ANALYSIS:
- Apply the concepts of limit of a function at a point (both finite and infinite) and side boundary to study the continuity of a function and the existence of vertical asymptotes.
- Learn to apply the concept of limit of a function at infinity to study the existence of horizontal and oblique asymptotes.
- Knowing the algebraic properties calculation of limits, the types of uncertainty following: infinity divided by infinity, zero divided by zero, zero by infinity, infinity minus infinity (and not the way one high to infinity, infinite high zero, zero raised to zero) and techniques to solve them.
- Learn to determine the equation of the tangent and normal lines to the graph of a function at a point.
- Learn to distinguish between derivative function and derived from a function at a point. Learn to find the domain of differentiability of a function.
- Understand the relationship between continuity and differentiability of a function at a point.
- Learn to identify local properties of growth or decrease in a differentiable function at a point and intervals of monotony of a differentiable function.
- Learn to determine the differentiability of functions defined in pieces.
- Know how to apply the derivation theorem for composite functions (chain rule) and its application to the calculation of the derivatives of functions with no more than two compositions and the derivatives of inverse trigonometric functions .
- Know the L'Hôpital rule and know how to calculate limits apply to resolve uncertainties.
- Learn to recognize whether the critical points of a function (points with zero derivative) are local extrema or inflection points.
- Ability to apply the theory of functions continuous and differentiable functions for solving ends.
- Knowing roughly represent the graph of a function of the form y = f (x) including: domain, symmetry, periodicity, cutting with axes, asymptotes, intervals of increase and decrease, local extremes, intervals of concavity (f''(x) \u0026lt;0) and convex (f''(x)> 0) and inflection points.
- On the representation of a function or its derivative, to be able to get the information from the function (range, lateral limits, continuity, asymptotes, differentiability, growth and decline, etc.)..
- Given two functions, using analytical expressions or through their graphical representations, if one is able to recognize each other primitive.
- Knowing the relationship between two primitives of the same function.
- Given a family of primitives, namely to determine a pass through a given point.
- Know how to calculate indefinite integrals of rational functions in the roots of the denominator are real.
- Know the method of integration by parts and how to apply consistently.
- Learn the technique of integration by change of variable, both in the calculation of primitives in the calculation of definite integrals.
- Learn about the property linearity of the definite integral with respect to integrating and meet the additivity property with respect to the interval of integration.
- Know the monotony properties of the integral defined with respect to integrating.
- Knowing the geometric interpretation of the definite integral of a function (the area as the limit of upper and lower sums.)
- Understand the concept of integral function (or function area), and knowing the fundamental theorem of calculus and the rule of Barrow.
- Know how to calculate the area enclosures bounded by curved planes.
LINEAR ALGEBRA:
- Knowledge and skilled in matrix operations: addition, scalar product, transpose, matrix multiplication, and know when can be made and when not. Knowing the noncommutativity of the product.
- I know the identity matrix and the definition of inverse matrix. Knowing when a matrix has an inverse and, where appropriate, calculate (up to 3x3 matrices of order).
- Know how to calculate determinants of order 2 and order 3.
- Know the properties of determinants and know how to apply to the calculation of these.
- Knowing that three vectors in three dimensional space are linearly dependent if and only if the determinant is zero.
- Know how to calculate the rank of a matrix.
- Solve problems that may arise through a system of equations.
- Know how to express a system of linear equations in matrix form and introduce the concept of the extended matrix.
- Know what you are compatible systems (determinate and indeterminate) and incompatible.
- Learn classified (as determined compatible, compatible or incompatible unspecified) a system of linear equations with no more than three unknowns and depends, at most, a factor and, if necessary, to resolve.
GEOMETRY:
- Knowledge and skilled in operations with vectors in the plane and in space.
- Given a set of vectors, namely whether they are linearly independent or linearly dependent.
- Know how to calculate and identify the expressions of a line or a plane with parametric equations and implicit equations and moving from one expression to another.
- Know how to determine a point, line or plane from the defining properties (eg, the symmetric of the other with respect to a third party, the line through two points or the plane contains three points or a point and a line, etc.)..
- Know how to approach, interpret and solve the problems of incidence and parallelism between lines and planes as systems of linear equations.
- Know and apply the notion of a bundle of planes containing a line.
- Know the properties of the scalar product, their geometric interpretation and the Cauchy-Schwarz inequality.
- Know how to approach and solve problems reasonably metric, angular and squareness (eg, distances between points, lines and planes, axial symmetry, angles between lines and planes, normal vectors to a plane perpendicular to two common lines, etc.).
- Know the vector product of two vectors and apply knowledge to determine a vector perpendicular to two others, and to calculate areas of triangles and parallelograms.
- Know the mixed product of three vectors and how to apply to calculate the volume of a tetrahedron and a parallelepiped.
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