Differential and Integral Calculus

2.1 The definite integral		2.3.9 The Approximate Representation of Arbitrary Functions by Linear Functions. Differentiation
2.1.1 The integral as an Area		2.3.10. Remarks on Applications to the Naturali Sciences
2.1.2 The Analytical Definition of the Integral		2.4. The Indefinite Integral, the Primitive Function and the Fundamental Theorems of the Differential and Integral Calculus
2.1.3 Extensions. Notation. Fundamental Rules		2.4.1 The Integral as a Function of the Upper Limit
2.2. Examples		2.4.2 The Derivative of the Indefinite Integral
2.2.1. Integration of a Linear Function		2.4.3 The Primitive Function; General Definition of the Indefinite Integral
2.2.2 Integration of x²		2.4.4 The use of the Primitive Function in the Evaluation of Definite Integrals
2.2.3 Integration of x^a, where a is any positive integer		2.4.5 Examples
2.2.4 Integration of x^a, where a is any Rational Number other than -1		2.5 Simple Methods of Graphical Integration
2.2.5 Integration of sin x and cos x		2.6. Further Remarks on the Connection between the Integral and the Derivative
2.3 The Derivative		2.6.1 Mass Distribution and Density; Total Quantity and Specific Quantity
2.3.1 The Derivative and the Tangent		2.6.2 The Question of Applications
2.3.2 The Derivative as a Velocity:		2.7 The estimation of Integrals and the mean Value Theorem of the Integral Calculus
2.3.3 Examples		2.7.1 The Mean Value Theorem of the Integral Calculus
2.3.4. Some Fundamental Rules of Differentiation		2.7.2 Applications. The Integratioa of x^a for any Irrational Value of a
2.3.5 Differentiability and Continuity of functions		2.7.3 Exercises
2.3.6. Higher Derivatives and their Significance		Appendix to Chapter II
2.3.7 The Derivative and the Difference Quotient		A2.1 The Existence of the Definite Integral of a Continuous Function
2.3.8 The Mean Value Theorem		A2.2 The Relation between the Mean Value Theorem of the Differential Calculus and the Mean Value Theorem of the Integral Calculus