JNTUK B.Tech Mathematics – I (Differential Equations) for R13 Batch

JNTUK B.Tech  Mathematics – I (Differential Equations)  Syllabus for Engineering R13 gives you detail information about Mathematics – I (Differential Equations) subject.

UNIT I: Differential equations of first order and first degree:
Linear-Bernoulli-Exact-Reducible to exact.

Applications : Newton’s Law of cooling-Law of natural growth and decay- orthogonal trajectories.

• Subject Category
  ABET Learning Objectives a d e
  ABET internal assessments 1 2 6
  JNTUK External Evaluation A B E

UNIT II: Linear differential equations of higher order:

Non-homogeneous equations of higher order with constant coefficients with RHS term of the type e ax

Applications: LCR circuit, Simple Harmonic motion in x, e V(x), xV(x)

• Subject Category
  ABET Learning Objectives a d e
  ABET internal assessments 1 2 6
  JNTUK External Evaluation A B E

UNIT III :  Laplace transforms:

Laplace transforms of standard functions-ShiftingTheorems, Transforms of derivatives and integrals – Unit step function –Dirac’s delta function- Inverse Laplace transforms– Convolution theorem (with out proof).

Application: Solutions of ordinary differential equations using Laplace transforms.

• Subject Category
  ABET Learning Objectives a e
  ABET internal assessments 1 2 6
  JNTUK External Evaluation A B E

UNIT IV : Partial differentiation:

Introduction- Total derivative-Chain rule-Generalized Mean Value theorem for single variable (without proof)-Taylors and Mc Laurent’s series for two variables– Functional dependence- Jacobian.

Applications: Maxima and Minima of functions of two variables with constraints and without constraints.

• Subject Category
• ABET Learning Objectives a c e
  ABET internal assessments 1 2 6
  JNTUK External Evaluation A B E

UNIT V  : First order Partial differential equations:

Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions –solutions of first order linear (Lagrange) equation and nonlinear (standard type) equations

• Subject Category
  ABET Learning Objectives a e
  ABET internal assessments 1 2 6
  JNTUK External Evaluation A B E

UNIT VI  : Higher order Partial differential equations:

Solutions of Linear Partial differential equations with constant coefficients- Method of separation of Variables.

Applications: One- dimensional Wave, Heat equations – two-dimensional Laplace Equation.

• Subject Category
  ABET Learning Objectives a e
  ABET internal assessments 1 2 6
  JNTUK External Evaluation B E

Books

• B.S.GREWAL, Higher Engineering Mathematics, 42nd Edition, Khanna Publishers.
• ERWIN KREYSZIG, Advanced Engineering Mathematics, 9th Edition, Wiley-India.
• GREENBERG, Advanced Engineering Mathematics, 2nd edition, Pearson edn.
• DEAN G. DUFFY, Advanced engineering mathematics with MATLAB, CRC Press.

PETER O’NEIL, advanced Engineering Mathematics, Cengage Learning.

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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