568Tsikkou

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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).