Download JNTUK B-Tech R19 1-1 And 1-2 I Year CE Syllabus 1

www.FirstRanker.com

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY: KAKINADA

KAKINADA – 533 003, Andhra Pradesh, India

--- Content provided by FirstRanker.com ---

DEPARTMENT OF CIVIL ENGINEERING

Course Objectives:

• This course will illuminate the students in the concepts of calculus.

--- Content provided by​ FirstRanker.com ---

• To enlighten the learners in the concept of differential equations and multivariable calculus.
• To equip the students with standard concepts and tools at an intermediate to advanced level mathematics to develop the confidence and ability among the students to handle various real world problems and their applications.

Course Outcomes: At the end of the course, the student will be able to:

• Utilize mean value theorems to real life problems (L3)
• Solve the differential equations related to various engineering fields (L3)

--- Content provided by‍ FirstRanker.com ---

• Familiarize with functions of several variables which is useful in optimization (L3)
• Apply double integration techniques in evaluating areas bounded by region (L3)
• Students will also learn important tools of calculus in higher dimensions. Students will become familiar with 2- dimensional and 3-dimensional coordinate systems (L5)

UNIT I: Sequences, Series and Mean value theorems: (10 hrs)

--- Content provided by‌ FirstRanker.com ---

Sequences and Series: Convergence and divergence – Ratio test – Comparison tests – Integral test – Cauchy's root test – Alternate series – Leibnitz's rule.

Mean Value Theorems (without proofs): Rolle's Theorem – Lagrange's mean value theorem – Cauchy's mean value theorem – Taylor's and Maclaurin's theorems with remainders.

UNIT II: Differential equations of first order and first degree: (10 hrs)

Linear differential equations – Bernoulli's equations – Exact equations and equations reducible to exact form.

--- Content provided by FirstRanker.com ---

Applications: Newton's Law of cooling – Law of natural growth and decay – Orthogonal trajectories – Electrical circuits.

UNIT III: Linear differential equations of higher order: (10 hrs)

Non-homogeneous equations of higher order with constant coefficients – with non-homogeneous term of the type e^ax, sin ax, cos ax, polynomials in xⁿ, e^ax V(x) and xⁿV(x) – Method of Variation of parameters.

Applications: LCR circuit, Simple Harmonic motion.

--- Content provided by‌ FirstRanker.com ---

UNIT IV: Partial differentiation: (10 hrs)

Introduction – Homogeneous function – Euler's theorem – Total derivative – Chain rule – Jacobian – Functional dependence – Taylor's and Mc Laurent's series expansion of functions of two variables.

Applications: Maxima and Minima of functions of two variables without constraints and Lagrange's method (with constraints).

UNIT V: Multiple integrals: (8 hrs)

Double and Triple integrals – Change of order of integration – Change of variables.

Applications: Finding Areas and Volumes.

Text Books:

--- Content provided by⁠ FirstRanker.com ---

1. B. S. Grewal, Higher Engineering Mathematics, 43rd Edition, Khanna Publishers.
2. B. V. Ramana, Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education.

Reference Books:

1. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India.

--- Content provided by FirstRanker.com ---

2. Joel Hass, Christopher Heil and Maurice D. Weir, Thomas calculus, 14th Edition, Pearson.
3. Lawrence Turyn, Advanced Engineering Mathematics, CRC Press, 2013.
4. Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press.

Course Objectives:

• To instruct the concept of Matrices in solving linear algebraic equations
• To elucidate the different numerical methods to solve nonlinear algebraic equations
• To disseminate the use of different numerical techniques for carrying out numerical integration.
• To equip the students with standard concepts and tools at an intermediate to advanced level mathematics to develop the confidence and ability among the students to handle various real world problems and their applications.

--- Content provided by‌ FirstRanker.com ---

Course Outcomes: At the end of the course, the student will be able to:

• Develop the use of matrix algebra techniques that is needed by engineers for practical applications (L6)
• Solve system of linear algebraic equations using Gauss elimination, Gauss Jordan, Gauss Seidel (L3)
• Evaluate approximating the roots of polynomial and transcendental equations by different algorithms (L5)
• Apply Newton's forward & backward interpolation and Lagrange's formulae for equal and unequal intervals (L3)

--- Content provided by​ FirstRanker.com ---

• Apply different algorithms for approximating the solutions of ordinary differential equations to its analytical computations (L3)

Unit I: Solving systems of linear equations, Eigen values and Eigen vectors: (10 hrs)

Rank of a matrix by echelon form and normal form – Solving system of homogeneous and non-homogeneous equations linear equations – Gauss Elimination for solving system of equations – Eigen values and Eigen vectors and their properties.

Unit-II: Cayley-Hamilton theorem and Quadratic forms: (10 hrs)

Cayley-Hamilton theorem (without proof) – Finding inverse and power of a matrix by Cayley-Hamilton theorem – Reduction to Diagonal form – Quadratic forms and nature of the quadratic forms – Reduction of quadratic form to canonical forms by orthogonal transformation.

Singular values of a matrix, singular value decomposition (Ref. Book – 1).

UNIT III: Iterative methods: (8 hrs)

--- Content provided by⁠ FirstRanker.com ---

Introduction – Bisection method – Secant method – Method of false position – Iteration method – Newton-Raphson method (One variable and simultaneous Equations) – Jacobi and Gauss-Seidel methods for solving system of equations.

UNIT IV: Interpolation: (10 hrs)

Introduction – Errors in polynomial interpolation – Finite differences – Forward differences – Backward differences – Central differences – Relations between operators – Newton's forward and backward formulae for interpolation – Interpolation with unequal intervals – Lagrange's interpolation formula - Newton's divide difference formula.

UNIT V: Numerical integration and solution of ordinary differential equations: (10 hrs)

Trapezoidal rule – Simpson's 1/3^rd and 3/8^th rule – Solution of ordinary differential equations by Taylor's series – Picard's method of successive approximations – Euler's method – Runge-Kutta method (second and fourth order).

Text Books:

1. B. S. Grewal, Higher Engineering Mathematics, 43rd Edition, Khanna Publishers.

--- Content provided by⁠ FirstRanker.com ---

2. B. V. Ramana, Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education.

Reference Books:

1. David Poole, Linear Algebra- A modern introduction, 4th Edition, Cengage.
2. Steven C. Chapra, Applied Numerical Methods with MATLAB for Engineering and Science, Tata Mc. Graw Hill Education.

--- Content provided by⁠ FirstRanker.com ---

3. M. K. Jain, S. R. K. Iyengar and R. K. Jain, Numerical Methods for Scientific and Engineering Computation, New Age International Publications.
4. Lawrence Turyn, Advanced Engineering Mathematics, CRC Press.