# Higher Engineering Mathematics by bs Grewal free pdf download

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### Higher Engineering Mathematics by bs Grewal free pdf

# Information of book

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### Engineering Mathematics Syllabus For All Branches of Engineerings in various Universities

*“HIGHER ENGINEERING MATHEMATICS BY BS GREWAL FREE PDF” IS VERY USEFUL FOR BELOW SYLLABUS.*

** Mathematics I:**

**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 algebra of matrices; types of matrices; Vector Space, Sub-space, Basis and dimension, linear the system of equations; consistency of linear systems; rank of matrix; Gauss elimination; 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; the transformation of forms to principal axis (conic section).

**MATHEMATICS-II**

**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.

**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.

**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

**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.

**V: Vector Integral Calculus**

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

** Engineering 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.* Higher Engineering Mathematics by bs Grewal free pdf*

**UNIT II: **Eigenvalues – Eigen*v*ectors 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

**UNIT VI:** Vector Integration:

Line integral – Work 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.

#### Book Content

** Unit I : Algebra , Vectors and Geometry**

1. Solution Of Equations

2. Linear Algebra: Determinants, Matrices

3. Vector Algebra and Solid Geometry

** UNIT II : CALCULUS**

4. Differential Calculus & Its Applications

5. Partial Differentiation & Its Applications

6. Intergral Calculus & Its Application

7. Multiple Integrals & Beta, Gamma Functions

8. Vector Calculus & Its Applications

** UNIT III : SERIES **

9. Infinite Series

10.Fourier Series & Harmonic Analysis

** UNIT IV : DIFFERENTIAL EQUATIONS**

11. Differential Equations Of First Order

12. Applications of Differential Equations Of First Order

13. Linear Differential Equations

14. Applications Of Linear Differential Eqautions

15. Differential Equations of Other Types

16. Series Solution Of Differential Equations And Special Funtions

17. Partial Differential Equations

18. Applications Of Partial Differential Equations

** ****UNIT V : COMPLEX ANALYSIS**

19. Complex Numbers And Functions

20.Calculus Of Complex Functions

** UNIT VI : TRANSFORMS**

21. Laplace Transforms

22. Fourier Transforms

23. Z- Transforms

** UNIT VII : NUMERICAL TECHNIQUES**

24. Empirical Laws and Curve – Fitting

25. Statistical Methods

26. Probability and Distributions

27. Sampling and Inference

28. Numerical Solution of Equations

29. Finite Differences and Interpolation

30. Numerical Differentiation and Integration

31. Difference Equations

32. Numerical Solution of Ordinary Differential Equations

33. Numerical solution of Partial Differential Equations

34. Linear Programming

** VIII : SPECIAL TOPICS**

35. Calculus of Variations

36. Integral Equations

37. Discrete Mathematics

38. Tensor Analysis

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