Basics of analysis

Basics of analysis

Usual functions and properties (integer and non-integer powers, absolute value, exp and ln)
Reciprocal bijection, formula for derivative of reciprocal bijection, trigo functions, reciprocal trigo functions
Hyperbolic functions, (no hyperbolic trigonometry,) only formula on ch^2-sh^2
Calculations on trigonometry
Parity, limits, domain of definition
IPP to be reviewed in exercises
Example of the integer part to be addressed


Differential equations with constant coefficients

First-order differential equations with constant coefficients and second member.
Exponential or trigonal form for the second member
Solution structure theorem, theorem on the particular solution form
Example using complexes for a lambda*e^{imx} second member


Linear differential equations of order 1

Definition, Structure of solutions , Study plan
Solution of the homogeneous equation, Search for a particular solution (obvious solution, cases already studied, method of varying the constant), Principle of superposition
Cauchy problem