MAT187 — Calculus II

Course focuses on single-variable calculus, ordinary differential equations, and vector-valued functions. Continuation of MAT186 — Calculus I; followed by MAT291 — Calculus III and MAT290 — Advanced Engineering Mathematics.

We used the Calculus Volume 2 and Calculus Volume 3 textbooks by Strang and Herman.

Concepts covered

Integral calculus

Integration

• Integration techniques
  • Integration by parts
  • Trigonometric substitution
  • Partial fraction decomposition
• Numerical integration
  • Trapezium rule
  • Riemann sum
• Improper integral

Differential equations

Differential equation

• Initial-value problem
• First-order ODE
  • Separation of variables
  • Integrating factor
  • Direction field
  • Phase plot
  • Equilibrium solution
• Second-order ODE
  • Homogeneous ODE
  • Non-homogeneous ODE
    • Method of undetermined coefficients
  • Oscillatory systems
    • Mass-spring system
• Complex number

Power series

Power series and Taylor series

• Taylor polynomial errors
• Sequence and series
• Series convergence
  • Ratio test

Vector-valued functions

• Parametric equation
• Polar coordinates
• Vector-valued function
• Arc length
• Curvature
• Normal-tangential coordinates