Math114E: Multivariable Calculus for Engineers at the University of Pennsylvania

All content from Jacob Nibauer 2018-2021

• A few additional worked problems and solutions
  • Vol. 1 Ch.1-6 | Solutions
  • Vol. 1 Ch.7-12 | Solutions
  • Vol. 1 Ch.10-15 | Solutions
  • Vol. 1 Ch.13-18 | Solutions
  • Vol. 1 Ch.16-18 ; Vol. 2 Ch.1-3 | Solutions
• Other Potentially Useful Material for the course
  • Volume 1
    • T,N,B Frame Acceleration Equation Derived
    • T,N,B Frame Example
    • Parametrizing the Intersection of Two Planes
    • Dot Product Formula Derived
    • Row Reduction Example
  • Volume 2
    • Inverse Function Theorem Example
    • Implicit Function Theorem Example
    • The Gradient is Perpendicular to Level Sets: Somewhat of a Proof
    • Tangent Plane Intuition
    • Tangent Planes and Gradients (Example)
    • Linearization (Example)
    • Hessian: Determinant and Trace Intuition
  • Volume 3
    • Lagrange Multiplier Example
    • Changing Integration Order (1)
    • Changing Integration Order (2)
    • Changing Integration Order (3)
    • Center of Mass Example
    • Inertia Matrix and Rotation about a Skew Axis
    • Change of Variables Intuition
  • Volume 4
    • Green's Theorem Intuition
    • Scalar Path Integral Intuition
    • Some Intuition on 1-Forms
    • Path Independence/Dependence
    • Integrating 2-Forms Example