I taught three calculus courses to undergraduate students majoring in Mathematics in three semesters (Fall 2017, Spring 2018, and Fall 2018). These courses provided students with core mathematical knowledge: limits, derivatives, integrals, and infinite series.

The topic covered during the courses

Calculus 1 (Differential Calculus)

Focus: Understanding and applying derivatives, introductory integration concepts.

• Functions, limits, and continuity
• Derivatives and differentiation rules (power, product, quotient, chain rules)
• Applications of derivatives:
  • Optimization problems
  • Related rates
  • Curve sketching (asymptotes, critical points, inflection points)
• Basic introduction to definite and indefinite integrals
• Fundamental Theorem of Calculus

Calculus 2 (Integral Calculus and Series)

Focus: Mastery of integration and introduction to infinite series and alternate coordinate systems.

• Advanced integration techniques:
  • Substitution, integration by parts, partial fractions, trigonometric integrals
• Applications of integrals:
  • Volume (solid of revolution), arc length, work, and surface area
• Infinite sequences and series:
  • Convergence tests (e.g., ratio, root, comparison tests)
  • Taylor and Maclaurin series
• Polar coordinates and parametric equations

Calculus 3 (Multivariable Calculus)

Focus: Extending calculus to higher dimensions and exploring vector fields.

• Functions of several variables, partial derivatives, and gradient
• Double and triple integrals and their applications (e.g., volume, mass)
• Vector calculus:
  • Line and surface integrals
  • Divergence and curl
  • Green’s, Stokes’, and Divergence theorems
• Cylindrical and spherical coordinate systems