About this Project
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1.2 Basic Concepts
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1.1 Applications Leading to Differential Equations
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2.1 Linear First-Order Differential Equations
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1.3 Direction Fields for First Order Equations
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2.2 Separable Equations
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2.3 Existence and Uniqueness of Solutions of Nonlinear Equations
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2.5 Exact Equations
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Transformation of Homogeneous Equations into Separable Equations
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2.4A Bernoulli’s Equations
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2.6 Integrating Factors
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Euler’s Method
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3.2 The Improved Euler Method and Related Methods
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3.3 Runge-Kutta Method
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4.1 Exponential Growth and Decay
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4.2A Newton’s Law of Cooling
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Mixing Problems
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4.3 Elementary Mechanics
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4.4 Autonomous Second Order Equations
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4.5 Applications to Curves
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5.1 Homogeneous Linear Equations
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5.2 Constant Coefficient Homogeneous Equations
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5.3 Nonhomogeneous Linear Equations
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5.4 The Method of Undetermined Coefficients I
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5.5 The Method of Undetermined Coefficients II
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5.6 Reduction of Order
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5.7 Variation of Parameters
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6.1 Spring Problems I
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6.2 Spring Problems II
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6.3 The RLC Circuit
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6.4 Motion Under A Central Force
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7.1 Review of Power Series
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7.2 Series Solutions Near an Ordinary Point I
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7.3 Series Solutions Near an Ordinary Point II
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7.4 Regular Singular Points: Euler Equations
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7.1 The Method of Frobenius I
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7.6 The Method of Frobenius II
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7.7 The Method of Frobenius III
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8.1 Introduction to the Laplace Transform
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8.2 The Inverse Laplace Transform
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8.3 Solution of Initial Value Problems
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8.4 The Unit Step Function
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8.5 Constant Coefficient Equations with Piecewise Continuous Forcing Functions
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8.6 Convolution
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8.7 Constant Coefficient Equations with Impulses
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8.8 A Brief Table of Laplace Transforms
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9.1 Introduction to Linear Higher Order Equations
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9.2 Higher Order Constant Coefficients Homogeneous Equations
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9.3 Undetermined Coefficients for Higher Order Equations
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9.4 Variation of Parameters for Higher Order Equations
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Introduction to Systems of Differential Equations
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10.2 Linear Systems of Differential Equations
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10.3 Basic Theory of Homogeneous Linear System
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Constant Coefficient Homogeneous Systems I
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10.5 Constant Coefficient Homogeneous Systems II
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Constant Coefficient Homogeneous Systems III
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10.7 Variation of Parameters for Nonhomogeneous Linear Systems
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Modeling a spring-mass system
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Hot Potato! Activity on heating and cooling
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Solving ODEs with Sage
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Experiment with Sage interacts
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An Epidemics Model
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Hot Potato! Cooling Activity
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The Simple Pendulum
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Tank Draining
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Overall
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