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Introduces engineers, computer scientists, and physicists to advanced math topics as they relate to practical problems. The material is arranged into seven independent parts: ODE; Linear Algebra, Vector calculus; Fourier Analysis and Partial Differential Equations; Complex Analysis; Numerical methods; Optimization, graphs; Probability and Statistics.
ORDINARY DIFFERENTIAL EQUATIONS.
First-Order Differential Equations.
Linear Differential Equations of Second and Higher Order.
Systems of Differential Equations.
Series Solutions of Differential Equations.
Laplace Transforms.
LINEAR ALGEBRA, VECTOR CALCULUS.
Matrices, Linear Systems of Equations.
Linear Algebra: Matrix Eigenvalue Problems.
Vector Differential Calculus.
Vector Integral Calculus.
FOURIER ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS.
Fourier Series, Integrals, and Transforms.
Partial Differential Equations.
COMPLEX ANALYSIS.
Complex Numbers and Functions.
Complex Integration.
Power Series, Taylor Series.
Laurent Series, Residue Integration.
Complex Analysis Applied to Potential Theory.
NUMERICAL METHODS.
Numerical Methods in General.
Numerical Methods in Linear Algebra.
Numerical Methods for Differential Equations.
OPTIMIZATION, GRAPHS.
Unconstrained Optimization, Linear Programming.
Graphs and Combinatorial Optimization.
PROBABILITY AND STATISTICS.
Data Analysis: Probability Theory.
Mathematical Statistics.
Appendices.
Index.
Introduces engineers, computer scientists, and physicists to advanced math topics as they relate to practical problems. The material is arranged into seven independent parts: ODE; Linear Algebra, Vector calculus; Fourier Analysis and Partial Differential Equations; Complex Analysis; Numerical methods; Optimization, graphs; Probability and Statistics.
Table of Contents
ORDINARY DIFFERENTIAL EQUATIONS.
First-Order Differential Equations.
Linear Differential Equations of Second and Higher Order.
Systems of Differential Equations.
Series Solutions of Differential Equations.
Laplace Transforms.
LINEAR ALGEBRA, VECTOR CALCULUS.
Matrices, Linear Systems of Equations.
Linear Algebra: Matrix Eigenvalue Problems.
Vector Differential Calculus.
Vector Integral Calculus.
FOURIER ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS.
Fourier Series, Integrals, and Transforms.
Partial Differential Equations.
COMPLEX ANALYSIS.
Complex Numbers and Functions.
Complex Integration.
Power Series, Taylor Series.
Laurent Series, Residue Integration.
Complex Analysis Applied to Potential Theory.
NUMERICAL METHODS.
Numerical Methods in General.
Numerical Methods in Linear Algebra.
Numerical Methods for Differential Equations.
OPTIMIZATION, GRAPHS.
Unconstrained Optimization, Linear Programming.
Graphs and Combinatorial Optimization.
PROBABILITY AND STATISTICS.
Data Analysis: Probability Theory.
Mathematical Statistics.
Appendices.
Index.