---

      Series

---

• sequences
  
• sequences properties
  
• series
  
• geometric series
  
• arithmetic series
  
• harmonic series
  
• properties of series
  
• convergence criteria
  
• power series
  
• series expansion
  
• algebraic operations
  
• particular sums
  
  
• sequences Examples
  
• CD_criteria
  
• conv & div strategy
  
• series worked examples
  
• lim n!/nⁿ at ∞
  
• lim (1 + x/n)ⁿ at ∞
  

---

     Integrals

---

• Differential of a function
  
• Primitive techniques
  
• Differential equations
  
• rational functions primitives
  
• partial fractions technique
  
• integration by parts
  
• trigonometric functions
  
• trigonometric substitutions
  

---

Definite integrals

---

• summation operations
  
• Riemann sum
  
• Fundamental Theorem
  of Calculus
  
• FTC applications
  
• improper integrals
  
• area integral
  
• arc length
  
• lateral area
  
• volume integral
  
• Volumes of Solids of Revolution
  

---

Some primitives

---

• ∫ sec³(x) dx
  
• Parabola element
  
• ∫ dx/(ax² + bx + c)
  

---

Numerical methods

---

• Rectangles method
  
• Trapezoidal rule
  
• Simpson's rule
  

---

      Exercices

---

• limits
  
• sequences & series
  
• integration
  
• volumes of revolution