Vector Calculus
(Math 105)

Instructor: Paul Aspinwall

Credits: 1.0

Time: MWF 1:30-2:20 PM

Location: Physics 235

Homework

• is on Sakai.

Prerequisites

• MATH 104 or equivalent or instructors permission

Exams

Synopsis

1. Multivariable differential calculus
   • Vectors, inner products (1.1, 1.2)
   • Functions of several variables, limits, partial derivatives (2.1, 2.2, 2.3, 2.4)
   • Acceleration, arc lengths (4.1, 4.2)
   • Chain rule, directional derivatives, gradient (2.5, 2.6)
   • Taylors Theorem, max/min problems, Lagrange multipliers (3.1, 3.2, 3.3, 3.4)
   • Implicit Function Theorem (3.5)
2. Multivariable integral calculus
   • Double and triple integrals (5.1, 5.2, 5.3, 5.4, 5.5)
   • Cylindrical/spherical coordinates, change of variables, Jacobian (1.4, 6.1, 6.2, 6.3)
3. Vector calculus
   • Vector fields, cross products, divergence/curl (1.3, 1.5, 4.3, 4.4)
   • Path and line integrals on curves (7.1, 7.2)
   • Scalar and vector integrals over surfaces (7.3, 7.4, 7.5, 7.6)
   • Green's, Stokes', Gauss's Theorems, conservative vector fields (8.1, 8.2, 8.3, 8.4)
   • Differential forms (8.6)

Textbooks

1. J. E. Marsden and A. J. Tromba, Vector Calculus, Freeman, 5th edition.

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