Designed for students in mathematics and actuarial science. Explore an introduction to predictive modeling that starts with least squares as a foundation and takes a modern approach applicable to classification and prediction in the presence of large datasets. Three lecture hours a week for one semester. Mathematics 339G and 375T (Topic: Predictive Analytics) may not both be counted. Prerequisite: The following with a grade of at least C-: Mathematics 341 or 340L; and Mathematics 378K.

Partial differential equations as basic models of flows, diffusion, dispersion, and vibrations. Topics include first- and second-order partial differential equations and classification (particularly the wave, diffusion, and potential equations), and their origins in applications and properties of solutions. Includes the study of characteristics, maximum principles, Green's functions, eigenvalue problems, and Fourier expansion methods. Three lecture hours a week for one semester. Prerequisite: Mathematics 427J or 427K with a grade of at least C-.


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Variational methods and related concepts from classical and modern applied mathematics. Models of conduction and vibration that lead to systems of linear equations and ordinary differential equations, eigenvalue problems, initial and boundary value problems for partial differential equations. Topics may include a selection from diagonalization of matrices, eigenfunctions and minimization, asymptotics of eigenvalues, separation of variables, generalized solutions, and approximation methods. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Mathematics 427J or 427K, and 340L or 341, with a grade of at least C- in each.

Same as Computational Science, Engineering, and Mathematics 386D. Topics include distributions, fundamental solutions of partial differential equations, the Schwartz space and tempered distributions, Fourier transform, Plancherel theorem, Green's functions, Sobolev spaces, weak solutions, differential calculus in normed spaces, implicit function theorems, applications to nonlinear equations, smooth variational problems, applications to classical mechanics, constrained variational problems. Three lecture hours a week for one semester. Computational Science, Engineering, and Mathematics 386D and Mathematics 383D may not both be counted. Prerequisite: Graduate standing; and Computational Science, Engineering, and Mathematics 386C or Mathematics 383C.

Designed for students in mathematics and actuarial science. Explore an introduction to predictive modeling that starts with least squares as a foundation and takes a modern approach applicable to classification and prediction in the presence of large datasets. Three lecture hours a week for one semester. Prerequisite: Graduate standing; an understanding of linear algebra and mathematical statistics.

Ethical Standards: Upholding ethical standards and understanding the broader impact of engineering solutions on society and the environment is increasingly important for modern mechanical engineers.

Goals: The primary goal of this course is to introduceyou to some modern mathematics, of which some you may have seen before, some may be completelyunfamiliar, some may be very useful, and some is just beautiful!Homework: Assignments will be announced in class andthen posted on this website. Any changes will be announced in class.Answers to odd-numbered exercises are in the back of the book.I highly recommend working jointly on homework problems with fellow students.Grading: The course grade will be determined as follows: 20% Quizzes + 45% Exams + 35% Final Exam.Without exception, you must take the final exam at the time scheduled by the university: Help: My office hours are Tuesdays 2:30-4:30pm and Thursdays 3:30-4:30pm in my office, 1S-209. Optimal Method of Study: (1.) Come to class. (2.) Read the relevant sections after class. (3.) Do thehomework. (4.) Compare your solutions with other students. (5.) Come to office hours or the help room with any remainingquestions. Written work:  We write to communicate. Work must be neat and legible to receive consideration. You must explain your work to obtain full credit. For specific suggestions see A guide to writing in mathematics classes.

Modern education differs significantly from traditional methods and is now widely practiced in schools with a greater emphasis on science and technology. A variety of computer technologies, the Internet, and projector presentations help modern education to make classes interesting and interactive for students. Unlike traditional textbooks and theoretical learning, modern education reduces the boundaries of the traditional system to learning through experimentation and experience. Students were provided with known facts and knowledge in traditional education, but at the same time, critical thinking and problem-solving skills were introduced so that they could conduct research and reach higher levels in online education. ff782bc1db

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