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Mathematics 214

Calculus IV

Length of Course: One Semester (14 weeks)

Classroom Hours per Week: 4 hours 

Number of Credits: 3 credits

Prerequisite: 213 with a minimum of C-.

Corequisite: none.


Course Description

This is a course in vector calculus that applies calculus to vector functions of a single variable as well as to scalar and vector fields. Topics include gradient, divergence, curl, line and surface integrals, the divergence theorem and the theorems of Green and Stokes.


Course Outline

Length Description

Week 1

Parametric and polar curves; Conic sections

  • Parametric equations, Tangent lines, Arc length for parametric curves
  • Polar coordinates
  • Tangent lines Arc length, and Area of polar curves

Week 2

Parametric and polar curves; Conic sections

  • Conic Sections
  • Conic sections in polar coordinates

Week 3

Three-dimensional space

  • Rectangular coordinates
  • Vectors
  • Dot product, Projections, Cross product

Week 4

Three-dimensional space

  • Parametrical equations of lines
  • Planes in 3-space

Week 5

Three-dimensional space

  • Quadric surface
  • Cylindrical and spherical coordinates

Week 6

Vector valued functions of one variable

  • Calculus of vector-valued functions
  • Change of parameter

Week 7

Vector valued functions of one variable

  • Arc length
  • Unit Tangent, Normal, and Binormal vectors

Week 8

Vector valued functions of one variable

  • Curvature
  • Motion along a curve

Week 9

Vector valued functions of several variables

  • Vector fields, Conservative fields and potential functions
  • Gradient, Curl, Divergence

Week 10

Vector valued functions of several variables

  • Line integrals, Fundamental theorem of line integrals
  • Green's theorem

Week 11

Vector valued functions of several variables

  • Parameterized surfaces, Surface area, Surface integrals

Week 12

Vector valued functions of several variables

  • Stokes’ theorem, Divergence theorem

Week 13

Review

Week 14

Final Exam 

Textbook

Calculus Early Transcendentals by Anton, Bivens, and Davis Latest Edition


Course Evaluation

Quizzes and Homework 10-20%
Midterm Exams 20-40%
Final Examination 40-50%

Transferability

Please refer to BC Transfer Guide


Instructors

Arman Ahmadieh B.Sc., M.Sc. (Sharif University of Technology)
Hayri Ardal, B.Sc.(Bogazici), Ph.D. (Simon Fraser)
Kim Peu Chew, B.Sc. (Nanjing), M.A., Ph.D. (British Columbia)
Ana Culibrk, B.Sc., M.Sc. (Belgrade), M.Sc. (British Columbia)
Rika Dong, B.Sc. (Simon Fraser), M.Sc. (Regina)
Sam Ekambaram, B.Sc., M.Sc. (Madras), M.Sc., Ph.D. (Simon Fraser)
Himadri Ganguli, B.Sc., M.Sc. (Chennai), Ph.D. (Simon Fraser)
Peter Hurthig, B.Sc., M.Sc. (British Columbia)
Kamyar Moshksar, B.Sc.(Shiraz), M.Sc. (Waterloo), PhD (Waterloo)