REAL ANALYSIS

Functions of Several Variables
Point sets, mapping, Graphs and level curves limits, Continuity , Sketching; curves, surfaces and solids

Partial Derivatives
Geometric interpretation
Total differentials, Sensitivity
Chain rules, Taylor’s expansion
Jacobians and its properties

Double and Triple Integration
Integration methods for areas of surfaces and volumes

Fields and Operators
Scalar fields and vector fields
Grad, div, curl
Geometrical and physical interpretations
3–D geometry; surfaces, tangent planes and normals

Orthogonal Curvilinear Coordinates

Integrals and Integral Theorems
A review
Line, surface and volume integrals
Gauss, Stokes and Green theorems
Conservative fields

Constrained Optimization of Functions of Several Variables
Unconstrained optimization
Constrained optimization, Lagrange multipliers

STATISTICS

Continuous Probability Distributions

Uniform distribution, Exponential distribution, Normal distribution, Weibull distribution

Sampling Distributions

Sampling distribution of sample mean X, Central Limit Theorem and Normal approximation to the Binomial Distribution, The sampling distribution of sample variance S2

Estimation and Confidence Intervals / Hypothesis Testing