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

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JNTUK R20 B.Tech ECE 1-1 Mathematics – I Material/ Notes PDF Download: Master mathematics effortlessly with our JNTUK R20 B.Tech ECE 1-1 Mathematics – I Material. Explore a variety of sequences and series, understanding their behavior and applications intuitively. Gain clarity on differential equations and multivariable calculus concepts, essential for solving real-world problems confidently.

Our material equips students with intermediate to advanced-level mathematical tools, building both competence and confidence. With accessible PDF downloads, elevate your mathematical skills and conquer academic challenges seamlessly. Embark on a journey of mathematical discovery and success with our comprehensive resources.

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

Unit 1 Syllabus PDF Download | JNTUK R20 B.Tech ECE M1 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.

Unit 2 Syllabus PDF Download | JNTUK R20 B.Tech ECE M1 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 ECE M1 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 ECE M1 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 ECE M1 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.

JNTUK R20 B.Tech Mathematics – I Material – Outcomes

• Understand how mean value theorems apply to real-life situations, connecting math concepts to practical problems.
• Solve engineering-related differential equations to develop problem-solving skills applicable across various engineering fields.
• Learn about functions with multiple variables to prepare for optimization tasks in engineering contexts.
• Use double integration techniques to calculate precise areas, particularly useful for spatial relationships in engineering and math.
• Master calculus tools for higher dimensions, improving proficiency in both 2D and 3D coordinate systems.
• Gain practical skills in calculus relevant to engineering applications.

For more details about JNTUK R20 B.Tech ECE 1-1 Mathematics – I Material and other materials follow our official website Freshersnow.com.