Fundamentals of Mathematics for Environmental Science (250554) – Course 2024/25 PDF
Contents
Basic definitions and types of matrices. Elemental row operations, Gauss method, rank of an array. Matrix transposed from a matrix; elementary column posts. Systems of linear equations. Elimination of parameters. Determinants. Definitions of linear and product combinations of matrices. Transposed matrix, determinant and rank of the matrix product. Relationship between matrix product and elementary operations. Regular matrices Calculation of the inverse matrix by the Gauss method and by determinants. Matrix of a linear application; Rotations and symmetries in the plane and space. Translations. Treatment with Matlab.
Specific Objectives
Learn how to use the matrices to solve certain types of problems. In particular, how to solve systems of linear equations. Use examples to illustrate poorly conditioned systems of linear equations Learn how to manipulate matrices loosely, and solve the problems for which they are especially useful. Learn how to use the matrices to solve certain types of problems. In particular, how to solve systems of linear equations. Use examples to illustrate poorly conditioned systems of linear equations
Dedication
7h 30m Large group + 7h 30m Medium group + 22h 30m Self StudyElemental functions Limits and indeterminations. Continuity. Functions defined in pieces. Derivability; Derivation rules, chain rule, logarithmic derivative. Extrema of a function. Drawing of functions: by hand and with Matlab.
Specific Objectives
Remember the basics of the differential calculation of a variable. Treatment of functions with Matlab. Know how to identify when a function is or not differentiable at a point. Solve optimization problems.
Dedication
7h 30m Large group + 7h 30m Medium group + 22h 30m Self StudyThe integral defined as an area under a curve. Primitives and Barrow rule. Change of variable. Calculation of areas and volumes of revolution. Numerical integration (trapezoidal rule, Simpson). Treatment with Matlab.
Specific Objectives
Learn to interpret the integral defined as an area under a curve, and the relationship between integrals and primitives. See how the value of an integral can be numerically approximated. Calculate integrals with Matlab. See applications of the integral in the calculation of areas, volumes of revolution, etc. Learn the utilities of the integral calculation. Know how to calculate integrals defined both analytically and numerically.
Dedication
7h 30m Large group + 7h 30m Medium group + 22h 30m Self StudyAffine space concept. Linear varieties: points, straight lines and planes. Straight line and plane equations. Relative positions. Perpendicularity. Distance between two linear varieties. Parameterization of curves.
Specific Objectives
Remember the concepts related to geometry in the plane and space. Acquire knowledge about curve parameterization Solve problems of incidence, relative position and perpendicularity of linear varieties. Know how to perform the parameterization of some curves Individual help students in the difficulties that can be encountered when trying to solve a problem
Dedication
7h 30m Large group + 7h 30m Medium group + 22h 30m Self Study