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Calculus 1 Dedication 2 Preface 3 Syllabus 4 Brief Contents 5 DIFFERENTIAL CALCULUS-1 6 DIFFERENTIAL CALCULUS-2 7 1. Differentiation 8 2. Successive Differentiation 24 3. Expansions of Functions 44 4. Partial Differentiation 58 5. Change of Independent Variables 74 6. Tangents and Normals 92 7. Curvature 114 8. Envelopes, Evolutes and Involutes 136 9. Asymptotes 158 10. Singular Points: Curve Tracing 184 INTEGRAL CALCULUS-1 226 INTEGRAL CALCULUS-2 227 1. Reduction Formulae (For Trigonometric Functions) 228 2. Reduction Formulae Continued (For Irrational Algebraic and Transcendental Functions) 256 3. Beta and Gamma Functions 270 4. Multiple Integrals 300 5. Dirichlet's and Liouville's Integrals 330 6. Areas of Curves 346 7. Rectification (Lengths of Arcs and Intrinsic Equations of Plane Curves) 370 8. Volumes and Surfaces of Solids of Revolution 392 9. Definite Integrals 424 10. Differentiation and Integration under the Sign of Integration 447

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