3110014,Mathematics-1 (M-1) EBooks free pdf file & GTU related Mathematics-1 syllabus Ravish R. SIngh & Mukul Bhatt gtu book pdf download in single click.You can also download free M-1 ( Mathematics-1) books PDF file and it's GTU related syllabus are also upload in this site.
Syllabus:-
| Sr. No. | Content | Total Hrs |
|---|---|---|
| 1 | Indeterminate Forms and L’Hôspital’s Rule. 01 15 % Improper Integrals, Convergence and divergence of the integrals, Beta and Gamma functions and their properties. 03 Applications of definite integral, Volume using cross-sections, Length of plane curves, Areas of Surfaces of Revolution | 0 |
| 2 | Convergence and divergence of sequences, The Sandwich Theorem for Sequences, The Continuous Function Theorem for Sequences, Bounded Monotonic Sequences, Convergence and divergence of an infinite series, geometric series, telescoping series, 𝑛 𝑛𝑛 term test for divergent series, Combining series, Harmonic Series, Integral test, The p - series, The Comparison test, The Limit Comparison test, Ratio test, Raabe’s Test, Root test, Alternating series test, Absolute and Conditional convergence, Power series, Radius of convergence of a power series, Taylor and Maclaurin series. | 08 |
| 3 | Fourier Series of 2𝑛 periodic functions, Dirichlet’s conditions for representation by a Fourier series, Orthogonality of the trigonometric system, Fourier Series of a function of period 2𝑛, Fourier Series of even and odd functions, Half range expansions. | 04 |
| 4 | Functions of several variables, Limits and continuity, Test for non existence of a limit, Partial differentiation, Mixed derivative theorem, differentiability, Chain rule, Implicit differentiation, Gradient, Directional derivative, tangent plane and normal line, total differentiation, Local extreme values, Method of Lagrange Multipliers. | 08 |
| 5 | Multiple integral, Double integral over Rectangles and general regions, double integrals as volumes, Change of order of integration, double integration in polar coordinates, Area by double integration, Triple integrals in rectangular, cylindrical and spherical coordinates, Jacobian, multiple integral by substitution. | 08 |
| 6 | Elementary row operations in Matrix, Row echelon and Reduced row echelon forms, Rank by echelon forms, Inverse by Gauss-Jordan method,n of system of linear equations by Gauss elimination and GaussJordan methods. Eigen values and eigen vectors, Cayley-Hamilton theorem, Diagonalization of a matrix. | 07 |
Suggested Specification table with Marks (Theory):
| Distribution of Theory Marks |
| R Level | U Level | A Level | N Level | E Level | C Level |
| 15 | 35 | 35 | 0 | 0 | 0 |
Legends: R: Remembrance; U: Understanding; A: Application, N: Analyze and E: Evaluate C: Create and above Levels (Revised Bloom’s Taxonomy)
Course Outcomes:-
| Sr. No | Course Outcomes | Weightage in % |
|---|---|---|
| 1 | To apply differential and integral calculus to improper integrals and to determine applications of definite integral. Apart from some other applications they will have a basic understanding of indeterminate forms, Beta and Gamma functions | 15 |
| 2 | To apply the various tests of convergence to sequence, series and the tool of power series and fourier series for learning advanced Engineering Mathematics. | 30 |
| 3 | To compute directional derivative, maximum or minimum rate of change and optimum value of functions of several variables | 20 |
| 4 | To compute the areas and volumes using multiple integral techniques. | 20 |
| 5 | To perform matrix computation in a comprehensive manner. | 15 |
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Mathematics is a key area of study in any engineering course. A sound knowledge
of this subject will help engineering students develop analytical skills, and thus
enable them to solve numerical problems encountered in real life, as well as apply
mathematical principles to physical problems, particularly in the field of engineering.
Users
This book is designed for the first year GTU engineering students pursuing the course
Mathematics-1, SUBJECT CODE: 3110014 in their first year Ist Semester. It covers
the complete GTU syllabus for the course on Mathematics-1, which is common to all
the engineering branches.
Objective
The crisp and complete explanation of topics will help students easily understand the
basic concepts. The tutorial approach (i.e., teach by example) followed in the text will
enable students develop a logical perspective to solving problems.
Features
Each topic has been explained from the examination point of view, wherein the theory
is presented in an easy-to-understand student-friendly style. Full coverage of concepts
is supported by numerous solved examples with varied complexity levels, which is
aligned to the latest GTU syllabus. Fundamental and sequential explanation of topics
are well aided by examples and exercises. The solu tions of examples are set following a
‘tutorial’ approach, which will make it easy for students from any background to easily
grasp the concepts. Exercises with answers immediately follow the solved examples
enforcing a practice-based approach. We hope that the students will gain logical
understanding from solved problems and then reiterate it through solving similar
exercise problems themselves. The unique blend of theory and application caters to
the requirements of both the students and the faculty. Solutions of GTU examination
questions are incorporated within the text appropriately.
Highlights
- Crisp content strictly as per the latest GTU syllabus of Mathematics-1(Regulation 2018)
- Comprehensive coverage with lucid presentation style
- ∑Each section concludes with an exercise to test understanding of topics
- Solutions of GTU examination questions included appropriately within the
chapters
- Rich exam-oriented pedagogy:
- Solved examples within chapters: 850+
- Unsolved exercises: 500+
- MCQs at the end of chapters: 300+
Chapter Organization
The content spans the following 10 chapters which wholly and sequentially cover each
module of the syllabus.
Chapter 1 introduces Indeterminate Forms.
Chapter 2 discusses Improper Integrals.
Chapter 3 presents Gamma and Beta Functions.
Chapter 4 covers Applications of Definite Integrals.
Chapter 5 deals with Sequences and Series.
Chapter 6 presents Taylor’s and Maclaurin’s Series.
Chapter 7 discusses Fourier Series.
Chapter 8 presents Partial Derivatives.
Chapter 9 covers Multiple Integrals.
Chapter 10 deals with Matrices.
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