Calculus is the study of change, in the same way that is the study of shape and is the study of operations and their application to solving equations. This book covers the two major branches of calculus, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves). These two branches are related to each other by the fundamental theorem of calculus.


1. Limits and Continuity

2. Differentiability

3. Differentiation

4. Successive Differentiation

5. Expansions Of Functions

6. Indeterminate Forms

7. Partial Differentiation

8. Jacobians

9. Maxima And Minima Of Functions of Two Independent Variables

10. Tangents And Normals

11. Curvature

12. Envelopes, Evolutes And Involutes

13. Asymptotes

14. Singular Points : Curve Tracing


1. Reduction Formulae (For Trigonometric Functions)

2. Reduction Formulae Continued (For Irrational Algebraic And Transcendental Functions)

3. Beta And Gamma Functions

4. Multiple Integrals

5. Dirichlet's And Liouville's Integrals

6. Areas Of Curves

7. Rectification (Lengths of Arcs and Intrinsic Equations of Plane Curves)

8. Volumes And Surfaces Of Solids Of Revolution