Catholic Tech

Calculus III – Multivariable Calculus

Course Topics

  1. Unit 1: Functions of Several Variables
    • Review of Cartesian coordinates, vectors, and vector operations.
    • Introduction to functions of several variables.
    • Limits and continuity in multivariable calculus.
    • Partial derivatives and their applications.
    • Tangent planes and linear approximations.
  2. Unit 2: Multiple Integration
    • Double integrals and their applications.
    • Change of variables in double integrals.
    • Triple integrals and their applications.
    • Applications of triple integrals in finding volumes, surface areas, and center of mass.
    • Introduction to numerical methods for integration.
  3. Unit 3: Vector Calculus
    • Vector fields and their properties.
    • Line integrals and their applications.
    • Green's theorem and its applications.
    • Surface integrals and their applications.
    • Stokes' theorem and its applications.
  4. Unit 4: Divergence, Curl, and Fundamental Theorem
    • Divergence and its physical interpretations.
    • Curl and its physical interpretations.
    • The divergence theorem and its applications.
    • The fundamental theorem of calculus in multiple dimensions.
    • Applications of vector calculus in physics and engineering.
  5. Unit 5: Applications of Multivariable Calculus
    • Optimization problems with multiple variables.
    • Lagrange multipliers and constrained optimization.
    • Applications of multivariable calculus in economics and finance.
    • Applications of multivariable calculus in computer science and data analysis.


The course syllabus is subject to change at the discretion of the instructor. Any modifications or updates will be communicated in advance.