공학 미분 방정식
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- 강의학기
- 2015년 1학기
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미분 방정식에 필요한 미적분을 복습한다음 상미분방정식 해를 구하는 여러가지 방법에 대하여 강의한다. LaplaceTransform을 이용하여 미분 방정식의 해를 구하는 방법에 대하여 알아본다.
- 수강안내 및 수강신청
- ※ 수강확인증 발급을 위해서는 수강신청이 필요합니다
Review of Calculus
차시별 강의
| 1. | |
Review of Calculus | Introduction to the elements of calculus, Fundamental theorem of calculus, Derivatives of elementary Functions |  |
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Review of Calculus | Leibnitz's rule, Leibnitz's Formula, Binomial Expansions | |
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| 2. | |
Review of Calculus | Taylor's Series with Remainder, Euler's Formula | |
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Review of Calculus | Examples of Taylor's Series, Factorial Polynomials, Appell's Symbol | |
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| 3. | |
Review of Calculus | Important Formulas, Elementary Integrals | |
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1st order Ordinary Differential Equations | 1st order O.D.E. , Complementary Solutions, Particular Solutions, Direction Fields, Method of Integrating Factors | |
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| 4. | |
1st order Ordinary Differential Equations | Inverse Operator, Short Cut for a paticular solution, Examples from Mechanics | |
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1st order Ordinary Differential Equations | Examples from Mechanics, Conservation of Mass, Autonomous Equations, Bifurcation Diagram, Pitchfork Bifurcation | |
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| 5. | |
1st order Ordinary Differential Equations | Exact differential Equations, Integrating Factors, Path Independent Integrals, 1st Law of Thermodynamics, Entropy | |
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1st order Ordinary Differential Equations, 2nd order Ordinary Differential Equations | Nonlinear 1st order O.D.E., Bernoulli Equations, Riccati Equations, Numerical Methods, Euler Method, Adams Method, Ruge-Kutta Method, 2nd order Linear O.D.E. Wronskian Determinant | |
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| 6. | |
2nd order Ordinary Differential Equations | Linear O.D.E. with constant coefficients, Complementary solutions, Characteristic Equation, Distinct roots, Real roots, Complex roots, Equal roots. | |
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2nd order Ordinary Differential Equations | Particular solutions for exponential function | |
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| 7. | |
2nd order Ordinary Differential Equations | Particular solutions for trigonometric functions, Particular solutions for polynomial functions, Particular solutions for products fo exponential and polynomial functions. | |
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2nd order Ordinary Differential Equations | Particular solutions for Linear O.D.E. with constant coefficients, Example from mechanical vibration. | |
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| 8. | |
2nd order Ordinary Differential Equations | Method of undetermined coefficients, Equidimensional linear differential Equations, Variation of parameters. | |
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2nd order Ordinary Differential Equations | Reduction of order applied to 2nd order linear ODE. | |
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| 9. | |
The Laplace Tranform | Dirac Delta function, Impulse, Convolution, Linear Time Invariant Differential Equations, Causality, The Laplace Trnaform. | |
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The Laplace Tranform | Properties of Laplace Transform, Existence of Laplace Transform | |
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| 10. | |
The Laplace Tranform | Gamma Function, Wallis's Formula | |
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The Laplace Tranform | Stirling Formula, Time Shifing, Initial Value Theorem, Final Value Theorem. | |
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| 11. | |
The Laplace Tranform | Frequency Shifting, Laplace Transform of integrals, Partial Fractions, Laplace Transform of Periodic functions | |
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The Laplace Tranform | The Convolution, Laplace trnasorm of Sine integral, Cosine integral, Exponential integral and Error funtion. | |
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| 12. | |
The Laplace Tranform | Impulse response function, Transfer function, Stability of the system | |
| 13. | |
The Laplace Tranform | Applications to integral, integro-differential equations, differtial Equations with coefficients of linear function of t. | |
| 14. | |
The Laplace Tranform | Convolution applied to multiple integral, Explicit inversion formula, Beta function, Riemann-Lebesgue lemma | |
| 15. | |
The Laplace Tranform | Tautochrone problem, Brachistochrone problem, Cycloid, Evolute, Involute,Abels Equation, Cauchy type Delta Function | |
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