INSTRUCTOR: DR. NICOLAS LARGE EMAIL: [email protected] OFFICE LOCATION: AET 3.392 OFFICE PHONE: (210)458-8279 OFFICE HOURS: M,W,F 11AM-12PM OR BY APPOINTMENT. COURSE DESCRIPTION The course is an introduction to mathematical concepts more advanced than what you have seen in the Calculus series. The concepts will be related to past and future Physics concepts in, for instance, Statistical Thermodynamics, Quantum Mechanics, Classical Mechanics, Electricity and Magnetism, etc. The course will try to interface mathematical and physics concepts. The “mechanics” and the theorems of some of the math will not be covered and assumed to be understood from the math courses (Calculus I, II and III, Linear Algebra, Differential Equations). This course covers topics such as vector analysis, introduction to complex variables, Fourier series, ordinary differential equations, and linear algebra.

COURSE CONTENT •

Power Series and Taylor (McLaurin) expansion (Chapter 1 Sections 1-6; Chapter 1 Sections 10-13)

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Review of Vector Calculus and applications. Transformation of coordinates, Jacobian matrix. (Chapter 5 Section 4; Chapter 6 from Section 8)

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Complex numbers and introduction to their application (Chapter 2)

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Introduction to linear algebra, linear vectors spaces, linear operators, eigenvalues and eigenfunctions, introduction to spaces. (Chapter 3 from Section 5)

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Fourier Transforms and application (Chapter 7)

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Introduction to Ordinary Differential Equations (only few examples for Physics. e.g., oscillations, central force, photon decay, Bessel equation, heat diffusion, etc.) (Chapter 8, Sections 1-4)

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Gamma function, Error Function, Stirling’s formula (Chapter 11, Sections 1-5)

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Probability and Statistics, Binomial distribution, Gaussian Distribution, Poisson distribution, Gaussian integral. Ergodicity. (Chapter 15, Sections 7-10)

STUDENT LEARNING OBJECTIVES/OUTCOMES The overall objective is the thorough understanding of how fundamental mathematical concepts apply to basic and advanced Physics concepts. Specific Aims include: (a) to provide a solid knowledge of the fundamental concept and theory; (b) to develop critical thinking skills and the ability to independently retrieve information from the textbook or other resources; (c) to develop the skills to use the conceptual and theoretical knowledge to the solution of problems with different degree of difficulty; (d) to develop the skills for the logical approach to physics problems and (e) to improve the understanding of how physics can be seen in action in our everyday activities.

Syllabus revised on Oct. 31, 2017

COURSE PREREQUISITES •

Calculus I, II, and III, Calculus-based Physics I and II, or consent of instructor. Completion of Linear Algebra is preferred but at least concurrent enrollment is strong encouraged.

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Concepts Assumed Covered in Other Courses: o

Criteria of Convergence of Series

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Basic Linear Algebra: # systems of linear equations; # row reduction; # operation between matrices (addition, multiplication, etc.); # rank of matrices; # determinants and Cramer’s rule; # addition of vectors, dot product, cross product

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Partial derivation, Chain rule

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Multiple Integration, Change of Variable and Jacobians

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Triple scalar product, Triple vector product, Differentiation of vectors, Gradient, Curl Divergence, Laplacian

COURSE TEXTBOOK AND MATERIALS

Mathematical Methods in the Physical Sciences by M.L. Boas, Pub. Wiley

COURSE REQUIREMENTS IMPORTANT: Students are expected to STUDY the material from textbooks and in-class notes that will be posted on BB. It is imperative that you prepare yourself before lecture. The material covered in class should be the starting point and not the end point of the study process. After reviewing the in-class notes students should integrate the material with what is explained more extensively in the textbook. ONLY A SOLID KNOWLEDGE OF THE MATERIAL GIVES YOU A GOOD CHANCE TO SOLVE THE PROBLEMS ASSIGNED IN THE PARTIAL EXAMS. Homework/Assignment: Groups of 2 students will be formed. Homework problems will be assigned and the solutions posted on blackboard OR discussed in class. For each assignment each group will turn-in one answer sheet. All the assignments will be graded based on the group’s work. The students are strongly encourage to discuss and work these problems together. Late homework policy: Late homework will not be graded. Homework quality: It is important that you prepare for the real world where the quality of the documents (resume, letters, reports, articles,…) must be neat, clean, well written, and organized. As such, negative points up to 10% of the HW grade will be applied to HWs that do not satisfy the “quality criteria”. Additionally, if the instructor, cannot read the answer to a problem/question, you will loose the all the points for that particular question. Attendance: Attendance will not be used as a grading factor. However, attending each class will help you assimilating the material and learning the strategies for solving problems.

GRADING The final course average grade will be based on the following scale: A = 90–100

B = 80–89

Syllabus revised on Oct. 31, 2017

C = 65–79

D = 45–64

F = 0–44

Assignments 10% Best point grade 35% Exam 2nd best point 20% grade Exam Worst point 10% grade Exam Final Exam 25% Total / 100% Final Grade

Homework assignments (l) Three partial exams (100 points each) will be given throughout the semester. Each exam will contain several problems to solve. In-class Exams will be Open book. Comprehensive in-class final Exam (Open book). May 2 nd, 7:00- 9:30 am

Exams: The three (3) partial exams are scheduled to be in-class exams, covering the part of the course seen between that partial exam and the partial exam before. However, some concepts seen early in the semester may be needed to solve problems in late semester exams. Be prepared. Depending on the speed at which we advance during the semester any/some of these three partial Exams may become take-home Exams. The final Exam will in-class, on May 2nd, 7:00- 9:30 am. Extra Credit: There is no extra credit.

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CHANGES This syllabus is provided for informational purposes regarding anticipated course content and schedule of courses. It is based upon the most recent information available on the date of its issuance and is as accurate and complete as possible. I reserve the right to make any changes necessary and/or appropriate. I will make every effort to communicate any changes in a timely manner. Students are responsible for the awareness of these changes.

Syllabus revised on Oct. 31, 2017