EE 250 Mathematics for Electrical Engineers

Professor Boesch; OFFICE B 210;

201- 216- 5624; fboesch@stevens.edu

MY OFFICE HOURS ARE THURSDAY AFTERNOONS 1 TO 3 PM

Grading:  Take Home Midterm 40%, HW 30%, and Final 30%

All HW, Take-home exams, and PowerPoint lectures can be found at

          <http://www.ece.stevens-tech.edu/~fboesch>.

PowerPoint lectures can be found at "Slides" button on home page

HW&Exams can be found at "EE250 HW&Exams" button on home page

Important information can be found at "Messages" button on home page

PLEASE CHECK MESSAGES WEEKLY

Course contents

Introduction to logic, methods of proof, proof by induction, and the pigeonhole principle with applications to logic design.    Analytic functions of a complex variable, Cauchy-Riemann equations, Taylor series.   Integration in the complex plane, Cauchy Integral formula Liouville’s theorem, maximum modulus theorem.   Laurent series, residues, the residue theorem.   Applications to system theory, Laplace transforms,  and transmission lines

TEXT –  COMPLEX VARIABLES AND APPLICATIONS, Seventh Edition, 2004, ISBN: 0-07-287252-7, James Ward Brown, & Ruel V. Churchill (deceased), McGraw Hill Higher Education

<http://www.mhhe.com/catalogs/0079121470.mhtml>

Week 1&2 - Logic, Propositional Equivalences, Predicates and Quantifiers, Sets, Set Operations, Functions (Instructor provided Notes )

Week 3&4 - Methods of Proof, Induction, Recursive Definitions, The Pigeonhole Principle, (Instructor provided Notes )

Week 5, 6 &7 - Analytic Functions, Derivatives, Cauchy-Riemann Equations, Sufficient

          Conditions for Differentiability

Week 8, 9 & 10 – Contours, Contour Integrals, Cauchy Integral Formula, Derivatives of

Analytic Functions, Liouville's Theorem, Maximum Moduli of Functions

Week 11&12 – Taylor & Laurent Series, Residues & Residue Theorems, Residues at Poles

Week 13&14 -  Applications of Residues, Evaluation of Improper Integrals, Inverse, Laplace Transforms

· Complex Variables and Applications, 7th Ed. ©2004, J. W. Brown, & R. V. Churchill, McGraw Hill

Chapter 2: Analytic Functions

                 14. Limits

                 15. Theorems on Limits

                 17. Continuity

                 18. Derivatives

                 19. Differentiation Formulas

                 20. Cauchy-Riemann Equations

                 21. Sufficient Conditions for Differentiability

                 22. Polar Coordinates

                 23. Analytic Functions

Chapter 3: Elementary Functions

                 28. The Exponential Function

                 29. The Logarithm Function

                 30. Branches and Derivatives of Logarithms

                 31. Some Identities involving Lorarithms

                 32. Complex Exponents

                 33. Trigonometric Functions

                 34. Hyperbolic Functions

                             The square root and its branches – (instructor provided notes)

Chapter 4: Integrals

                 37. Definite Integrals of Complex Functions of a real variable.

                 38. Contours

                 39. Contour Integrals

                 40. Examples

                 41. A useful upper bound

                 42. Antiderivatives

                 43. Examples

                 44. Cauchy-Goursat Theorem

                 47. Cauchy Integral Formula

                 48. Derivatives of Analytic Functions

                      Finding the area under the spectrum of a pulse using Jordan's Inequality & the

                      Cauchy Goursat Theorem – ( instructor provided notes & p212 )

                 49. Liouville's Theorem

                 50. Maximum Moduli of Functions

                     The RC transmission Line – ( instructor provided notes)

Chapter 5: Series

                 51. Convergence of Sequences

                 52. Convergence of Series

                 53. Taylor Series

                 54. Examples

                 55. Laurent Series

                 56. Examples

                      Fourier Transforms, band-limited functions – ( instructor provided notes)

                      The Gaussian – ( instructor provided notes)

Chapter 6: Residues and Poles

                 62. Residues

                 63. Cauchy's Residue Theorem

                 64. Using a Single Residue

                 65. The Three Types of Isolated Singular Points

                 66. Residues at Poles

                 67. Examples

                 68. Zeros of Analytic Functions

                 69. Zeros and Poles

Chapters 7: Applications of Residues  

                 71. Evaluation of Improper Integrals

                 72. Example

                 73. Improper Integrals from Fourier Analysis

                 74. Jordan's Lemma

                 81. Inverse Laplace Transforms

     82. Examples

Assessment Performance Criteria

OUTCOMES for EE250 - Mathematics for Electrical Engineers

Outcome 1 (Scientific Foundation): The student will be able to -

· State the definitions and laws of basic logic, set theory, and functions.

           · Produce a mathematical induction proofs for topological and geometric results.

· State the pigeonhole principle and use it to derive a basic counting result

· State the definition of an analytic function and know the test using the
                    Cauchy-Rieman Equations

· Derive the properties of complex trigonometric and hyperbolic functions

· Define a branch of a "multi-valued" function

· State and explain the Cauchy-Goursat Theorem, Liouville Theorem, and
                    the Cauchy Integral Formula

· Derive the equations for the step response of an RC or an LC transmission line

· State Jordan's Lemma and the Residue Theorem and use them to find inverse Laplace
                    transforms of hyperbolic functions and functions that have a branch-cut.