Calculus III: Differential Vector Calculus

used at Union College

Educator Edition

CourseMTH 115, Calculus 3: Differential Vector Calculus and Matrix Theory. Geometry of 3-space, differential calculus of functions of several variables, linear systems, matrices.
TextbookCalculus: Early Transcendentals, 10th Edition: Howard Anton, Irl Bivens,‎ Stephen Davis, or a textbook of your choice.

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Intended for students who have passed a Integral Calculus course.

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This problem series includes WeBWorK-enhanced problems. WeBWorK problems are highly sophisticated, supporting the representation and manipulation of mathematical objects such as vectors, points, matrices, intervals, and complex numbers, with customizable answer checkers. Students are encouraged to make multiple attempts until they succeed, and given immediate feedback on correctness.

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Problem Sets

  1. Multi-variable Functions
  2. Graphs of Functions \(f\colon{\bf R}^2\to{\bf R}\)
  3. Level Sets of Functions \(f\colon{\bf R}^2\to{\bf R}\)
  4. Level Surfaces of Functions \(f\colon{\bf R}^3\to{\bf R}\)
  5. Vectors and Vector Algebra
  6. Dot Products, Cross Products, Vector Projections, and Parametric Lines
  7. Planes in 3D and Partial Derivatives
  8. Directional Derivatives, Gradient Vectors, and Critical Points
  9. Gradient Vectors in \({\bf R}^3\), Critical Points, and Vector-valued Derivatives
  10. Linear Systems
  11. Systems of Linear Equations (optional)


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