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MATH 3012

Vector Analysis

0.5 credits · Undergraduate

Spring 2026

Topics

  • operations on vectors, space coordinates, lines, planes, surfaces, vector-valued
  • functions and their differentiation and integration, tangent and normal vec
  • functions of several variables, tangent planes and normal lines, iterated inte
  • grals, double integrals, triple integrals, volume and surface areas, Jacobians
  • Stokes’ Theorem

Readings

  • Recommended: Any edition of the following:
  • Recommended: ˆ Calculus: Early Transcendentals, by Ron Larson and Bruce Edwards, (8th Edition Hardcopy early-transcendental-functions-8e-larson-edwards/9780357759325), (Chancellor Paterson Library, Paterson Books - 4th floor; QA 303 L3274 2003).
  • Recommended: ˆ Multivariable Calculus by James Stewart, (9th Edition Hardcopy calculus-9e-stewart-clegg-watson/9780357042922), (Chancellor Paterson Library, Paterson Books - 4th floor ; QA 303 S845 2009 Metric Intl.).
Fall 2025

Topics

  • Vectors and spatial geometry
  • curves, arclength and curvature
  • partial and directional derivatives
  • gradients, optimization and Lagrange multipliers
  • double and triple integrals
  • coordinate systems
  • line and surface integrals
  • conservative fields
  • Green, Stokes and divergence theorems.

Readings

Fall 2019

Topics

  • tions on vectors, space coordinates, lines, planes, surfaces in space, vector
  • valued functions and their differentiation and integration, tangent vectors
  • and normal vectors, functions of several variables, limits, continuity, partial
  • derivatives of functions of several variables, tangent planes and normal lines
  • iterated integrals, double integrals, triple integrals, volume and surface ar
  • eas, Jacobians, line integrals, Green’s Theorem, surface integrals, Divergence
  • Theorem, Stokes’ Theorem
  • Hour: (:30-9:30 in RB 1042) No new material
  • provide students with the opportunity to ask questions about the content
  • is beneficial to attend
2016–2017

Topics

  • Cartesian coordinates, vectors in two and three dimensions, equations
  • cross product
  • Cylindrical and spherical coordinates, the geometry of real valued
  • functions, limits and continuity
  • Differentation of functions from Rm to Rn, paths and curves, properties
  • of the derivative
  • Test # 1 on
  • Gradients and directional derivatives, iterated partial derivatives, ac
  • celeration and Newton’s second law
  • Arc-length and the differential geometry of curves
  • Vector fields, divergence and curl
  • Test # 2 on
  • Double and triple integrals
  • Change of variables in double and triple integrals
  • Applications of double and triple integrals
  • Test # 3 on
  • Path integrals, line integrals, parametrised surfaces
  • Area of a surface, integrals of scalar functions over surfaces, surface
  • integrals of vector fields
  • Green’s theorem, Stokes theorem, conservative fields, Gauss’ theorem

Readings

  • Recommended: Vector Calculus, J. Marsden and A. Tromba, 6-th edition, W.H. Freeman and Company, New York.
  • Recommended: Other acceptable texts: Calculus, R. Larson and B.H. Edwards, published by Brooks/Cole. Calculus, one and several variables, Salas, Hille, and Etgen, published by John Wiley and Sons. Multivariable Calculus, James Stewart, published by Brooks/Cole. Advanced Engineering Mathematics, D.G. Zill and M.R. Cullen, published by Jones and Bartlett.
2011–2012

Topics

  • Cartesian coordinates, vectors in two and three dimensions, equations
  • cross product
  • Cylindrical and spherical coordinates, the geometry of real valued
  • functions, limits and continuity
  • Differentation of functions from Rm to Rn, paths and curves, properties
  • of the derivative
  • Test # 1 on
  • Gradients and directional derivatives, iterated partial derivatives, accel
  • eration and Newton’s second law
  • Arc-length and the differential geometry of curves
  • Vector fields, divergence and curl
  • Test # 2 on
  • Double and triple integrals
  • Change of variables in double and triple integrals
  • Applications of double and triple integrals
  • Test # 3 on
  • Path integrals, line integrals, parametrised surfaces
  • Area of a surface, integrals of scalar functions over surfaces, surface
  • integrals of vector fields
  • ( and ) Green’s theorem, Stokes theorem, conservative
  • fields, Gauss’ theorem

Readings

  • Recommended: Vector Calculus, J. Marsden and A. Tromba, 5-th edition, W.H. Freeman and Company, New York.
  • Recommended: Other acceptable texts: Calculus, R. Larson and B.H. Edwards, 5-th edition, Brooks/Cole. Calculus, one and several variables, Salas, Hille, and Etgen, 10-th edition, John Wiley and Sons. Multivariable Calculus, 6-th edition, James Stewart, Brooks/Cole.
Sources