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16:642:528 - Methods of Applied Mathematics II

Spring 2026

Liping Liu

Course Description:

Please check Canvas at least weekly for updates and answers to your questions.

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The information contained in this class syllabus is subject to change without notice. Students are expected to be aware of any additional course policies presented by the instructor during the course.

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I. READING MATERIALS

Michael D. Greenberg, Advanced Engineering Mathematics (second edition), Prentice-Hall, 1998

Further references will be provided in class.

A second semester graduate course primarily intended for students in mechanical and aerospace engineering, biomedical engineering, and other engineering programs. There will be three parts:

1. Complex variable theory, including the differential and integral calculus of functions of a complex variable, conformal mapping, Taylor series, Laurent series and the residue theorem. Introduction to the calculus of variations.

Calculus of variation, including the motivation of variational principles from physical laws, derivation of Euler-Lagrange equations, stability criterion, linearization, and brief introduction of the foundation of finite element method.

Perturbation methods, including applications to ode systems, examples of boundary layer, multiple-scale problems, and eigenvalue problems.

Emphasis on applications and calculations which graduate students in engineering may encounter in their courses.

Text:

Michael D. Greenberg, Advanced Engineering Mathematics (second edition), Prentice-Hall

Prerequisites:

527

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Spring 2025

Liping Liu

Course Description:

A second semester graduate course primarily intended for students in mechanical and aerospace engineering, biomedical engineering, and other engineering programs. There will be three parts: 

1. Complex variable theory, including the differential and integral calculus of functions of a complex variable, conformal mapping, Taylor series, Laurent series and the residue theorem. Introduction to the calculus of variations.

2. Calculus of variation, including the motivation of variational principles from physical laws, derivation of Euler-Lagrange equations, stability criterion, linearization, and brief introduction of the foundation of finite element method.

3. Perturbation methods, including applications to ode systems, examples of boundary layer, multiple-scale problems, and eigenvalue problems.

Emphasis on applications and calculations which graduate students in engineering may encounter in their courses.

Text:

Michael D. Greenberg, Advanced Engineering Mathematics (second edition), Prentice-Hall

Prerequisites:

Math 642:527 

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Spring 2024

Marcio Fuzeto Gameiro

Course Description:

A second semester graduate course primarily intended for students in mechanical and aerospace engineering, biomedical engineering, and other engineering programs. There will be three parts: 

1. Complex variable theory, including the differential and integral calculus of functions of a complex variable, conformal mapping, Taylor series, Laurent series and the residue theorem. Introduction to the calculus of variations.

2. Calculus of variation, including the motivation of variational principles from physical laws, derivation of Euler-Lagrange equations, stability criterion, linearization, and brief introduction of the foundation of finite element method.

3. Perturbation methods, including applications to ode systems, examples of boundary layer, multiple-scale problems, and eigenvalue problems.

Emphasis on applications and calculations which graduate students in engineering may encounter in their courses.

Text:

Michael D. Greenberg, Advanced Engineering Mathematics

Prerequisites:

Math 642:527 

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Spring 2023

Liping Liu

Course Description:

Same as above.

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Spring 2022

Liping Liu

Course Description:

Same as above.

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Spring 2021 - Liping Liu

Course Description:

Same as above.

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Schedule of Sections:

 

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