MATLAB Mathematical Analysis

MATLAB Mathematical Analysis is a reference book that presents the techniques of mathematical analysis through examples and exercises resolved with MATLAB software. The purpose is to give you examples of the mathematical analysis functions offered by MATLAB so that you can use them in your daily work regardless of the application. The book supposes proper training in the mathematics and so presents the basic knowledge required to be able to use MATLAB for calculational or symbolic solutions to your problems for a vast amount of MATLAB functions. The book begins by introducing the reader to the use of numbers, operators, variables and functions in the MATLAB environment. Then it delves into working with complex variables. A large section is devoted to working with and developing graphical representations of curves, surfaces and volumes. MATLAB functions allow working with two-dimensional and three-dimensional graphics, statistical graphs, curves and surfaces in explicit, implicit, parametric and polar coordinates. Additional work implements twisted curves, surfaces, meshes, contours, volumes and graphical interpolation. The following part covers limits, functions, continuity and numerical and power series. Then differentiation is addressed in one and several variables including differential theorems for vector fields. Thereafter the topic of integration is handled including improper integrals, definite and indefinite integration, integration in multiple variables and multiple integrals and their applications. Differential equations are exemplified in detail, Laplace transforms, Tayor series, and the Runga-Kutta method and partial differential equations. Curves in Explicit, Implicit, Parametric and Polar CoordinatesThree-Dimensional (3D) Curves; Explicit and Parametric Surfaces: Contour Plots; Three-Dimensional Geometric Forms; Specialized Graphics; 2D and 3D Graphics Options; Chapter 5: Limits of Sequences and Functions. Continuity in One and Several Variables; Limits; Sequences of Functions; Continuity; Limits in Several Variables. Iterated and Directional Limits; Continuity in Several Variables; Chapter 6: Numerical Series and Power Series; Numerical Series of Non-negative Terms; Convergence Criteria: The Ratio Test; Raabe's Criterion Elements of Matrix VariablesSpecific Matrix Functions; Random Numbers; Operators; Arithmetic Operators; Logical Operators; Relational Operators; Symbolic Variables; Symbolic Functions and Functional Operations: Composite and Inverse Functions; Commands that Handle Variables in the Workspace and Store them in Files; Chapter 3: Complex Numbers and Functions of Complex Variables; Complex Numbers; General Functions of Complex Variables; Trigonometric Functions of a Complex Variable; Hyperbolic Functions of a Complex Variable; Exponential and Logarithmic Functions of a Complex Variable The Root TestOther Convergence Criteria; Alternating Numerical Series. Dirichlet and Abel's Criteria; Power Series; Power Series Expansions; Chapter 7: Derivatives. One and Several Variables; Derivatives; Partial Derivatives; Applications of Differentiation. Tangents, Asymptotes, Extreme Points and Points of Inflection; Differentiation in Several Variables; Extreme Points in Several Variables; Conditional minima and maxima. The method of "Lagrange multipliers"; Vector Differential Calculus; The Composite Function Theorem; The Implicit Function Theorem; The Inverse Function Theorem Specific Functions of a Complex VariableBasic Functions with a Complex Vector Argument; Basic Functions with a Complex Matrix Argument; General Functions with a Complex Matrix Argument; Trigonometric Functions of a Complex Matrix Variable; Hyperbolic Functions of a Complex Matrix Variable; Exponential and Logarithmic Functions of a Complex Matrix Variable; Specific Functions of Complex Matrix Variables; Operations with Real and Complex Matrix Variables; Chapter 4: Graphics in MATLAB. Curves, Surfaces and Volumes; Introduction; Exploratory Graphics López, César Pérez.