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Modeling 2 1. Modeling 12 1. Integrating Factors 20 1. Bernoulli Equation. Population Dynamics 27 1. Optional 36 1. Optional 60 2. Wronskian 74 2. Resonance 85 2. Phase Plane. Qualitative Methods 4. Wronskian 4. Phase Plane Method 4.

Stability 4. Special Functions 5. Legendre Polynomials Pn x 5. Bessel Functions Jv x 5. First Shifting Theorem s-Shifting 6. ODEs 6. Second Shifting Theorem t-Shifting 6. Partial Fractions 6. Integral Equations 6. ODEs with Variable Coefficients 6. Linear Systems 7. Gauss Elimination 7. Rank of a Matrix. Vector Space 7. Gauss—Jordan Elimination 7. Linear Transformations. Determining Eigenvalues and Eigenvectors 8. Quadratic Forms 8. Grad, Div, Curl 9. Vector Calculus: Derivatives 9.

Arc Length. Torsion 9. Optional 9. Directional Derivative 9. Integral Theorems Optional Divergence Theorem of Gauss Even and Odd Functions.

Half-Range Expansions Orthogonal Functions Generalized Fourier Series Discrete and Fast Fourier Transforms Use of Fourier Series Characteristics Heat Equation Steady Two-Dimensional Heat Problems.

Dirichlet Problem Solution by Fourier Integrals and Transforms Double Fourier Series Circular Membrane. Fourier—Bessel Series Potential Complex Differentiation Powers and Roots Analytic Function General Power.

Residue Integration Infinity Modeling Irregular Boundary Linear Programming Unconstrained Optimization: Method of Steepest Descent Combinatorial Optimization Complexity Probability Theory Spread Probability Distributions Random Sampling Decisions Fitting Straight Lines.

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## Advanced Engineering Mathematics 10th Edition

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