JNTUK B.Tech Complex Varibles gives you detail information of Complex Varibles R13 syllabus It will be help full to understand you complete curriculum of the year.
UNIT – I : Functions of a complex variable: Introduction -Continuity – Differentiability – Analyticity – Properties – Cauchy-Riemann equations in Cartesian and polar coordinates. Harmonic and conjugate harmonic functions – Milne – Thompson method
Applications: Potential between parallel plates, coaxial cylinders, potential in angular regions
- Subject Category
ABET Learning Objectives a e
ABET internal assessments 1 2 6
JNTUK External Evaluation A B E
UNIT – II : Elementary functions: Exponential, trigonometric, hyperbolic functions and their properties – General power Z (c is complex), principal value.
- Subject Category
ABET Learning Objectives a e
ABET internal assessments 1 6
JNTUK External Evaluation A B
UNIT – III : Complex integration: Line integral – Cauchy’s integral theorem – Cauchy’s integral formula – Generalized integral formula -Liouville Theorem – Morera’s Theorem
Applications: Circulation along closed curve, conservative fields
- Subject Category
ABET Learning Objectives a e k
ABET internal assessments 1 2 6
JNTUK External Evaluation A B E
UNIT – IV : Power series: Radius of convergence – Taylor’s series,-Maclaurin’s series -Laurent series- Singular point – Isolated singular point – pole of order m – essential singularity.
- Subject Category
ABET Learning Objectives a e
ABET internal assessments 1 2 6
JNTUK External Evaluation A B E
UNIT – V : Residue theorem and applications Residue- Residue theorem
Applications: Evaluation of integrals of the type
- Subject Category
ABET Learning Objectives a e
ABET internal assessments 1 2 6
JNTUK External Evaluation A B E
UNIT – VI : Conformal mapping: Transformation by exp z, ln z, z2, z ^n (n positive integer), Sin z, cos z, z + a/z. Translation, rotation, inversion and bilinear transformation – fixed point – cross ratio – properties – invariance of circles
Application: Potential between Noncoaxial cylinders, Flow around a corner
- Subject Category
ABET Learning Objectives a e k
ABET internal assessments 1 2 6
JNTUK External Evaluation A B E
Text Books
- Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, Wiley 2011.
- Michael Greenberg, Advanced Engineering Mathematics, International Edition, Pearson, 1998.
- Grewal, B. S., Higher Engineering Mathematics, Khanna Publishers, 2012.
Reference Books
- John H. Mathews, Russell W. Howell, Complex Analysis for Mathematics and Engineering, 5th Edition, Jones and Bartlett Publishers, 2006.
- Saff, E. B and A. D. Snider, Fundamentals of Complex Analysis, 3rd Edition, Pearson, 2003.
- Dennis G. Zill and Patrick Shanahan, A First course in Complex Analysis with Application, Jones and Bartlett Publishers, 2011.
| Subject Category | ABET Learning Objectives | ABET Internal Assessments | JNTUK External Evalution | Remarks |
|---|---|---|---|---|
| Theory Design Analysis Algorithms Drawing Others | a) Apply knowledge of math, science, & engineering | 1. Objective tests | A. Questions should have: | |
| b) Design & conduct experiments, analyze & interpret data | 2. Essay questions tests | B. Definitions, Principle of operation or philosopy of concept. Mathematical | ||
| c) Design a system/process to meet desired needs within economic, social, political, ethical, health/safety, manufacturability, & sustainability constraints | 3. Peer tutoring based | C. treatment, derivations, analysis, synthesis, numerical problems with inference. Design oriented problems | ||
| d) Function on multidisciplinary teams | 4. Simulation based | D. Trouble shooting type of | ||
| e) Identify, formulate, & solve engineering problems | 5. Design oriented | E. Questions Applications related questions | ||
| f) Understand professional & ethical responsibilities | 6. Problems based | F. Brain storming questions | ||
| g) Communicate effectively | 7. Experiential (project based) based | |||
| h) Understand impact of engineering solutions in global, economic, environmental, & societal context | 8. Lab work or field work based | |||
| i) Recognize need for & be able to engage in lifelong learning | 9. Presentation based | |||
| j) Know contemporary issues | 10. Case Studies based | |||
| k)Use techniques, skills, modern tools for engineering practices | 11. Role- Play based | |||
| 12. Portfolio based |
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