Engineering Mathematics- Tutorial
Chapter 1: Linear Algebra
1.1 Matrices and Types
1.2 Determinants and Properties
1.3 System of Linear Equations
▪ Gauss elimination, Gauss-Jordan method
1.4 Eigenvalues and Eigenvectors
1.5 Diagonalization of Matrices
Chapter 2: Calculus
2.1 Differentiation
▪ Partial derivatives, chain rule
2.2 Maxima and Minima of Functions
2.3 Multiple Integrals
▪ Double and triple integrals, applications
2.4 Line and Surface Integrals
2.5 Green’s, Stokes’, and Gauss Theorems
Chapter 3: Differential Equations
3.1 First-Order Differential Equations
▪ Separable, linear, exact equations
3.2 Second-Order Linear Equations
▪ Homogeneous and non-homogeneous
3.3 Applications to Electrical Circuits and Systems
3.4 Laplace Transforms
▪ Definition, properties, inverse Laplace
3.5 Solving Differential Equations using Laplace Transforms
Chapter 4: Probability and Statistics
4.1 Probability Concepts
▪ Conditional probability, Bayes’ theorem
4.2 Random Variables
▪ Discrete and continuous
4.3 Probability Distributions
▪ Binomial, Poisson, Normal
4.4 Statistical Measures
▪ Mean, median, variance, standard deviation
4.5 Hypothesis Testing and Confidence Intervals
Chapter 5: Numerical Methods
5.1 Solution of Algebraic and Transcendental Equations
▪ Bisection, Newton-Raphson methods
5.2 Interpolation
▪ Newton’s and Lagrange’s formulae
5.3 Numerical Differentiation and Integration
▪ Trapezoidal and Simpson’s rules
5.4 Numerical Solution of ODEs
▪ Euler’s and Runge-Kutta methods
5.5 Error Analysis and Stability
Chapter 6: Complex Numbers and Functions
6.1 Complex Number Algebra
6.2 Analytic Functions and Cauchy-Riemann Equations
6.3 Conformal Mapping
6.4 Complex Integration
▪ Cauchy’s integral theorem and formula
6.5 Residue Theorem and Contour Integration
Chapter 7: Transform Techniques
7.1 Fourier Series
▪ Dirichlet’s conditions, even/odd extensions
7.2 Fourier Transforms
Sine and cosine transforms
7.3 Z-Transforms and Applications
7.4 Applications in Signal and Image Processing
7.5 Discrete Transforms