Engineering Mathematics
Course Progress: 0% (0/62 topics completed)
⏹️ Course Syllabus
Linear Algebra
- ⬛ Vector algebra
- ⬛ Dot & Cross Product Operations
- ⬛ Matrices: types & basic operations
- ⬛ Determinants & Properties
- ⬛ Systems of Linear Equations
- ⬛ Rank of a Matrix
- ⬛ Gauss elimination & Gauss–Jordan method
- ⬛ Eigenvalues & eigenvectors
- ⬛ Diagonalization & characteristic polynomial
Calculus
- ⬛ Functions & graphs
- ⬛ Limits and continuity
- ⬛ Differentiability & derivative rules
- ⬛ Mean value theorems
- ⬛ Chain rule & implicit differentiation
- ⬛ Partial derivatives & total derivative
- ⬛ Maxima & minima (single/multivariable)
- ⬛ Gradient
- ⬛ Divergence
- ⬛ Curl
- ⬛ Directional derivatives
- ⬛ Single-variable integration basics
- ⬛ Multiple integrals: double, triple
- ⬛ Line integrals
- ⬛ Surface integrals
- ⬛ Volume integrals
- ⬛ Green’s theorem
- ⬛ Gauss divergence theorem
- ⬛ Stokes theorem
Differential Equations
- ⬛ First-order ODEs: linear & nonlinear
- ⬛ Separation of variables
- ⬛ Exact equations & integrating factor
- ⬛ Second & higher order linear ODEs
- ⬛ Constant coefficient ODEs
- ⬛ Complementary & particular solutions
- ⬛ Method of undetermined coefficients
- ⬛ Variation of parameters
- ⬛ Systems of linear ODEs
- ⬛ PDE basics: order, degree, classification
- ⬛ Standard PDEs: heat, wave, Laplace
Fourier Series
- ⬛ Basics of Fourier series
- ⬛ Fourier coefficients
- ⬛ Even & odd functions
- ⬛ Half-range expansions
- ⬛ Simple applications in PDEs
Laplace Transforms
- ⬛ Basic formulas laplace transforms
- ⬛ First shifting theorem
- ⬛ Inverse Laplace Transformations
- ⬛ Solving simple linear ODEs laplace
Numerical Methods
- ⬛ Numerical root-finding: Newton–Raphson
- ⬛ Numerical root-finding: Bisection
- ⬛ Numerical integration: Trapezoidal
- ⬛ Numerical integration: Simpson’s rule
- ⬛ Numerical differentiation: finite differences
Complex Analysis
- ⬛ Analytic functions & Cauchy–Riemann equations
- ⬛ Basic contour integrals
- ⬛ Poles & residues
- ⬛ Evaluation of simple real integrals
Probability and Statistics
- ⬛ Basic probability rules
- ⬛ Conditional probability & Bayes
- ⬛ Random variables: expectation & variance
- ⬛ Probability Distributions
- ⬛ Central Limit Theorem
