Chapter 1: Limited Developments

1. Comparison relations

2. Limited developments in the vicinity of zero

(a) Definitions of a limited development and Taylor-Lagrange theorem

(b) Usual limited development

(c) Operations on limited developments

3. Limited developments in the vicinity of a point, in the vicinity of infinity and generalized

limited developments.

4. Applications of limited developments (calculation of limits, equations of tangent and

asymptote)

Chapter 2: Calculation of Primitives 

1. Definitions and properties (primitive, integral, and definite integral)

2. Integration methods

(a) Integration by parts

(b) Integration by change of variable

3. Integration of a rational fraction

4. Integration of a rational fraction in sin and cos

5. Integration of a rational fraction in exponential

6. Integration of a rational in sin(h) or cos(h).

Chapter 3: Differential Equations 

The main topics in this chapter are:

1. Definitions

2. First-order differential equations.

(a) Separable variable differential equations.

(b) Linear differential equations.

(c) Bernoulli differential equations.

(d) Homogeneous differential equations with respect to x and y :

3. Second-order linear differential equations with constant coefficients.