MAT186 — Calculus I

Course focuses on single-variable calculus with an introduction to ODEs. Followed by MAT187 — Calculus II. We used the Calculus Volume 1 and Calculus Volume 2 textbooks by Strang and Herman.

Concepts covered

• Trigonometric function
• Inverse relation
• Logarithmic function and exponential function
• Safe-side strategy
• Limit
  • Squeeze theorem
  • Continuity
  • Intermediate value theorem
• Differentiation
  • Chain rule
  • Implicit differentiation
  • Inverse differentiation
  • Related rates
  • Linear approximation
  • L’Hôpital’s rule
  • Function extrema
• Differential equation and First-order ODE
  • Initial-value problem
  • Euler’s method
• Riemann sum
  • Derivation of area and volume formulas
  • Arc length
  • Work (physics)
• Fundamental theorem of calculus
• Integration
  • U-substitution