Higher Engineering Maths – Video Tutorials in Hindi

1. Linear Algebra

• Matrix Algebra (Multiplication, Rank, and Inverse)
• Solution of the system of Linear Equations
• Eigen Values and Eigen Vectors (Plus Cayley Hamilton Theorem & Inverse)

2. Calculus

• Taylor and Maclaurin Series
• Rolle’s, Mean Value, and Cauchy’s Mean Value Theorems
• Partial Derivatives (Multivariable Function)
• Maxima, Minima and Saddle Point ( Function in two variables)
• Gradient of Function
• Directional Derivative of the Function
• Divergence of the Vector Field
• Curl of the Vector Field

3. Differential Equations

• First order equations (Leibnitz’s and Bernoulli’s Linear Equations)
• Higher order linear differential equations with constant coefficients
• Cauchy’s homogenous equation
• Laplace Transforms

4. Complex Variables

• Complex Number Basics
• Representation on Complex Plane or Argand’s Plane
• Polar and Euler form of the complex number
• Triangle Inequality.

5. Probability and Statistics

• Conditional Probability (Baye’s Theorem)
• Binomial Distribution (Repeated Trials / Bernoulli’s Trials)
• Poisson Distribution
• Normal Distribution
• Mean, Median, and Mode
• Standard Deviation & Variance

6. Numerical Mehods

• Numerical solutions of linear algebraic equations:
  1. Gauss elimination and back substitution method
  2. Gauss-Jordan method
  3. LU Decomposition method
  4. Jacobi’s method
  5. Gauss-Siedel method
• Numerical solutions of non-linear algebraic equations:
  1. Bisection method
  2. Method of false position / Regula-Falsi method
  3. Newton-Raphson method
• Integration by trapezoidal rule
• Integration by Simpson’s rule:
  1. Simpson’s One-Third rule
  2. Simpson’s Three-Eighth rule
• Single and multi-step methods for the numerical solution of differential equations:
  1. Explicit Euler’s method / Forward Euler’s Method
  2. Implicit Euler’s method / Backward Euler’s Method
  3. Heun’s method / Improved Euler’s method
  4. Runge-Kutta method (RK4 Method)