一、Course Description
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<br>This course aims to provide sufficient mathematic training for students whose majors are in engineering or physics. The content emphasizes in ordinary and partial differential equations and complex variables. This course is the mathematic foundation of electromagnetics, modern physics, solid-state physics and so on.
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<br> 二、Text Book
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<br>E. Kreyszig, Advanced Engineering Mathematics, 10th Ed., John Wiley & Sons, Inc., 2011.
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<br>三、References
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<br>S. J. Farlow, Partial differential Equations for Scientists and Engineers, Dover Publications, Inc., 1993.
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<br>四、Teaching Method
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<br>Lectures
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<br>五、Syllabus
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<br>Part I Ordinary Differential Equations
<br>1. First Order ODEs
<br>2. Seconder Order ODEs
<br>3. Systems of ODEs
<br>4. Laplace Transforms
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<br>Part II Partial Differential Equations
<br>1. Basic concepts and derivations of PDEs in physics problems
<br>2. 1st Order PDEs
<br>3. Classifications of linear 2nd order PDEs, Characteristics, d’Alembert’s solution
<br>4. Separation of variables and Fourier series
<br>5. Sturm-Liouville systems and eigenfunction expansions
<br>6. Solutions of homogeneous problems by separation of variables
<br>7. Nonhomogeneous problems
<br>8. Problems on infinite spatial domains: Fourier Integral and Fourier Transform
<br>9. Problems in polar, cylindrical and spherical coordinates
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<br>Part III Complex Analysis
<br>1. Complex numbers and functions
<br>2. Complex integration
<br>3. Power series, Taylor series
<br>4. Laurents series, Residue integration
<br>5. Conformal mapping
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<br>六、Evaluation
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<br>Midterm and final exams (70%),	quizes(30%)
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<br>七、可連結之網頁位址
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<br>moodle.nthu.edu.tw
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