• Fundamental theorem of calculus and its proof
  
• Techniques: substitution, parts, partial fractions, trigonometric integrals
  
• Improper integrals, numerical methods
  
• Applications: area under curves, volumes (disk & shell), arc lengths
  

• Area between intersecting curves
  
• Solids of revolution: volume & surface area
  
• Physical models: work done by variable forces, fluid pressure, center of mass
  
• Engineering contexts: beam deflection, material strength
  

• First‑order: separable, exact, linear integrating factors
  
• Second‑order linear equations: homogeneous & non‑homogeneous solutions
  
• Modeling: exponential growth/decay, mixing problems, harmonic motion
  
• Real‑life systems: electrical circuits, population dynamics, heat flow
  

• Vector operations: addition, scalar multiplication, linear combinations
  
• Dot & cross products: projections, angles, areas
  
• Vector functions: velocity, acceleration, space curves
  
• Geometric applications: lines & planes in space, distance formulas
  

• Coordinate systems: Cartesian, cylindrical, spherical
  
• Quadric surfaces: spheres, cones, cylinders, paraboloids, hyperboloids
  
• Intersections: line-plane, plane-surface
  
• Distance & angle calculations in ℝ³
  

• Formulating optimization problems: objective functions & constraints
  
• Feasible region & corner‑point method (graphical solutions)
  
• Economic applications: resource allocation, production planning
  
• Intro to simplex concepts for higher‑dimensional problems
  

• Axioms & basic theorems of probability
  
• Discrete distributions: binomial, Poisson, geometric
  
• Continuous distributions: normal, exponential
  
• Expectation, variance, and real‑world modeling (risk analysis, quality control)
  

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