Engineering Mathematics (AS PER GTU SYLLABUS 4320002)

Engineering Mathematics

1. Calculus:

   • Limits, continuity, and differentiability of functions
   • Differentiation techniques: Chain rule, product rule, quotient rule
   • Applications of derivatives: Maxima and minima, rate of change, approximation
   • Integration techniques: Indefinite and definite integrals, integration by parts, substitution method
   • Applications of definite integrals: Area under curves, volume of solids

2. Linear Algebra:

   • Matrices and determinants: Operations on matrices, properties, rank, inverse, determinants, and their properties
   • System of linear equations: Gaussian elimination, matrix representation, and solutions
   • Eigenvalues and eigenvectors: Characteristic equation, diagonalization

3. Differential Equations:

   • Ordinary differential equations (ODEs): First-order ODEs, linear and nonlinear higher-order ODEs
   • Initial value problems and boundary value problems
   • Solution techniques: Separation of variables, homogeneous and non-homogeneous linear equations, exact equations
   • Applications of differential equations in engineering

4. Probability and Statistics:

   • Probability theory: Basic concepts, probability distributions (binomial, Poisson, and normal distributions)
   • Random variables and probability density functions
   • Statistical measures: Mean, variance, standard deviation, correlation, regression analysis
   • Probability distributions in engineering applications

5. Numerical Methods:

   • Approximation and interpolation: Polynomial interpolation, Newton's forward and backward difference formulas
   • Numerical integration techniques: Trapezoidal rule, Simpson's rule
   • Numerical solutions of ODEs: Euler's method, Runge-Kutta methods
   • Numerical solutions of algebraic equations: Newton-Raphson method, bisection method

6. Transform Techniques:

   • Laplace transform: Definition, properties, inverse Laplace transform, solving initial value problems
   • Fourier series: Periodic functions, Fourier series representation, properties
   • Fourier transform: Fourier transform pair, properties, applications in signal processing

7. Complex Analysis:

   • Complex numbers: Algebraic properties, polar representation, De Moivre's theorem
   • Functions of complex variables: Analytic functions, Cauchy-Riemann equations
   • Contour integration: Cauchy's integral theorem, Cauchy's integral formula

These brief notes cover the key topics included in the Engineering Mathematics syllabus as per the GTU (4320002) syllabus. It is important to consult the prescribed textbooks and reference materials for a more detailed understanding of each topic and to solve practice problems to strengthen your knowledge and problem-solving skills.

1. EXPLANATION OF CHAPTER 
2. CHAPTER WISE GTU QUESTION 
3. TUTORIAL 
4. MCQ