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

JNTUK R20 B.Tech Mechanical 1-1 Mathematics – I Material/ Notes PDF Download: The study material designed for JNTUK R20 B.Tech 1-1 Mathematics – I is crafted to acquaint students with diverse sequences and series, nurturing a thorough understanding of their characteristics. Furthermore, it delves into the realm of differential equations and multivariable calculus concepts to elevate students’ comprehension levels. Tailored for intermediate to advanced-level mathematics, this resource equips students with essential concepts and methodologies necessary for effectively tackling real-world challenges. By instilling confidence and refining problem-solving skills, the material fosters a holistic approach to learning.

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

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 M1 Notes – Outcomes

• In this course, students will apply mean value theorems to solve practical problems encountered in real life.
• They will also learn how to solve differential equations that are important in various engineering fields.
• Additionally, students will get familiar with functions involving multiple variables, which are crucial for optimization purposes.
• They will use double integration methods to determine areas enclosed by different regions.
• Furthermore, students will explore calculus concepts in higher dimensions, including 2-dimensional and 3-dimensional coordinate systems.