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Course
Outline |
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1. First Order Differential Equations 1.1
Differential equations and models 1.2
Solutions given by integrals 1.3
Direction fields and solution curves 1.4
Separable equations 1.5 Linear
first order equations 1.6
Substitution methods and exact equations 2.1
Population models 2.2
Equilibrium solutions and stability 2.3 Velocity and acceleration |
9 lectures |
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2. Linear Equations
of Higher Order 3.4, 3.6 Mechanical vibrations, oscillations,
resonance 3.1 Second order linear equations 3.2 General solutions 3.3 Homogeneous, constant coefficient equations 3.5
Nonhomogenous equations |
6 lectures |
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3. Laplace Transforms 7.1 Laplace transforms 7.2 Initial value problems 7.3, 7.4 Operating with the Laplace transform 7.5,
7.6 Special cases |
6 lectures |
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4. Systems of Linear Equations ---- Introduction to linear
algebra 4.1, 5.3 Mechanics, first and second order systems 5.1 Matrices and linear systems 5.2 Eigenvalues 5.4 Characterization of solutions 5.5
Matrix exponentials |
12 lectures |
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5. Numerical Methods for
Differential Equations 2.4, 25. Euler's method and variations 4.3 Numerical methods for systems |
3 lectures |
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6. Nonlinear Differential
Equations 6.3, 6.4 Population models and Mechanics 6.1 Stability and the phase plane 6.2 Linearization 6.5
Chaos |
7 lectures |