**JNTUK R20 1-1 Mathematics – I Material PDF Download**

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:**

- To become familiar with a range of well-known sequences and shows with a growing understanding of how they behave in new series.
- To help the students understand the notion of differential equations and multivariable calculus.
- 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.

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**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.

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**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.

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**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.

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**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.

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**TEXTBOOKS:**

- B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers.
**⇒****BUY NOW****⇐** - B. V. Ramana, Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education.
**⇒****BUY NOW****⇐**

**REFERENCE BOOKS:**

- Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India.
**⇒****BUY NOW****⇐** - Joel Hass, Christopher Heil, and Maurice D. Weir, Thomas calculus, 14th Edition, Pearson.
**⇒****BUY NOW****⇐** - Lawrence Turyn, Advanced Engineering Mathematics, CRC Press, 2013.
**⇒****BUY NOW****⇐** - Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press.

**OUTCOMES:**

- utilize mean value theorems to real-life problems (L3)
- solve the differential equations related to various engineering fields (L3)
- 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 )