JNTUk B.Tech Mathematics – III (Linear Algebra & Vector Calculus) R13 Syllabus for Engineering it gives you detail information about Mathematics – III (Linear Algebra & Vector Calculus) syllabus.
UNIT I Linear systems of equations:
Rank-Echelon form, Normal form – Solution of Linear Systems – Direct Methods- Gauss Elimination – Gauss Jordon and Gauss Seidal Methods.
Application: Finding the current in a electrical circuit.
- Subject Category
ABET Learning Objectives a e k
ABET internal assessments 1 2 6 4
JNTUK External Evaluation A B E
UNIT II Eigen values – Eigen vectors and Quadratic forms:
Eigen values – Eigen vectors– Properties – Cayley-Hamilton Theorem – Inverse and powers of a matrix by using Cayley-Hamilton theorem- Quadratic forms- Reduction of quadratic form to canonical form – Rank – Positive, negative definite – semi definite – index – signature.
Application: Free vibration of a two-mass system.
- Subject Category
ABET Learning Objectives a d e k
ABET internal assessments 1 2 4 6
JNTUK External Evaluation A B E
UNIT III Multiple integrals:
Review concepts of Curve tracing (Cartesian – Polar and Parametric curves)- Applications of Integration to Lengths, Volumes and Surface areas of revolution in Cartesian and Polar Coordinates. Multiple integrals – double and triple integrals – change of variables – Change of order of Integration
Application: Moments of inertia
- Subject Category
ABET Learning Objectives a e d
ABET internal assessments 1 2 6
JNTUK External Evaluation A B E
UNIT IV Special functions:
Beta and Gamma functions- Properties – Relation between Beta and Gamma functions- Evaluation of improper integrals.
Application: Evaluation of integrals
- Subject Category
ABET Learning Objectives a e
ABET internal assessments 1 2 6
JNTUK External Evaluation A B E
UNIT V Vector Differentiation:
Gradient- Divergence- Curl – Laplacian and second order operators -Vector identities.
Application: Equation of continuity, potential surfaces
- Subject Category
ABET Learning Objectives a e
ABET internal assessments 1 2 6
JNTUK External Evaluation A B E
UNIT VI Vector Integration:
Line integral – work done – Potential function – area- surface and volume integrals Vector integral theorems: Greens, Stokes and Gauss Divergence Theorems (Without proof) and related problems.
Application : work done, Force
- Subject Category
ABET Learning Objectives a e
ABET internal assessments 1 2 6
JNTUK External Evaluation A B E
BOOKS
- GREENBERG, Advanced Engineering Mathematics, 9th Edition, Wiley-India.
- B.V. RAMANA, Higher Engineering Mathematics, Tata Mc Grawhill.
- ERWIN KREYSZIG, Advanced Engineering Mathematics, 9th Edition, Wiley-India.
- PETER O’NEIL, Advanced Engineering Mathematics, Cengage Learning.
- D.W. JORDAN AND T. SMITH, Mathematical Techniques, Oxford University Press.
| 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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