Veja grátis o arquivo Geometria Analitica Steinbruch e Winterle enviado para a disciplina de Geometria Analítica Categoria: Outros – 27 – Ivan de C. e Oliveira e Paulo Boulos, “Geometria Analítica. Um Tratamento Alfredo Steinbruch e Paulo Winterle, “Álgebra Linear”, McGraw-Hill, Brasil, Algebra Linear .. Ciência e Engenharia de Materiais uma Calculo com Geometria analitica vol 2 – Louis Leithold

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Real numbers, decimal representation. Limit of a function, limits at infinity and asymptotes. Derivatives of elementary functions and their graphs. The fundamental theorem of calculus, antiderivatives.

Volumes I e II. Prentice-Hall do Brasil, Courses with same content in the undergraduate and graduate programs are indicated by “SD” in each syllabus.

Review of topology and continuity of real functions. Integration in the sense geomtria Riemann. The Fundamental Theorem of Calculus. Power series and analytic functions. The Theorem of Arzela-Ascoli. geoometria


Introduction to harmonic analysis and Fourier series. Mathematical Association of America, Numbers, approximations of real numbers with sequences. Solution of equations and inequalities. Coordinate geometry, equations, lines, parabolas, equilateral hyperbola and circles. Affine function, quadratic function, polynomial and rational functions, roots. Derivatives of Trigonometric functions. Differentiation rules, including the chain rule.

Exponential and logarithm functions. Derivatives of inverse functions. Definite integrals, indefinite integrals. Continuity and differentiability of functions of 2 and 3 variables: Double and triple integrals in Cartesian, polar, cylindrical and spherical coordinates.

Vector functions and their derivatives: The general chain-rule and the inverse function theorem. Double and triple integrals: Path integrals, conservative fields and scalar potentials. Curl and divergence operators; the vector potential.

The implicit function theorem. Surface integrals for scalar fields.

Oriented surfaces and surface integrals for vector fields. Stokes and Gauss’ theorems. Differential equations of the first order: Separable, exact and linear differential equations of the first order homogeneous and nonhomogeneous.


Linear difference equations of first order with constant coefficients. Linear differential and difference equations of the second order with constant coefficients. Linear systems in the plane. Power series resolution of differential equations. Systems of linear equations. Cartesian coordinates in two and three dimensions.

Vectors, scalar product, determinants, vector product, triple product. Sequences; sequence limits; subsections; series; convergence criteria; comparison, geometia reason; alternating series; power series; Taylor series; Fourier series. Cartesian coordinates in plane and space. Vectors in the plane and space.

Determinant as area and volume.

Equations of straight line and equations of planes. Change of coordinates and linear transformation. Implicit functions and their derivatives. Geometric meaning of derivative tangent and normal to a curve.

Definite and indefinite integrals. Real numbers; Equations and linear systems; the quadratic equation; elementary functions and graphic representation, limits and continuity of functions. In all the previous topics there are examples and applications related to Management. Matrix Algebra; Input-output analysis; Derivation of functions of a real variable and its applications when plotting.

Maximum and minimum; Marginal analysis, related rates, optimization process. In all the previous topics there are examples and applications related to Management.

Function of more than one variable, partial derivatives, maximum and minimum conditional; integration; Marginal analysis, consumer and producer surplus; Linear differential equations of the first order and those of differential variables.

Matrices, determinants and systems of linear equations. Plane and space vectors. Distance between two points. Midpoint of a segment. Inner product and dot product. Angle between two vectors. Cross product and mixed product. Parametric equations of the line and plane. Vector spaces real vector spaces, linear subspaces, dependent and independent linear equation, vector space base, base change.

Linear transformations definition, core and image of a linear transformation, applications of linear equations and matrices.

Linear Algebra And Analytical Geometry I

Eigenvalues and eigenvectors Eigenvalues and Eigenvectors matrix calculus, diagonalization of operator: A detailed study of certain key topics, such as Euclid’s Elements, the creation of calculus by Newton and Leibniz and the discovery of Non-Euclidean Geometry.


Brief presentation of other linar moments with the intent of creating a general and broad view of the organic development of Mathematics. Other highlighted topics presented are the origins of concepts and notations, ways of thinking and different mathematicians points of view alongside history.

Kernel, image and the rank—nullity theorem. Eigenvalues and eigenvectors with numerical methods. Harcourt Brace Linera, Fields, analirica spaces, bases, dimension, matrix algebra, linear operators. Eigenvalues, eigenvectors, invariant subspaces. Real and complex Jordan forms. Self-adjoint operators, symmetric matrices. Rings, polynomial rings, Ideals. Field of fractions of an integral domain.

Homomorphisms and quotient groups. Fields and Field extensions. Characteristic of a field.

Álgebra linear e geometria analítica – Alfredo Steinbruch – Google Books

Constructions by ruler and compass. Examples of low degree. Resolution of polynomials equations of degree 3 and 4 in one variable.

Solvable groups, resolution by radicals. Examples of equations that cannot be solved by radicals. Vector and matrix norms, orthogonal projections. Matrix algebra algorithms with rounding error analysis.

System of linear equations: LU decomposition, positive definite systems, band symmetric, bloc and sparse matrices. QR and SVD decompositions with applications. Iterative methods, Krylov subspace methods, conjugate gradient and related methods.

Algorithms for eigenvalue decomposition. Johns Hopkins University Press, Splines; geometric interpolation; Delaunay triangulations; mesh data structure; parametric and implicit surfaces; boolean operations. Set theory, functions and relations.