Advanced Calculus II-Differential Equations
| Numbering Code | U-LAS10 20004 LE55 | Year/Term | 2022 ・ Second semester | |
|---|---|---|---|---|
| Number of Credits | 2 | Course Type | Lecture | |
| Target Year | 2nd year students or above | Target Student | For science students | |
| Language | English | Day/Period | Wed.5 | |
| Instructor name | QURESHI，Ali Gul (Graduate School of Engineering Associate Professor) | |||
| Outline and Purpose of the Course | Based on the knowledge of Calculus with Exercises A/B and Linear Algebra with Exercises A/B or Calculus A/ B and Liner Algebra A/B, this course explains ordinary differential equations. Starting from the basic solutions techniques (such as separation of variables and integrating factors) for differential equations, the course introduces the second order linear differential equations and their solution. Differential equations are studied in context of modelling of various physical situations (for example, vibrations, mixing problem, population dynamics, etc.). | |||
| Course Goals | To learn the different types of differential equations and their solution methods. | |||
| Schedule and Contents |
1. Elementary methods of solution (6 weeks) - Separation of variables, linear first order differential equations, total differential equations (exact differential equations) and integrating factors 2. Existence and uniqueness of the solution of initial value problems (4 weeks) - Space of continuous functions and it's properties (normed spaces, completeness), iterated approximation, Cauchy-Lipschitz's theorem and the connection of solution 3. Linear differential equations (4 weeks) - Space of solutions of homogeneous equations, variation of parameters, exponential function for matrices and Wronskian determinant. 4. Feedback (1 week) |
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| Evaluation Methods and Policy | Weekly submission of class examples, class participation and homework (25%), Snap quizzes (25%), Final examination(50%). | |||
| Course Requirements | To understand Calculus with Exercises A/B and Linear Algebra with Exercises A/B or Calculus A/B and Linear Algebra A/B. | |||
| Study outside of Class (preparation and review) | Students are encouraged to do assigned homework related to the classes. | |||
| Textbooks | Textbooks/References | Advanced Engineering Mathematics, 9th ed., Erwin Kreyszig, (Wiley, 2006) | ||
| References, etc. |
Thomas' Calculus, 14th ed., Joel R. Hass, Christopher E. Heil and Maurice D. Weir, (Pearson) Calculus Vol. 2 and Vol. 3, Gilbert Strang et al., (OpenStax), Books are available online at https:// openstax.org/details/books/calculus-volume-2 and https://openstax.org/details/books/calculus-volume-3 Differential Equations, 4th ed., Richard Bronson and Gabriel Costa, (McGraw-Hill) |
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