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| Ordinary Differential Equations | |
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| First-Order Differential Equations Terminology and Separable Equations | |
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| Linear Equations | |
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| Exact Equations | |
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| Additional Applications | |
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| Existence and Uniqueness Questions | |
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| Direction Fields | |
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| Numerical Approximation of Solutions | |
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| Linear Second-Order Equations | |
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| Theory of the Linear Second-Order Equation | |
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| The Constant Coefficient Homogeneous Equation | |
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| Solutions of the Nonhomogeneous Equation | |
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| Spring Motion | |
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| The Laplace Transform Definition and Notation | |
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| Solution of Initial Value Problems | |
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| Shifting and the Heaviside Function | |
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| Convolution | |
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| Impulses and the Dirac Delta Function | |
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| Appendix on Partial Fractions Decompositions | |
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| Series Solutions Power Series Solutions | |
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| Frobenius Solutions | |
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| Vectors, Linear Algebra, and Systems of Linear Differential Equations | |
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| Algebra and Geometry of Vectors Vectors in the Plane and 3-Space | |
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| The Dot Product | |
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| The Cross Product | |
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| The Vector Space Rn | |
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| Matrices and Systems of Linear Equations Matrices | |
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| Linear Homogeneous Systems | |
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| Nonhomogeneous Systems of Linear Equations | |
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| Matrix Inverses | |
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| Determinants Definition of the Determinant | |
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| Evaluation of Determinants | |
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| Evaluationof Determinants | |
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| A Determinant Formula for A-1 | |
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| Cramer's Rule | |
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| Eigenvalues and Diagonalization Eigenvalues and Eigenvectors | |
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| Diagonalization | |
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| Some Special Matrices | |
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| Systems of Linear Differential Equations Systems of Linear Differential Equations | |
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| Solution of X_ = AX when a Is Constant | |
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| Solution of X_ = AX + G | |
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| Vector Analysis | |
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| Vector Differential Calculus Vector Functions of One Variable | |
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| Velocity and Curvature | |
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| Vector Fields and Streamlines | |
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| The Gradient Field | |
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| Divergence and Curl | |
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| Vector Integral Calculus | |
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| Line Integrals | |
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| Green's Theorem | |
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| An Extension of Green's Theorem | |
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| Potential Theory | |
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| Surface Integrals | |
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| Applications of Surface Integrals | |
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| The Divergence Theorem of Gauss | |
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| Stokes's Theorem | |
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| Fourier Analysis and Eigenfunction Expansions | |
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| Fourier Series the Fourier Series of a Function | |
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| Sine and Cosine Series | |
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| Derivatives and Integrals of Fourier Series | |
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| Complex Fourier Series | |
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| The Fourier Integral and Transforms | |
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| The Fourier Integral | |
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| Fourier Cosine and Sine Integrals | |
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| The Fourier Transform | |
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| Fourier Cosine and Sine Transforms | |
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| Eigenfunction Expansions General Eigenfunction Expansions | |
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| Fourier-Legendre Expansions | |
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| Fourier-Bessel Expansions | |
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| Partial Differential Equations | |
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| The Wave Equation Derivation of the Equation | |
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| Wave Motion on an Interval | |
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| Wave Motion in an Infinite Medium | |
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| Wave Motion in a Semi-Infinite Medium. d'Alembert's Solution | |
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| Vibrations in a Circular Membrane | |
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| Vibrations in a Rectangular Membrane | |
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| The Heat Equation Initial and Boundary Conditions | |
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| The Heat Equation on [0, L] | |
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| Solutions in an Infinite Medium | |
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| Heat Conduction in an Infinite Cylinder | |
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| Heat Conduction in a Rectangular Plate | |
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| The Potential Equation Laplace's Equation | |
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| Dirichlet Problem for a Rectangle | |
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| Dirichlet Problem for a Disk | |
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| Poisson's Integral Formula | |
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| Dirichlet Problem for Unbounded Regions | |
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| A Dirichlet Problem for a Cube | |
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| Steady-State Heat Equation for a Sphere | |
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| Appendix a Guide to Notation | |
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| Appendix B a MAPLE Primer | |
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| Answers to Selected Problems | |
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| Index | |