# Math 2nd Year Notes

2nd year Math chapter 5 notes are being uploaded here. Math part 2 chapter no. 5: Linear Inequalities and Linear Programming notes are in. Aug 29, 2014 Mathematics (Maths) XII (Practical Centre Notes for Second Year Class)All Exercise - Binary, Straight Line, General Equations, Fractions, Differentiablity, Calculus, Antiderivatives, Circle, Parabola, Ellipse, Hyperbola & Vectors Solved All Questions with Answers for All Chapters - Class XII, 12th, Second Year. Notes (Solutions) of Unit 02: Differentiation, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. Jul 16, 2018 2nd Year Math Notes Mathematics 2nd Year All Chapter Notes -If you are a 2nd-year student and looking for 2nd Year Math Notes then you are at right place. These Mathematics-XII FSc Part 2 (2nd year) Notes are according to “Punjab Text Book Board, Lahore”. There are seven units in this book and we have to work hard to make easy and suitable solutions for students and teachers so that it helps them learn things quickly and easily.

B.Tech Engineering Mathematics Pdf – 1st Year: Guys who are looking for Engineering Mathematics Textbooks & Notes Pdf everywhere can halt on this page. Because here we have jotted down a list of suggested books for b.tech first-year engg. mathematics to help in your exam preparation. So, check out the engineering M1, M2, M3 Books & Lecture Notes & prepare well for your exams.

You can access these best engg. 1st-year mathematics study materials and books in pdf format by downloading from our page. However, we have furnished some more details like engineering mathematics reference books list, syllabus, and important questions list. Along with the pdf formatted Btech 1st year Engg. Mathematics Books Download links on this article for your better preparation.

• Latest Engineering Mathematics Syllabus – First Year BTech
• FAQs on First-Year Engineering Maths Pdf Lecture Notes & Textbooks Download

## Engineering Mathematics Books & Lecture Notes Pdf

### Mathematics 2nd Year Notes

Engineering Mathematics provides the strong foundation of concepts like Advanced matrix, increases the analytical ability in solving mathematical problems, and many other advantages to engineering students. If you want to familiarize with all concepts of engineering maths and enhance your problem-solving ability and time-management skills, then choose the best book on engineering mathematics for btech 1st-year exams. Here, we have listed a few maths textbooks, mathematics 1, 2, 3 books, and study materials for you all in the form of quick download links. So, Download Maths 1st year Books & Notes in Pdf format from the below table and score more than pass marks in the final sem exams.

Also, Go through with the below articles:

### List of Suggested Engg. Mathematics Books for Reference

Refer to the B.Tech 1st year Engineering Maths Books along with Author Names recommended by subject experts and prepare well for your final exams. Verify the following list of M1, M2, M3 Engg. Mathematics Recommended Textbooks and select one or two books that suit your level of understanding and practice more y solving numerous problems accordingly.

• Kreyszig E., Advanced Engineering Mathematics, Wiley, 9th edition.
• Grewal B.S., Higher Engineering Mathematics, Khanna Publishers, 36th edition
• Dass H.K., Introduction to engineering Mathematics, S.Chand & Co Ltd, 11th edition
• Ramana B.V., Higher Engineering Mathematics, TMH, Ist edition
• J.Sinha Roy and S Padhy, A course on ordinary and partial differential Equation, Kalyani Publication, 3rd edition
• Shanti Narayan and P.K.Mittal, Differential Calculus, S. Chand, reprint 2009
• Chakraborty and Das; Principles of transportation engineering; pHI
• Rangwala SC; Railway Engineering; Charotar Publication House, Anand
• Ponnuswamy; Bridge Engineering; TMH

### Latest Engineering Mathematics Syllabus – First Year BTech

If you are looking for a detailed syllabus of Engineering mathematics then you are on the right page. Here, we have updated an Engineering Maths 1st year Syllabus in a full-fledged way. Plan your preparation by covering all these concepts and clear the exam. Having prior knowledge of the topics helps you in clearing the exam easily. So, refer to the below sections and collect all MI, MII, MIII Syllabus and start your preparation.

#### Mathematics M1 Syllabus – 1st Year M1 PDF Notes

I: Ordinary Differential Equations :

Basic concepts and definitions of 1st order differential equations; Formation of differential equations; solution of
differential equations: variable separable, homogeneous, equations reducible to homogeneous form, exact differential equation, equations reducible to exact form, linear differential equation, equations reducible to linear form (Bernoulli’s equation); orthogonal trajectories, applications of differential equations.

II: Linear Differential equations of 2nd and higher-order

Second-order linear homogeneous equations with constant coefficients; differential operators; solution of homogeneous equations; Euler-Cauchy equation; linear dependence and independence; Wronskian; Solution of nonhomogeneous equations: general solution, complementary function, particular integral; solution by variation of parameters; undetermined coefficients; higher order linear homogeneous equations; applications.

III: Differential Calculus(Two and Three variables)

Taylor’s Theorem, Maxima, and Minima, Lagrange’s multipliers

IV: Matrices, determinants, linear system of equations

Basic concepts of an algebra of matrices; types of matrices; Vector Space, Sub-space, Basis, and dimension, linear the system of equations; consistency of linear systems; the rank of a matrix; Gauss elimination; the inverse of a matrix by Gauss Jordan method; linear dependence and independence, linear transformation; inverse transformation; applications of matrices; determinants; Cramer’s rule.

V: Matrix-Eigen value problems

Eigenvalues, Eigenvectors, Cayley Hamilton theorem, basis, complex matrices; quadratic form; Hermitian, SkewHermitian forms; similar matrices; diagonalization of matrices; transformation of forms to principal axis (conic section).

#### Syllabus of Engg. Maths M2 – Mathematics II Books Pdf

Unit I: Laplace Transforms Laplace Transform, Inverse Laplace Transform, Linearity, transform of derivatives and Integrals, Unit Step function, Dirac delta function, Second Shifting theorem, Differentiation and Integration of Transforms, Convolution, Integral Equation, Application to solve differential and integral equations, Systems of differential equations. Unit II: Series Solution of Differential Equations

Power series; the radius of convergence, power series method, Frobenius method; Special functions: Gamma function, Beta function; Legendre’s and Bessel’s equations; Legendre’s function, Bessel’s function, orthogonal functions; generating functions.

### 2nd Year Math Key Book

Unit III: Fourier series, Integrals and Transforms

Periodic functions, Even and Odd functions, Fourier series, Half Range Expansion, Fourier Integrals, Fourier sine, and cosine transforms, Fourier Transform

Unit IV: Vector Differential Calculus

Vector and Scalar functions and fields, Derivatives, Gradient of a scalar field, Directional derivative, Divergence of a vector field, Curl of a vector field.

Unit V: Vector Integral Calculus

Line integral, Double Integral, Green’s theorem, Surface Integral, Triple Integral, Divergence Theorem for Gauss, Stoke’s Theorem

#### Engg. Mathematics M3 Syllabus – Best Books for Mathematics III

UNIT I: Linear systems of equations:

Rank-Echelon form-Normal form – Solution of linear systems – Gauss elimination – Gauss Jordon- Gauss Jacobi and Gauss-Seidel methods. Applications: Finding the current in electrical circuits.

UNIT II: Eigenvalues – Eigenvectors and Quadratic forms:

Eigenvalues – Eigenvectors– Properties – Cayley-Hamilton theorem Inverse and powers of a matrix by using Cayley-Hamilton theorem- Diagonalization- Quadratic forms- Reduction of quadratic form to canonical form – Rank – Positive, negative and semidefinite – Index – Signature. Applications: Free vibration of a two-mass system.

UNIT III: Multiple integrals:

Curve tracing: Cartesian, Polar, and Parametric forms. Multiple integrals: Double and triple integrals – Change of variables –Change of order of integration. Applications: Finding Areas and Volumes.

UNIT IV: Special functions:

Beta and Gamma functions- Properties – Relation between Beta and Gamma functions- Evaluation of improper integrals.
Applications: Evaluation of integrals.

UNIT V: Vector Differentiation:

Gradient- Divergence- Curl – Laplacian and second-order operators -Vector identities. Applications: Equation of continuity, potential surfaces

Payroll software free full version with crack free. UNIT VI: Vector Integration:

Line integral – Work is done – Potential function – Area- Surface and volume integrals Vector integral theorems: Greens, Stokes, and Gauss Divergence theorems (without proof) and related problems.
Applications: Work is done, Force.

Here is the book which is very important for all btech first-year candidates to get pass marks in the engineering Mathematics exam. B.S. Grewal is one of the famous authors in the market for Engg. Mathematics Textbooks. You can see all the concepts in a concise and understandable manner from the B.S. Grewal Engineering maths textbook. So, download B.tech 1st year engg. maths M1, M2, M3 Books pdf by Grewal B.S. for free by clicking on the below quick link. Here we have also listed the contents included in the Grewal B.S. Engineering Maths 1st year Text Books Pdf.

Index Content of B.S. Grewal Engg. Mathematics Book:

1 Algebra
1.1 Introduction
1.2 Revision of basic laws
1.3 Revision of equations
1.4 Polynomial division
1.5 The factor theorem
1.6 The remainder theorem
2 Partial fractions
2.1 Introduction to partial fractions
2.2 Worked problems on partial fractions with
linear factors
2.3 Worked problems on partial fractions with
repeated linear factors
2.4 Worked problems on partial fractions with
3 Logarithms
3.1 Introduction to logarithms
3.2 Laws of logarithms
3.3 Indicial equations
3.4 Graphs of logarithmic functions
4 Exponential functions
4.1 Introduction to exponential functions
4.2 The power series forex
4.3 Graphs of exponential functions
4.4 Napierian logarithms
4.5 Laws of growth and decay
4.6 Reduction of exponential & More

### Important Sample Questions for B.Tech Engineering Mathematics – 1st Year

Contenders can have a look at the Engg. Mathematics Review Questions in advance along with books & study materials from this page to prepare accordingly. Get to know the important questions related to the 1st year Mathematics and solve all concepts without any fail.

1. Show that if A is a complex triangular matrix and AA∗ = A∗A then A is a diagonal matrix.
2. Restate the results on transpose in terms of the conjugate transpose.
3. Give examples of Hermitian, skew-Hermitian, and unitary matrices that have entries with non-zero imaginary parts.
4. Show that for any square matrix A, S = A+A* 2 is Hermitian, T = A−A ∗ 2 is skew-Hermitian, and A=S+T.

### FAQs on First-Year Engineering Maths Pdf Lecture Notes & Textbooks Download

1. What books should I prepare for Engineering Mathematics Exam?

Candidates can check out the following books led by subject experts to prepare for Engg 1st year Mathematics exam. The M1, M2, M3 Books are as follows:

• Grewal B.S., Higher Engineering Mathematics, Khanna Publishers, 36th edition
• Dass H.K., Introduction to engineering Mathematics, S.Chand & Co Ltd, 11th edition
• Ramana B.V., Higher Engineering Mathematics, TMH, Ist edition

2. How to download Pdf formatted B.S Grewal Engineering Mathematics Pdf Textbook & Study Material?

Tap on the quick link available on this page and get Engineering Mathematics by B.S. Grewal Textbook & Study Material in PDF format for free of cost. If you wish you can get them online too.

3. Which is the Best Engineering Mathematics Book for Btech 1st year & GATE Exams?

Advanced Engineering Mathematics by Erwin Kreyszig is the best one for the first-year examination preparation & Higher Engineering mathematics by B.S. Grewal is the good book for GATE preparation. So, download B.Tech 1st-year Engg. Mathematics Books & Notes Pdf from our page & for more please visit our site Ncertbooks.guru.

4. What are some good resources for preparing Engineering M1, M2 & M3?

You can get all preparation associated resources such as Books, Lecture Notes, Study Material, Reference Textbooks for Mathematicsto have an in-depth knowledge of concepts.

### Conclusion

We hope the detailed provided on this page regarding Engineering Mathematics will help you to solve the engg maths paper easily. If you require more about B.Tech 1st year Engg. Mathematics M1, M2, M3 Textbooks & study materials do refer to our page and attain what you need. Else, leave your comment in the below section and clarify your doubts by our experts at the soonest possible. Visit our site Ncertbooks.guru to get the latest updates on Engineering 1st year Mathematics I, II, III Syllabus, Reference Books, and Questions.