JNTUK R20 B.Tech CSE 1-1 Mathematics – I Material/ Notes PDF Download: If you’re pursuing JNTUK R20 B.Tech CSE 1-1 Mathematics – I Material is designed to provide a comprehensive understanding of well-known sequences and series, fostering an intuitive grasp of their behavior. This material not only covers fundamental concepts but delves into the intricacies of differential equations and multivariable calculus, enlightening learners on their applications in real-world scenarios.
The JNTUK R20 B.Tech Mathematics – I Material aims to equip students with intermediate to advanced-level mathematical concepts and tools. By offering a structured approach, it enhances students’ confidence and ability to tackle diverse real-world problems effectively. To access this valuable resource, the JNTUK R20 B.Tech CSE 1-1 Mathematics – I Material PDF Download is available, ensuring easy and convenient access to this essential learning material.
JNTUK R20 B.Tech CSE 1-1 Mathematics – I Material – Units
| No. Of Units | Name of the Unit |
| Unit – 1 | Sequences, Series, and Mean Value Theorems |
| Unit – 2 | Differential equations of first-order and first-degree |
| Unit – 3 | Linear differential equations of higher-order |
| Unit – 4 | Partial differentiation |
| Unit – 5 | Multiple integrals |
Unit 1 Syllabus PDF Download | JNTUK R20 B.Tech CSE 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.
| JNTUK R20 B.Tech CSE 1-1 Mathematics – I Material – PDF Download | |
| To Download The JNTUK R20 B.Tech CSE 1-1 Mathematics – I Unit 1 Notes | Download PDF |
Unit 2 Syllabus PDF Download | JNTUK R20 B.Tech CSE 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.
| JNTUK R20 B.Tech CSE 1-1 Mathematics – I Material – PDF Download | |
| To Download The JNTUK R20 B.Tech CSE 1-1 Mathematics – I Unit 2 Notes | Download PDF |
Unit 3 Syllabus PDF Download | JNTUK R20 B.Tech CSE 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.
| JNTUK R20 B.Tech CSE 1-1 Mathematics – I Material – PDF Download | |
| To Download The JNTUK R20 B.Tech CSE 1-1 Mathematics – I Unit 3 Notes | Download PDF |
Unit 4 Syllabus PDF Download | JNTUK R20 B.Tech CSE 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.
| JNTUK R20 B.Tech CSE 1-1 Mathematics – I Material – PDF Download | |
| To Download The JNTUK R20 B.Tech CSE 1-1 Mathematics – I Unit 4 Notes | Download PDF |
Unit 5 Syllabus PDF Download | JNTUK R20 B.Tech CSE 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.
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| To Download The JNTUK R20 B.Tech CSE 1-1 Mathematics – I Unit 5 Notes | Download PDF |
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JNTUK R20 B.Tech Mathematics – I Material – Outcomes
- Real-Life Applications of Mean Value Theorems: Apply mean value theorems to address practical problems, connecting mathematical concepts to real-world scenarios.
- Engineering Differential Equations: Solve differential equations relevant to various engineering fields, developing problem-solving skills in engineering applications.
- Optimization with Functions of Several Variables: Familiarize students with functions involving multiple variables, preparing them for optimization tasks in engineering contexts.
- Area Calculations using Double Integration: Utilize double integration methods for precise area calculations, offering a valuable tool for spatial relationships in engineering and mathematics.
- Mastery of Calculus in Higher Dimensions: Equip students with essential calculus tools for higher dimensions, enhancing their proficiency in both 2-dimensional and 3-dimensional coordinate systems.