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Differential Equations

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Differential Equations

Differential Equations
English | Size: 4.44 GB
Category: CBTs

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Dr. William Murray's Differential Equations course will help you solve problems from all over biology, physics, chemistry, and engineering. Dr. Murray demonstrates his extensive teaching experience with easy to understand theory and a wide array of examples and helpful tips. Each lesson also includes several completely worked out practice problems like the ones you will see on homework and tests. Sample topics include linear and separable equations, second order equations, series solutions, systems of equations, and Laplace transforms. Dr. Murray received his Ph.D from UC Berkeley, his BS from Georgetown University, and has been teaching in the university setting for 10+ years.
I. First-Order Equations
Linear Equations 1:07:21
Separable Equations 35:11
Slope & Direction Fields 1:11:36
Applications, Modeling, & Word Problems of First-Order Equations 1:05:19
Autonomous Equations & Phase Plane Analysis 1:01:20
II. Second-Order Equations
Distinct Roots of Second Order Equations 28:44
Complex Roots of Second Order Equations 31:49
Repeated Roots & Reduction of Order 43:02
Undetermined Coefficients of Inhomogeneous Equations 50:01
Inhomogeneous Equations: Variation of Parameters 49:22
III. Series Solutions
Review of Power Series 57:38
Series Solutions Near an Ordinary Point 1:20:28
Euler Equations 24:42
Series Solutions 1:20:26
IV. Laplace Transform
Laplace Transforms 41:52
Inverse Laplace Transforms 47:05
Laplace Transform Initial Value Problems 45:15
V. Review of Linear Algebra
Review of Linear Algebra 57:30
VI. Systems of Equations
Distinct Real Eigenvalues 59:26
Complex Eigenvalues 1:03:54
Repeated Eigenvalues 45:17
VII. Inhomogeneous Systems
Undetermined Coefficients for Inhomogeneous Systems 43:37
Variation of Parameters for Inhomogeneous Systems 1:08:12
VIII. Numerical Techniques
Euler's Method 45:30
Runge-Kutta & The Improved Euler Method 41:04
IX. Partial
Review of Partial Derivatives 38:22
The Heat Equation 44:40
Separation of Variables 57:44
Fourier Series 1:24:33
Solution of the Heat Equation 47:41
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