JNTUK R20 B.Tech EEE 1-1 Mathematics – I Material/ Notes PDF Download

JNTUK R20 B.Tech EEE 1-1 Mathematics – I Material/ Notes PDF Download: The study material for JNTUK R20 B.Tech 1-1 Mathematics – I aim to introduce students to various sequences and series, fostering an understanding of their behavior. Additionally, the material covers differential equations and multivariable calculus concepts to enhance students’ comprehension. With a focus on intermediate to advanced-level mathematics, the material provides standard concepts and tools to tackle real-world problems effectively, promoting confidence and problem-solving skills among students. Access the JNTUK R20 B.Tech Mathematics – I material and notes, including JNTUK R20 B.Tech EEE M1 material, for comprehensive learning.

JNTUK R20 B.Tech 1-1 Mathematics – I Material – Chapters

Unit 1 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – I Material

Sequences, Series, and Mean value theorems: Sequences and Series: Convergences 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, Problems and applications on the above theorem.

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Unit 2 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – I Material

Differential equations of first order and first degree: Linear differential equations– Bernoulli’s equations –Exact equations and equations reducible to exact form. Applications: Newton’s Law of Cooling– Law of natural growth and decay– Orthogonal trajectories– Electrical circuits.

Unit 3 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – I Material

Linear differential equations of a higher order: Homogeneous and Non-homogeneous differential equations of higher order with constant coefficients – with non-homogeneous terms of the type eax, sin ax, cos ax, polynomials in xn, e axV(x) and xnV(x) – Method of Variation of parameters, Cauchy and Legendre’s linear equations. Applications: LCR circuit, Simple Harmonic motion.

Unit 4 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – I Material

Partial differentiation: Introduction – Homogeneous function – Euler’s theorem– Total derivative– Chain rule– Jacobian – Functional dependence –Taylor’s and MacLaurin’s series expansion of functions of two variables. Applications: Maxima and Minima of functions of two variables without constraints and Lagrange’s method.

Unit 5 Syllabus PDF Download | JNTUK R20 B.Tech 1-1 Mathematics – I Material

Multiple integrals: Double and Triple integrals – Change of order of integration in double integrals – Change of variables to polar, cylindrical, and spherical coordinates. Applications: Finding Areas and Volumes.

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JNTUK R20 B.Tech 1-1 Mathematics – I Notes – Outcomes

• In this course, students will use mean value theorems to solve real-life problems.
• They’ll also learn to solve differential equations relevant to different engineering fields.
• Additionally, they’ll become acquainted with functions of several variables, essential for optimization.
• Students will apply double integration techniques to find areas bounded by regions. Moreover, they’ll explore calculus tools in higher dimensions, gaining familiarity with 2-dimensional and 3-dimensional coordinate systems.