Download Course Outline-Complex Variables And Transforms-Handout and more Exercises Electronics in PDF only on Docsity!
Complex Variables & Transforms Credit Hours: 3+
Textbook: Advanced Engineering Mathematics 8th edition Author: Erwin Kreyszig
Reference book: Advanced Engineering Mathematics Author: Alan Jeffrey.
Course Description: The course gives the students a sound knowledge of Fourier Transforms along with Fourier Integrals, Partial Differential Equations, advanced vector analysis, complex variables and complex integrals.
Equipped with the Knowledge gained in this course, the students
will be able to apply mathematics as a strong tool to model and
solve the practical problems they come across in engineering and
technology.
Course Description:
The course comprises four parts. The first part consists of Partial Differential Equations. This part helps the students in mathematical modeling of engineering problems depending on more than one variable.
In the second part Fourier Transform and Fourier Integrals are covered. Advanced topics of Laplace Transform not covered in the course of calculus II are covered in this course.
In the third part advanced topics in vector analysis like calculus of del operator, gradient, curl and divergence along with their physical interpretations are covered.
The fourth part covers complex variable and complex integration. Harmonic functions, line integrals, poles residues and singularities are covered in this part.
Course Evaluation: There will be five quizzes two assignments one Mid-Term Exam and one end semester examination. Evaluation will be on the basis of following criteria:
Quizzes 10% Assignments 10% Mid-Term Exam 30% Final Examination 50% Total 100
docsity.com
Detailed Syllabus for
Complex Variable & Transforms
Week Ch. Sect Topics
1 Notes Kreyszic Sec 12.1^ Partial differential Equa equations by Operator Method.tions, Fundamental theorem, Solution of Partial^ differential
2 Notes Kreyszic Sec 12. 1 Solution of partial differential equations by the initial & boundary value problems.^ method of separating^ of variables,
3 Notes Kreyszic Sec 12. 5 Derivation of Wave equation and its solution by Fourier Series.
4 Notes Kreyszic Sec 12. 2 Derivation of heat equation and its solution by Fourier series. More initial and boundary value problems.
5 Notes Kreyszic Sec 12. 4 D ‘Alembert’s solution of wave equation.
6 1 st^ One Hour Test
7 Notes Kreyszic Sec 11.7,11.8 Fourier Integrals, Fourier Sine and Cosine integrals.
8 Notes Kreyszic Sec 11.9 Fourier Transforms, Fourier Sine and Cosine transforms.
Notes Kreyszic Sec 9.4, 9.
Scalar & Vector fields, Gradient of a scalar function and its physical and geometrical significance.
Notes/Handouts Kreyszic Sec 9.8, 9.
Divergence of a vector field & its significance, curl of a vector field & its significance.
Notes/Handouts Kreyszic Sec 9. 9 , 10.1, 10.
Calculus of del operator, Irrotational & Solenoidal vector fields and their Scalar & vector potentials.
12 2 nd^ One Hour Test
Notes Kreyszic Sec 10.1, 10.4, 10.5, 10.6, 10.7,
Line, surface and volume integrals. Divergence Theorem, Stokes Theorem and Green’s Theorem and their applications.
Notes Kreyszic Sec 13.1, 13.2, 13.3, 13.
Review of Complex algebra, Complex functions, Analytic functions, uv- functions, CR-equations. Properties of uv- function. Harmonic function.
Notes Kreyszic Sec 16.3, 14.2, 14.
Cauchy Integral Theorem and formula, singularities, Poles & Residues, Residue Theorem.
Notes Kreyszic Sec 16.1, 16.
Evaluation of residues by Laurent Series.
Notes Kreyszic Sec 16.1, 16.2, 16.
Definite integrals of different forms by using contour integration.
18 End Semester Exam
docsity.com
