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A Complete First Course in Differential Equations
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8. Nonlinear Systems (Size: 4.19 GB) (Files: 344)
8. Nonlinear Systems
6. Review of Linear Systems Phase Portraits.mp4
1. Intro. Ex. of First Order Nonlinear DEs Equilibriums, Stability, Maple!.mp4
1. Intro. Ex. of First Order Nonlinear DEs Equilibriums, Stability, Maple!.vtt
1.1 make_handouts_4page.pdf.pdf
2. Intro. Ex. of First Order DEs Equilibriums, Stability, Maple! Continued....mp4
2. Intro. Ex. of First Order DEs Equilibriums, Stability, Maple! Continued....vtt
3. Logistic growth with constant harvest, equilib. points, stability, bifurcation.mp4
3. Logistic growth with constant harvest, equilib. points, stability, bifurcation.vtt
4. Logistic growth with constant harvest, numerical solve Maple.mp4
4. Logistic growth with constant harvest, numerical solve Maple.vtt
5. Logistic periodic harvesting, equilibrium and stability defn. for systems.mp4
5. Logistic periodic harvesting, equilibrium and stability defn. for systems.vtt
6. Review of Linear Systems Phase Portraits.vtt
7. Linearization of Nonlinear System - Jacobian - Example as well.mp4
7. Linearization of Nonlinear System - Jacobian - Example as well.vtt
8. Equilibrium Points, Stability, Phase Portrait, Numerical Solution in Maple.mp4
8. Equilibrium Points, Stability, Phase Portrait, Numerical Solution in Maple.vtt
9. Equilibrium Points, Stability, Phase Portrait, Numerical Solution in Maple.mp4
9. Equilibrium Points, Stability, Phase Portrait, Numerical Solution in Maple.vtt
10. Hopf Bifurcation Part 2.mp4
10. Hopf Bifurcation Part 2.vtt
11. Hopf Bifurcation Part 2.mp4
11. Hopf Bifurcation Part 2.vtt
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1. Introduction to Differential Equations and their Applications
1. Object falling under the force of gravity.mp4
1. Object falling under the force of gravity.vtt
2. Object falling under the force of gravity and air resistance.mp4
2. Object falling under the force of gravity and air resistance.vtt
3. Motion of a mass on a spring.mp4
3. Motion of a mass on a spring.vtt
4. RLC Circuits.mp4
4. RLC Circuits.vtt
5. Motion of a simple pendulum.mp4
5. Motion of a simple pendulum.vtt
6. More Differential Equation Models.mp4
6. More Differential Equation Models.vtt
7. Defining and Classifying Differential Equations.mp4
7. Defining and Classifying Differential Equations.vtt
8. Solutions of Differential Equations.mp4
8. Solutions of Differential Equations.vtt
9. Explicit and Implicit Solutions.mp4
9. Explicit and Implicit Solutions.vtt
Must Read.txt
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2. First Order Differential Equations
1. Slope Fields and Solution Curves.mp4
1. Slope Fields and Solution Curves.vtt
2. Existence and Uniqueness for first order Differential Equations.mp4
2. Existence and Uniqueness for first order Differential Equations.vtt
3. Separable Differential Equations.mp4
3. Separable Differential Equations.vtt
4. Separable Differential Equation Examples.mp4
4. Separable Differential Equation Examples.vtt
5. Newtons Law of Cooling.mp4
5. Newtons Law of Cooling.vtt
6. Newtons Law of Cooling Homicide Victim Example.mp4
6. Newtons Law of Cooling Homicide Victim Example.vtt
7. Torricellis Law.mp4
7. Torricellis Law.vtt
8. Torricellis Law Example.mp4
8. Torricellis Law Example.vtt
9. Linear First Order Differential Equations.mp4
9. Linear First Order Differential Equations.vtt
10. Differential Equation for Mixing Problems.mp4
10. Differential Equation for Mixing Problems.vtt
11. Mixing Problem Example.mp4
11. Mixing Problem Example.vtt
12. Exact Differential Equations.mp4
12. Exact Differential Equations.vtt
13. Exact Differential Equation Example 1.mp4
13. Exact Differential Equation Example 1.vtt
14. Exact Differential Equation Example 2.mp4
14. Exact Differential Equation Example 2.vtt
15. Introduction to Substitution Methods.mp4
15. Introduction to Substitution Methods.vtt
16. Homogenous Differential Equations.mp4
16. Homogenous Differential Equations.vtt
17. Homogeneous Differential Equation Example 1.mp4
17. Homogeneous Differential Equation Example 1.vtt
18. Homogeneous Differential Equation Example 2.mp4
18. Homogeneous Differential Equation Example 2.vtt
19. Bernoulli Differential Equations.mp4
19. Bernoulli Differential Equations.vtt
20. Reduction of a Second Order Differential Equation to a First Order One.mp4
20. Reduction of a Second Order Differential Equation to a First Order One.vtt
21. Assignment #1.pdf
3. Higher Order Differential Equations
1. Higher Order Differential Equations.mp4
1. Higher Order Differential Equations.vtt
2. Linear Differential Operators.mp4
2. Linear Differential Operators.vtt
3. Principal of Superposition.mp4
3. Principal of Superposition.vtt
4. Existence and Uniqueness Theorem.mp4
4. Existence and Uniqueness Theorem.vtt
5. The Wronskian Determinant.mp4
5. The Wronskian Determinant.vtt
6. General Solutions of Second Order Linear Homogenous Equations.mp4
6. General Solutions of Second Order Linear Homogenous Equations.vtt
7. Summary of Theory for Second Order Homogenous Equations.mp4
7. Summary of Theory for Second Order Homogenous Equations.vtt
8. Linear Independence and the Wronskian.mp4
8. Linear Independence and the Wronskian.vtt
9. Wronskian of Solutions.mp4
9. Wronskian of Solutions.vtt
10. Theory of Higher Order Equations.mp4
10. Theory of Higher Order Equations.vtt
11. Solving Second Order Equations with Constant Coefficients.mp4
11. Solving Second Order Equations with Constant Coefficients.vtt
12. Second Order Equations with Constant Coefficients Distinct Roots.mp4
12. Second Order Equations with Constant Coefficients Distinct Roots.vtt
13. Solving Second Order Equations with Constant Coefficients 1 Root.mp4
13. Solving Second Order Equations with Constant Coefficients 1 Root.vtt
14. Solving Second Order Equations with Constant Coefficients Complex Roots.mp4
14. Solving Second Order Equations with Constant Coefficients Complex Roots.vtt
15. Method of Reduction.mp4
15. Method of Reduction.vtt
16. Higher Order Equations Distinct Real Roots.mp4
16. Higher Order Equations Distinct Real Roots.vtt
17. Higher Order Equations Repeated Real Roots.mp4
17. Higher Order Equations Repeated Real Roots.vtt
18. Higher Order Equations Distinct Complex Roots.mp4
18. Higher Order Equations Distinct Complex Roots.vtt
19. Higher Order Equations Repeated Complex Roots.mp4
19. Higher Order Equations Repeated Complex Roots.vtt
20. Higher Order Equations Example With All Cases.mp4
20. Higher Order Equations Example With All Cases.vtt
21. Nonhomogenous Differential Equations.mp4
21. Nonhomogenous Differential Equations.vtt
22. Method of Undetermined Coefficients Example 1.mp4
22. Method of Undetermined Coefficients Example 1.vtt
23. Method of Undetermined Coefficients Example 2.mp4
23. Method of Undetermined Coefficients Example 2.vtt
24. Method of Undetermined Coefficients Example 3.mp4
24. Method of Undetermined Coefficients Example 3.vtt
25. Method of Undetermined Coefficients Avoiding Duplication.mp4
25. Method of Undetermined Coefficients Avoiding Duplication.vtt
26. Method of Undetermined Coefficients In General.mp4
26. Method of Undetermined Coefficients In General.vtt
27. Method of Undetermined Coefficients Example 4.mp4
27. Method of Undetermined Coefficients Example 4.vtt
28. Method of Undetermined Coefficients Example 5.mp4
28. Method of Undetermined Coefficients Example 5.vtt
29. Method of Undetermined Coefficients Example 6.mp4
29. Method of Undetermined Coefficients Example 6.vtt
30. Assignment 2.pdf
31. Reduction of Order The General Formula.mp4
31. Reduction of Order The General Formula.vtt
32. Reduction of Order An Example.mp4
32. Reduction of Order An Example.vtt
33. Variation of Parameters.mp4
33. Variation of Parameters.vtt
34. Variation of Parameters An Example.mp4
34. Variation of Parameters An Example.vtt
35. Assignment 3.pdf
ReadMe.txt
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4. Laplace Transforms
1. The Laplace Transform.mp4
1. The Laplace Transform.vtt
2. Laplace Transform Example Unit Step Function.mp4
2. Laplace Transform Example Unit Step Function.vtt
3. Laplace Transform Example First Derivative.mp4
3. Laplace Transform Example First Derivative.vtt
4. Laplace Transform Example Second Derivative.mp4
4. Laplace Transform Example Second Derivative.vtt
5. Existence of the Laplace Transform.mp4
5. Existence of the Laplace Transform.vtt
6. Laplace Transform Example Exponential Function.mp4
6. Laplace Transform Example Exponential Function.vtt
7. Laplace Transform Example Cosine, Sine, Hyperbolic Cosine and Sine.mp4
7. Laplace Transform Example Cosine, Sine, Hyperbolic Cosine and Sine.vtt
8. The Inverse Laplace Transform.mp4
8. The Inverse Laplace Transform.vtt
9. Solving Differential Equations with Laplace Transform.mp4
9. Solving Differential Equations with Laplace Transform.vtt
10. Solving Differential Equations with Laplace Transform.mp4
10. Solving Differential Equations with Laplace Transform.vtt
11. Partial Fractions to Invert Transforms.mp4
11. Partial Fractions to Invert Transforms.vtt
12. First Translation Theorem.mp4
12. First Translation Theorem.vtt
13. First Translation Theorem Inverting Transforms.mp4
13. First Translation Theorem Inverting Transforms.vtt
14. First Translation Theorem Inverting Transforms Completing Square.mp4
14. First Translation Theorem Inverting Transforms Completing Square.vtt
15. Second Translation Theorem.mp4
15. Second Translation Theorem.vtt
16. Piecewise Continuous Functions with Unit Step Functiond.mp4
16. Piecewise Continuous Functions with Unit Step Functiond.vtt
17. Laplace Transform of Piecewise Continuous Functions.mp4
17. Laplace Transform of Piecewise Continuous Functions.vtt
18. Laplace Transform of Piecewise Continuous Functions.mp4
18. Laplace Transform of Piecewise Continuous Functions.vtt
19. Solving an IVP with a Piecewise continuous Non-homogenous Term.mp4
19. Solving an IVP with a Piecewise continuous Non-homogenous Term.vtt
20. Solving an IVP with a Piecewise continuous Non-homogenous Term.mp4
20. Solving an IVP with a Piecewise continuous Non-homogenous Term.vtt
21. Assignment 4.pdf
22. Derivatives of Transforms.mp4
22. Derivatives of Transforms.vtt
23. Laplace Transform of Piecewise Periodic Functions.mp4
23. Laplace Transform of Piecewise Periodic Functions.vtt
24. Solving an IVP with a Piecewise Periodic Non-homogenous Term.mp4
24. Solving an IVP with a Piecewise Periodic Non-homogenous Term.vtt
25. The Dirac Delta Function.mp4
25. The Dirac Delta Function.vtt
26. Solving an IVP with a Delta Function Term.mp4
26. Solving an IVP with a Delta Function Term.vtt
27. Solving an IVP with Multiple Delta Function Term.mp4
27. Solving an IVP with Multiple Delta Function Term.vtt
28. The Convolution Theorem.mp4
28. The Convolution Theorem.vtt
29. Convolution Theorem Finding Integral Solutions.mp4
29. Convolution Theorem Finding Integral Solutions.vtt
30. Convolution Theorem Finding Integral Solutions.mp4
30. Convolution Theorem Finding Integral Solutions.vtt
31. Assignment 5.pdf
5. Power Series Methods
1. Power Series Template Slides.pdf
2. Review of Second Order Equations (Constant Coefficients) and Power Series.mp4
2. Review of Second Order Equations (Constant Coefficients) and Power Series.vtt
3. Solving Airy's Differential Equation with Power Series Solution.mp4
3. Solving Airy's Differential Equation with Power Series Solution.vtt
4. Plotting Solutions of Airy's DE and using Maple to find Series Solutions.mp4
4. Plotting Solutions of Airy's DE and using Maple to find Series Solutions.vtt
5. Finding a Power Series Solution, Using Maple as well, Ordinary Points.mp4
5. Finding a Power Series Solution, Using Maple as well, Ordinary Points.vtt
6. Ordinary Points. Chebyshev's Differential Equation.mp4
6. Ordinary Points. Chebyshev's Differential Equation.vtt
7. Previous Video Continued Chebyshev Polynomials.mp4
7. Previous Video Continued Chebyshev Polynomials.vtt
8. Quiz Power Series Solution about Ordinary Point.pdf
9. Quiz Solution Power Series Solution about Ordinary Point.pdf
10. Singular Points. Regular Singular Points. Euler's Differential Equation.mp4
10. Singular Points. Regular Singular Points. Euler's Differential Equation.vtt
11. Euler's Differential Equation Continued.mp4
11. Euler's Differential Equation Continued.vtt
12. Frobenius Series Solutions and Beginning of Example.mp4
12. Frobenius Series Solutions and Beginning of Example.vtt
13. Frobenius Series Solution Roots Differing by Non Integer.mp4
13. Frobenius Series Solution Roots Differing by Non Integer.vtt
14. Frobenius Series Roots Differing by an Integer - 2 Frobenius Solutions.mp4
14. Frobenius Series Roots Differing by an Integer - 2 Frobenius Solutions.vtt
15. Roots Differing by an Integer - 1 Frobenius Solution Continued.mp4
15. Roots Differing by an Integer - 1 Frobenius Solution Continued.vtt
16. Frobenius Series Roots Differing by an Integer- 1 Frobenius Solution.mp4
16. Frobenius Series Roots Differing by an Integer- 1 Frobenius Solution.vtt
17. Quiz Frobenius Series.pdf
18. Method of Reduction with Frobenius Series.mp4
18. Method of Reduction with Frobenius Series.vtt
19. Method of Reduction with Frobenius Series Continued.mp4
19. Method of Reduction with Frobenius Series Continued.vtt
20. Quiz Frobenius and Reduction of Order.pdf
6. Partial Differential Equations and Fourier Series
1. Partial Differential Equations and Fourier Series Template Slides.pdf
2. Intro to PDEs.mp4
2. Intro to PDEs.vtt
3. Separation of Variables Heat Equation - Zero B.C..mp4
3. Separation of Variables Heat Equation - Zero B.C..vtt
4. Heat Equation - Zero B.C. - Sine Fourier Series.mp4
4. Heat Equation - Zero B.C. - Sine Fourier Series.vtt
5. Heat Equation - Zero B.C. - Sine Fourier Series Continued.mp4
5. Heat Equation - Zero B.C. - Sine Fourier Series Continued.vtt
6. Sine Fourier Series Continued and Heat Equation.mp4
6. Sine Fourier Series Continued and Heat Equation.vtt
7. Heat Equation - Zero Flux B.C. - Cosine Fourier Series.mp4
7. Heat Equation - Zero Flux B.C. - Cosine Fourier Series.vtt
8. Heat Equation - Periodic B.C. General Fourier Series.mp4
8. Heat Equation - Periodic B.C. General Fourier Series.vtt
9. Fourier Series Continued.mp4
9. Fourier Series Continued.vtt
10. Quiz - Fourier Series.pdf
11. Fourier Series of Piecewise Continuous Function.mp4
11. Fourier Series of Piecewise Continuous Function.vtt
12. Fourier Series - Convergence.mp4
12. Fourier Series - Convergence.vtt
13. Cosine and Sine Fourier Series - Even and Odd Extensions.mp4
13. Cosine and Sine Fourier Series - Even and Odd Extensions.vtt
14. Removing Inhomogeneous Terms in PDE Heat Equation.mp4
14. Removing Inhomogeneous Terms in PDE Heat Equation.vtt
15. Removing Inhomogeneous Terns in Boundary Conditions Heat Equation.mp4
15. Removing Inhomogeneous Terns in Boundary Conditions Heat Equation.vtt
16. Wave Equation.mp4
16. Wave Equation.vtt
ReadMe.txt
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7. Sturm-Liouville Eigenvalue Problems and Theory
1. Slides for This Chapter.pdf
2. Self Adjoint Operators.mp4
2. Self Adjoint Operators.vtt
3. Regular Sturm-Liouville Eigenvalue Problems.mp4
3. Regular Sturm-Liouville Eigenvalue Problems.vtt
4. Regular Sturm-Liouville Operator is Self Adjoint.mp4
4. Regular Sturm-Liouville Operator is Self Adjoint.vtt
5. Regular Sturm-Liouville Orthogonal Eigen Functions and Real Eigenvalues.mp4
5. Regular Sturm-Liouville Orthogonal Eigen Functions and Real Eigenvalues.vtt
6. Regular Sturm-Liouville Theorem and Eigen Function Expansions.mp4
6. Regular Sturm-Liouville Theorem and Eigen Function Expansions.vtt
7. Converting DEs to Sturm Liouville FOrm.mp4
7. Converting DEs to Sturm Liouville FOrm.vtt
8. Sturm Liouville Example with Euler's Equation.mp4
8. Sturm Liouville Example with Euler's Equation.vtt
9. Nonhomogenous Sturm Liouville Problem.mp4
9. Nonhomogenous Sturm Liouville Problem.vtt
ReadMe.txt
9. Numerical Solutions to Differential Equations
1. Intro to Euler's Method.mp4
1. Intro to Euler's Method.vtt
2. Euler's Method Example (by hand).mp4
2. Euler's Method Example (by hand).vtt
3. Euler's Method in Maple.mp4
3. Euler's Method in Maple.vtt
4. Euler's Method in Excel.mp4
4. Euler's Method in Excel.vtt
5. Euler's Method In Maple (Another Example) and Dsolve Numeric in Maple.mp4
5. Euler's Method In Maple (Another Example) and Dsolve Numeric in Maple.vtt
6. Stability of Euler's Method Part 1.mp4
6. Stability of Euler's Method Part 1.vtt
7. Stability of Euler's Method Part 2.mp4
7. Stability of Euler's Method Part 2.vtt
8. BackwardImplicit Euler Part 1.mp4
8. BackwardImplicit Euler Part 1.vtt
9. Implicit Trapezoid Stability.mp4
9. Implicit Trapezoid Stability.vtt
10. Accuracy of Euler Method.mp4
10. Accuracy of Euler Method.vtt
11. Accuracy of Implicit Trapezoid Method.mp4
11. Accuracy of Implicit Trapezoid Method.vtt
12. Hints for an assignment #7. Random Review Stuff. For Students in Math 3120.mp4
12. Hints for an assignment #7. Random Review Stuff. For Students in Math 3120.vtt
13. Coding Implicit Trapezoid.mp4
13. Coding Implicit Trapezoid.vtt
14. Heun's Method.mp4
14. Heun's Method.vtt
15. Runge Kutta (RK2) Derivation.mp4
15. Runge Kutta (RK2) Derivation.vtt
16. Runge Kutta (RK4) Method.mp4
16. Runge Kutta (RK4) Method.vtt
17. Review of some Numerical Stability Concepts and the Methods we have looked at.mp4
17. Review of some Numerical Stability Concepts and the Methods we have looked at.vtt
18. Polynomial Interpolation (Vandermonde Matrix).mp4
18. Polynomial Interpolation (Vandermonde Matrix).vtt
19. Newton Divided Difference Polynomial Interpolation.mp4
19. Newton Divided Difference Polynomial Interpolation.vtt
20. Backward Differentiation BDF1.mp4
20. Backward Differentiation BDF1.vtt
21. Backward Differentiation BDF2.mp4
21. Backward Differentiation BDF2.vtt
ReadMe.txt
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