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- 1 Information of book
- 1.1 Mathematics I:
- 1.2 MATHEMATICS-II
- 1.3 Engineering Mathematics III:
Higher Engineering Mathematics by bs Grewal free pdf
Information of book
Additionally, the book consists of a couple of lit up and unsolved Request for through adjustment and last practice.
This book is Major for all Engineering Understudies getting ready for various competitive exams like Graduate Aptitude Test in Engineering, Engineering Service exam et cetera.
This book gives a sensible Organization of central gadgets of Associated Mathematics from a propelled viewpoint and meets complete Essentials of Engineering and programming engineering understudies. Every effort has been made to keep the presentation immediately essential and clear.
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To achieve this, more than the run of the mill number of clarified cases, trailed by property evaluated problems have been given.
Colossal quantities of the delineations and issues have been looked over late papers of various school and other Engineering examinations. Fundamental thoughts and important Information has been giving in a Reference area.
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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.
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).
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;
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 – 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
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.
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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