —Pgs. 321

8.4 Product of Vectors —Pgs. 321

9. Vector Calculus —Pgs. 353

9.1 Differential Operators —Pgs. 353

9.2 Vector Identities —Pgs. 358

9.3 Gauss’s, Stoke’s and Green’s Theorems —Pgs. 360

Mock Test Module V —Pgs. 391

MODULE VI

10. Group Theory —Pgs. 403

10.1 Integer —Pgs. 403

10.2 Group Theory —Pgs. 403

10.3 Subgroup —Pgs. 407

10.4 Homomorphism —Pgs. 414

10.5 Isomorphism —Pgs. 414

10.6 Automorphism —Pgs. 416

11. Linear Algebra —Pgs. 439

11.1 Vector Space —Pgs. 439

11.2 Vector Subspaces —Pgs. 440

11.3 Algebra of Subspaces —Pgs. 441

11.4 Isomorphism —Pgs. 442

11.5 Linear Functional —Pgs. 444

11.6 Linear Transformations —Pgs. 445

11.7 Matrices —Pgs. 450

11.8 Invariance and Reducibility —Pgs. 455

11.9 Matrix of A Projection —Pgs. 457

12. Real Analysis —Pgs. 481

12.1 Power Series —Pgs. 481

12.2 Differentiation and Integration of Ps —Pgs. 481

Mock Test Module VI —Pgs. 489

MOCK TEST MATHEMATICS —Pgs. 503

Being an M. Sc. (Physics) from the University of Rajasthan, Subhash Jain is an experienced educator and teacher-trainer, and an enthusiastic presenter, who has conducted numerous workshops, training seminars, professional development programmes, and consultations for educators and parents for over twenty years. He has also trained teachers of six senior secondary schools of NIMS, Dubai. Some of his papers and articles have been published in national and international newspapers, journals and magazines. One of his published books, How to Prepare for HT-JEE' is an informative/instructive publication for students preparing for the HT-JEE examinations.