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

JNTUK R20 B.Tech Civil 1-1 Mathematics – I Material/ Notes PDF Download: Our comprehensive content is prepared for the syllabus, covering well-known sequences and series, differential equations, and multivariable calculus. Designed to equip students with intermediate to advanced mathematical concepts and tools, our material fosters confidence in handling real-world problems and applications. Download our JNTUK R20 B.Tech 1-1 Mathematics – I Material PDF now for a thorough understanding and preparation to excel in your studies.

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 higher order: Homogeneous and Non-homogeneous differential equations of higher order with constant coefficients – with non-homogeneous term 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:

• Apply mean value theorems practically to solve real-world issues.
• Address differential equations within various engineering disciplines.
• Gain familiarity with multi-variable functions for optimization applications.
• Employ double integration methods to assess area bounds.
• Acquire knowledge of calculus tools in higher dimensions, encompassing 2D and 3D coordinate systems.