MATH 210: Calculus with Analytic Geometry lll

Citrus College Course Outline of Record

Citrus College Course Outline of Record
Heading Value
Effective Term: Fall 2021
Credits: 5
Total Contact Hours: 90
Lecture Hours : 90
Lab Hours: 0
Hours Arranged: 0
Outside of Class Hours: 180
Prerequisite: MATH 191.
District General Education: A3. Mathematics
Transferable to CSU: Yes
Transferable to UC: Yes - Approved
Grading Method: Standard Letter, Pass/No Pass

Catalog Course Description

Vectors, calculus of functions of more than one variable, partial derivatives, multiple integration, vector calculus, Green's Theorem, Stokes' Theorem, and divergence theorem. 90 lecture hours.

Course Objectives

  • Perform vector operations
  • Evaluate derivatives.
  • Write the equation of a tangent plane at a point.
  • Find local extrema and test for saddle points.
  • Solve constraint problems using Lagrange multipliers.
  • Compute arc length.
  • Find the divergence and curl of a vector field.
  • Determine differentiability.
  • Determine equations of lines and planes.
  • Find the limit of a function at a point.
  • Illustrate calculus operations on vector valued functions, including derivatives, integrals, curvature, displacement, velocity, acceleration, and torsion.
  • Perform calculus operations on functions of several variables, including partial derivatives, directional derivatives, and multiple integrals.
  • Find extrema and tangent planes.
  • Solve problems using the Fundamental Theorem of Line Integrals, Green's Theorem, the Divergence Theorem, and Stokes' Theorem.
  • Apply the computational and conceptual principles of calculus to the solutions of real-world problems.
  • Evaluate two and three dimensional integrals.

Major Course Content

  1. Vectors and the Geometry of Space
    1. Vectors in the plane
    2. Performing vector operations
    3. Space coordinates and vectors in space
    4. The dot product of two vectors
    5. The cross product of two vectors in space
    6. Lines and planes in space
    7. Surfaces in space
    8. Rectangular equations of a plane.
    9. Cylindrical and spherical coordinates
  2. Vector-Valued Functions
    1. Vector-valued functions
    2. Differentiation and integration of vector-valued functions
    3. Velocity and acceleration
    4. Tangent vectors and normal vectors
    5. Arc length and curvature
    6. Vector and parametric equations of lines and planes.
  3. Functions of Several Variables
    1. Introduction to functions of several variables
    2. Limits and continuity
    3. Properties of limits and continuity
    4. Partial derivatives
    5. Differentials
    6. Chain rules for functions of several variables
    7. Differentiability and higher order derivatives.
    8. Directional derivatives and gradients
    9. Tangent planes and normal lines
    10. Extrema of functions of two variables
    11. Local and global maxima and minima
    12. Saddle points
    13. Applications of extrema of functions of two variables
  4. Multiple Integration
    1. Iterated integrals and area in the plane
    2. Double integrals and volume
    3. Change of variable: polar coordinates
    4. Center of mass and moments of inertia
    5. Surface area
    6. Triple integrals and applications
    7. Triple integrals in cylindrical and spherical coordinates
    8. Triple products and projections.
    9. Change of variables: Jacobians
  5. Vector Analysis
    1. Vector fields
    2. Line integrals
    3. Binormal Vectors
    4. Level curves and surfaces
    5. Langrage Multipliers
    6. Gradient Vector Field
    7. Conservative vector fields and independence of path
    8. Green's Theorem
    9. Parametric surfaces
    10. Surface integrals
    11. Integrals of real-valued functions over surfaces
    12. Divergence theorem
    13. Divergence and curl
    14. Stokes' Theorem

Examples of Outside Assignments

1. A student will analyze higher dimensional coordinate systems by differentiation and integration on functions of several variables.
2. Students will apply the techniques of Gauss-Jordan elimination to transform matrices to reduced row echelon form.

Instruction Type(s)

Lecture, Online Education Lecture

IGETC Area 2: Mathematical Concepts and Quantitative Reasoning