568Tsikkou
Spring 2017
Course Information
Description: Advanced Calculus II
Instructor: Charis Tsikkou. Email
Class Schedule: Tuesdays, Thursdays 04:00-05:15 PM in Armstrong Hall 415
Office Hours: Tuesdays, Thursdays 02:30-03:30 PM, and by appointment, in Armstrong Hall 405
Info Sheet containing more or less the stuff on this webpage.
Textbook
Textbook:
Erwin Kreyszig, Advanced Engineering Mathematics (10th edition)
Evaluation
Grading Scheme
- 35% Final exam on Wednesday, May 3, 2017, 08:00-10:00 AM in Armstrong Hall 415
- 25% Exam I
- 25% Exam II
- 15% Homework assignments
- Letter grades will be assigned according to the scheme
- A 90-100% | B 80-90% | C 70-80% | D 60-70% | F 0-60%
Homework
- Homework will be assigned every Thursday and will be collected on the following Thursday (please see the course schedule below for exact dates).
- Homework will always be collected at the beginning of the class.
- Late turn-ins will not be accepted.
- The accuracy of your work will be checked on selected problems.
Exams I and II
- There will be two 75-minutes in-class exams, on February 21 and April 6.
- These exams will test material covered after the previous exam (they are not cumulative).
- Calculators will not be allowed.
- No make-up exam will be given.
Final Exam
- Wednesday, May 3, 2017, 08:00-10:00 AM in Armstrong Hall 415.
- Final is cumulative.
Course Schedule (subject to changes)
Date | Topic | Resources | HW |
---|---|---|---|
Tuesday, Jan 10 | Fourier Integral | 11.7 | |
Thursday, Jan 12 | Fourier Cosine and Sine Transforms; Fourier Transform | 11.8, 11.9 | |
Tuesday, Jan 17 | Wave Equation. Solution by Separating Variables. Use of Fourier Series | 12.3 | |
Thursday, Jan 19 | D' Alembert's Solution of the Wave Equation; Heat Equation: Modeling Very Long Bars | 12.4, 12.7 | HW 1 posted, solutions |
Tuesday, Jan 24 | Rectangular Membrane - Double Fourier Series | 12.9 | |
Thursday, Jan 26 | Solutions of PDEs by Laplace Transforms; Complex Numbers and Their Geometric Representation | 12.12, 13.1 | HW 2 posted, solutions |
Tuesday, Jan 31 | Polar Form of Complex Numbers. Powers and Roots; Derivative. Analytic Function | 13.2, 13.3 | |
Thursday, Feb 2 | Derivative. Analytic Function; Cauchy-Riemann Equations. Laplace's Equation | 13.3, 13.4 | HW 3 posted, solutions |
Tuesday, Feb 7 | Exponential Function | 13.5 | |
Thursday, Feb 9 | Trigonometric and Hyperbolic Functions. Euler's Formula; Logarithm. General Power. Principal Value | 13.6, 13.7 | HW 4 posted, solutions |
Tuesday, Feb 14 | Review | ||
Thursday, Feb 16 | Line Integral in the Complex Plane | 14.1 | HW 5 posted, solutions |
Tuesday, Feb 21 | Exam I | Exam I, solutions | |
Thursday, Feb 23 | Cauchy's Integral Theorem | 14.2 | HW 6 posted, solutions |
Tuesday, Feb 28 | Cauchy's Integral Theorem and Formula | 14.2, 14.3 | |
Thursday, Mar 2 | Derivatives of Analytic Functions; Sequences, Series, Convergence Tests | 14.4, 15.1 | HW 7 posted, solutions |
Tuesday, Mar 7 | No Class (Spring Recess) | ||
Thursday, Mar 9 | No Class (Spring Recess) | ||
Tuesday, Mar 14 | Power Series; Functions Given by Power Series | 15.2, 15.3 | |
Thursday, Mar 16 | Taylor and Maclaurin Series | 15.4 | HW 8 posted, solutions |
Tuesday, Mar 21 | Laurent Series; Singularities and Zeros. Infinity | 16.1, 16.2 | |
Thursday, Mar 23 | Singularities and Zeros. Infinity; Residue Integration Method | 16.2, 16.3 | HW 9 posted, solutions |
Tuesday, Mar 28 | Residue Integration Method ; Geometry of Analytic Functions: Conformal Mapping | 16.3, 17.1 | |
Thursday, Mar 30 | Geometry of Analytic Functions: Conformal Mapping | 17.1 | HW 10 posted, solutions |
Tuesday, Apr 4 | Review | ||
Thursday, Apr 6 | Exam II | Exam II, solutions | |
Tuesday, Apr 11 | Review | ||
Thursday, Apr 13 | Linear Fractional Transformation | 17.2 | HW 11 posted, solutions |
Tuesday, Apr 18 | Special Linear Fractional Transformations | 17.3 | |
Thursday, Apr 20 | Conformal Mapping by Other Functions | 17.4 | HW 12 posted, solutions |
Tuesday, Apr 25 | Conformal Mapping by Other Functions; Electrostatic Fields | 17.4, 18.1 | |
Thursday, Apr 27 | Review |
Doing Well in This Class
Although the prerequisites for the class are minimal, the material is dense and not trivial, especially if you have not seen mathematical proofs before. As is often the case in math courses, we will constantly build upon previous stuff; therefore, not leaving gaps in your understanding of the material is crucial for succeeding. This will require a sustained effort on your part, and in addition to attending lectures, you are encouraged to take advantage of instructor's office hours and the drop-in Math Learning Center. Of course, this is not a substitute for also working on your own; it is essential to think about the material, read the suggested texts, and solve homework problems by yourself. This last bit is a prerequisite to being able to solve problems under the pressure of an exam.
Inclusivity Statement
The West Virginia University community is committed to creating and fostering a positive learning and working environment based on open communication, mutual respect, and inclusion. If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Accessibility Services (293-6700). For more information on West Virginia University's Diversity, Equity, and Inclusion initiatives, please see http://diversity.wvu.edu.
Accessibility Needs
If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Disability Services (304-293-6700).