This book covers the following topics: The
Exponential Function, Exponentials and Logarithms, Exponential Models,
Recursion, Recursive Models, Investigating Recursive Models, The Derivative,
Discovering the Derivative, The Derivative at a Point, The Derivative of a
Function, Computing the Derivative, The Power Rule, Linearity, Products and
Quotients, Exponentials and Logarithms, The Chain Rule, Interpreting and
Using the Derivative, Curve Sketching, Newton’s Method, The Chain Rule
Revisited, Marginals, Linear Optimization, Simple Examples, More
Complicated, Shadow Prices Lagrange Multipliers, The Integral,
Antiderivatives, The Definite Integral, Riemann Sums, Interpreting and Using
the Integral, Anti Rates, Area, Probability, Quantities in Economics, Matrix
Algebra, Matrix Arithmetic, Applications of Matrix Algebra, Linear
Equations, Equations and Solutions, Matrix Inverse, Applications of Linear
Equations, Partial Derivatives, Partial derivatives, Higher Order
Derivatives, The Chain Rule, Non Linear Optimization, The First Derivative
Test, Lagrange Multipliers, Fitting a Model to Data, Spread sheet Formulas,
Function Values, Recursion Calculations and Matrix Calculations.
This note covers boundary value
problems in one dimension, Fourier series,Fourier analysis,
Vibration and diffusion in one dimensional media, The planar laplace equation,
Complex analysis, Dynamics of planar media, Partial differential equations in
space, Nonlinear systems, Nonlinear ordinary differential
equations, The calculus of variations, Nonlinear partial differential
equations.
This Lecture note explains the following topics: Elementary Matrix Theory, Vector Spaces,
Linear Transformations, Vector Spaces with Inner Product, Eigenvalue
Problems and Additional Topics Relating to Eigenvalue Problems.
Author(s): Ray M.Bowen, University College Station
Texas
These are notes
on various topics in applied mathematics.Major topics covered are:
Differential Equations, Qualitative Analysis of ODEs, The Trans-Atlantic
Cable, The Laplace Transform and the Ozone Layer, The Finite Fourier
Transform, Transmission and Remote Sensing, Properties of the Fourier
Transform, Transmission Tomography,The ART and MART, Vectors,A Brief History
of Electromagnetism, Changing Variables in Multiple Integrals, Kepler’s Laws
of Planetary Motion, Green’s Theorem, Complex Analysis, The Quest for
Invisibility, Calculus of Variations, Bessel’s Equations, Hermite’s
Equations and Quantum Mechanics.
This book explains the
following topics: Linear Equations, Matrices, Linear Programming, Mathematics of
Finance, Sets and Counting, Probability, Markov Chains, Game Theory.
This note explains the
following topics: Linear Algebra, Fourier series, Fourier transforms, Complex
integration, Distributions, Bounded Operators, Densely Defined Closed Operators,
Normal operators, Calculus of Variations, Perturbation theory.
This Handbook of Mathematics is designed to contain, in compact form,
accurate statements of those facts and formulas of pure mathematics which are
most likely to be useful to the worker in applied mathematics. Many topics of
an elementary character are presented in a form which permits of immediate
utilization even by readers who have had no previous acquaintance with the
subject; for example, the practical use of logarithms and logarithmic
cross-section paper, and the elementary parts of the modern method of
nomography (alignment charts), can be learned from this book without the
necessity of consulting separate treatises.
This lecture note covers the
following topics related to applied mathematics: Dimensional Analysis, Scaling,
and Similarity, Calculus of Variations, Sturm-Liouville Eigenvalue Problems and
Stochastic Processes.
This book covers
the following topics in applied mathematics: Dimensional Analysis,
Scaling and Similarity, Calculus of Variations, Sturm-Liouville Eigenvalue
Problems and Stochastic Processes.
Derivations
of Applied Mathematics is a book of applied mathematical proofs. This book
covers the following topics in applied mathematics: Classical algebra and
geometry, Trigonometry, derivative, The complex exponential, Primes, roots and
averages, Taylor series, Integration techniques, Matrices and vectors,
Transforms and special functions.
This text concentrates on mathematical
concepts rather than on details of calculations, which are often done with
software, such as Maple or Mathematica. The book is targeted at engineering
students who have had two years of calculus, introductory linear algebra, and
introductory ordinary differential equations.
This book covers the following topics in applied mathematics: Linear
Algebraic Systems, Vector Spaces and Bases, Inner Products and Norms,
Minimization and Least Squares Approximation, Orthogonality, Equilibrium,
Linearity, Eigenvalues, Linear Dynamical Systems, Iteration of Linear Systems,
Boundary Value Problems in One Dimension, Fourier Series, Fourier Analysis,
Vibration and Diffusion in One-Dimensional Media, The Laplace Equation, Complex
Analysis, Dynamics of Planar Media, Partial Differential Equations in Space,
Nonlinear Systems, Nonlinear Ordinary Differential Equations, The Calculus of
Variations and Nonlinear Partial Differential Equations.
This course note develops mathematical techniques which
are useful in solving `real-world' problems involving differential equations,
and is a development of ideas which arise in the second year differential
equations course. This note embraces the ethos of mathematical modelling, and
aims to show in a practical way how equations `work', and what kinds of
solution behaviours can occur.