This book presents the techniques of mathematical analysis through examples and exercises resolved with MATLAB software. The sections of your content are as follows: Introduction And MATLAB environment Numerical calculus with Matlab Symbolic calculus with Matlab Matlab and maple Graphics with Matlab Environment and general notation Help with commands Escape and exit commands to the MS-DOS environment Matlab and programming Limits and continuity. One and several variables Limits of successions Functions limits. Lateral limits Successions functions Continuity Several variables: limits and continuity. Characterization theorems Iterated and directional limits Continuity in several variables Numerical series and power series Series. Convergence criteria Numerical series with not negative terms Numerical alternate series Powers series Formal powers series Development power series and functions Developments in Taylor, Laurent, Pade and Chebyshev series Derivatives And applications, one and several VARIABLES Derivative concept Calculation derivative Tangents, asymptotes, concavity, convexity, maximum, minimum, inflection points and growth Applications to practical problems Partial derivatives Implicit derivative Differentiation in several variables Maximum and minima of functions of several variables Maximum and conditioned minima. The method of "Lagrange multipliers" Some applications of the maxima and minima in several variables Vector differential calculus and theorems in several variables Vector differential calculus concepts The chain rule Theorem implicit function Inverse function theorem Change of variable theorem Taylor to n variables theorem Fields vector. Rotational, divergence and laplacian Transformation coordinate Integration and applications Immediate integrals Integration by substitution (or change of variable) Integration by parties Integration reduction and cyclic integration Definite integral Arc of curve length Area including between curves Revolution surfaces Volumes of revolution Curvilinear integrals Integration approximate numeric Improper integrals Parameter -dependent integrals Riemann integral Integration in several variables and applications Regions area and double integration Area surface by double integration Calculation volume by double integrals Calculation volumes and triple integrals Green theorem Divergence theorem Stokes theorem Differential equations Equations in separated variables Homogeneous differential equations Exact differential equations Linear differential equations Ordinary high -order equations Linear higher-order homogeneous in constant coefficients equations Homogeneous equations in constant coefficients, variation of parameters Non-homogeneous equations with variable coefficients. Cauchy -Euler equations Laplace transformed Systems homogeneous linear equations with constant coefficients Systems of non-homogeneous linear equations with constant coefficients Equations order and top grade one, linear and nonlinear, approximate methods Taylor series method The Runge -Kutta method Partial derivative equations Equations in finite differences