# JNTUK 1-1 R20 Civil Materials PDF Mathematics – I Material

Students studying JNTUK’s syllabus for R20 Civil, CSE, ECE, EEE, and Mech Branches can download The unit-specific R20 1-1 Mathematics I (M1) Notes and Material PDFs below.

OBJECTIVES:

1. To become familiar with a range of well-known sequences and shows with a growing understanding of how they behave in new series.
2. To help the students understand the notion of differential equations and multivariable calculus.
3. To provide the students with the basic concepts and tools appropriate for Intermediate to Advanced levels in mathematics to build confidence and competence for students to tackle diverse real-world issues and their solutions.

UNIT-1
Sequences Series, Sequences, and Mean value theories: Sequences and Series: Convergences as well as divergence tests – Ratio test – Tests for comparison Integral test – Cauchy’s root test – Alternate series- Leibnitz’s Rule. Mean Value Theorems (without proofs) of Rolle Lagrange’s Mean Value Theorem Cauchy’s Mean Value Theorem Maclaurin and Taylor’s theorems, with problems, the remainders, and their applications to this theorem.

UNIT-2
Differential equations of first and first degrees Linear differential equations the Bernoulli equations -exact equations and equations that can be reduced to a precise form. Applications Newton’s Law of cooling- Law of natural decay and growth orthogonal trajectories- Electrical circuits.

UNIT-3
Linear differential equations of higher level: Homogeneous as well as non-homogeneous differential equations of higher order, with constant coefficients, accompanied by a non-homogeneous expression that is each type, syntax, and cos Polynomials in xn and e ax(x) in(x) and in(x) in(x) – methods of variation for Parameters, Cauchy and Legendre’s linear equations. The applications include LCR circuits, Simple Harmonic motion.

UNIT-4
Partially Differentiation: Introduction Homogeneous Function – Euler’s Theorem- Total derivative – Chain rule Jacobian Functional dependence- Taylor’s and MacLaurin’s series extension of functions with two variables. The applications: Maxima and Minima of functions of two variables with no limitations and Lagrange’s method.

UNIT-5
Multiple integrals: Triple and Double integrals – Change the order that integrates double integrals. Variables can be changed to either polar or cylindrical and Spherical coordinates. Applications: Finding Areas and Volumes.

TEXTBOOKS:

1. B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers. BUY NOW
2. B. V. Ramana, Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education. BUY NOW

REFERENCE BOOKS: