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SMC|Academic Programs|Mathematics|Math 11 - Multivariable Calculus

Math 11 - Multivariable Calculus

Course Details

Description

Topics include vectors and analytic geometry in two and three dimensions, vector functions with applications, partial derivatives, extrema, Lagrange multipliers, multiple integrals with applications, vector fields, Green's Theorem, Divergence Theorem, and Stokes' Theorem.

Prerequisites

Math 8

How It Transfers

UC, CSU IGETC AREA 2 (Mathematical Concepts)

Textbook

Swokowski, Calculus, Classic Ed., Brooks/Cole, 1991

Mathematics Skills Associated With This Course

 

Entry Level Skills

 

Skills the instructor assumes you know prior to enrollment in this course

  • Apply concepts of limits, continuity and differentiability in two dimensions. 
  • Differentiate and integrate exponential and logarithmic functions. 
  • Differentiate and integrate transcendental functions and inverses. 
  • Perform integration by parts. 
  • Perform integration using trigonometric functions. 
  • Resolve indeterminate forms using L'Hopital's rule. 
  • Set up Taylor series representations of transcendental functions. 
  • Use polar coordinates for plane curves. 
  • Use of parametric equations for plane curves.
  • Find center of mass/centroid.

 

 

Course Objectives

Skills to be learned during this course

  • Perform the basic algebra of vectors including dot and cross products
  • Write the equations of lines and planes in three dimensions, both in non-vector and vector forms.
  • Sketch planes, cylinders and quadric surfaces.
  • Distinguish between scalar-valued and vector-valued functions.
  • Differentiate and integrate vector-valued functions.
  • Represent curvilinear motion in vector form both algebraically and geometrically.
  • Find the derivatives of scalar-valued and vector-valued functions of two or more independent variables.
  • Find extrema of functions of two or more independent variables both by the Second Derivative Test and by Lagrange Multipliers.
  • Evaluate double and triple integrals.
  • Use multiple integrals to solve various applied problems.
  • Use rectangular, cylindrical and spherical coordinates for graphing and the evaluation of multiple integrals.
  • Set up and evaluate line integrals and surface integrals and apply them to physical applications.
  • Apply Green’s Theorem, Divergence Theorem, and Stokes’ Theorem.
  • Apply the concepts of the gradient, divergence and curl.