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MATH-503In Development

Calculus & University Mathematics

Multivariable Calculus

Apply calculus to functions of several variables, vectors, surfaces, multiple integrals, and vector fields.

Level
Level 5 — Higher Mathematics
Learning time
20 hours
Format
Extended Course
Modules
12

Course structure

A clear outline before lessons begin.

This course is published as a development map. Full lessons, practice, and assessments will be added after content review.

Prerequisites

Complete these courses before beginning when they are available.

Recommended preparation

These courses strengthen preparation but are not strict prerequisites.

Learning outcomes

By the end, learners will be able to…

  • Use vectors and three-dimensional coordinate geometry to model position and direction.
  • Analyze multivariable functions with partial derivatives and linear approximations.
  • Optimize functions with and without constraints.
  • Set up and evaluate double and triple integrals.
  • Parameterize curves and surfaces and interpret vector fields.
  • Apply line or surface integral concepts to physical and geometric models.

Module outline preview

12 planned modules

Estimated times add up to the course’s planned learning time. Every module is in development.

  1. 01

    Vectors and Three-Dimensional Geometry

    Represent direction, magnitude, lines, planes, and spatial relationships.

    1.75 hours · In Development
  2. 02

    Functions of Several Variables

    Analyze domains, level curves, and level surfaces.

    1.75 hours · In Development
  3. 03

    Partial Derivatives and Linear Approximation

    Measure directional change and approximate multivariable functions locally.

    1.75 hours · In Development
  4. 04

    Gradients and Unconstrained Optimization

    Use gradients and second-derivative information to locate extrema.

    1.75 hours · In Development
  5. 05

    Constrained Optimization

    Apply Lagrange-multiplier reasoning to constrained models.

    1.75 hours · In Development
  6. 06

    Double Integrals

    Set up and evaluate accumulated quantities across planar regions.

    1.75 hours · In Development
  7. 07

    Triple Integrals and Coordinate Changes

    Integrate across solids using efficient coordinate systems.

    1.75 hours · In Development
  8. 08

    Parameterized Curves and Motion

    Model curves, velocity, and acceleration in space.

    1.75 hours · In Development
  9. 09

    Vector Fields

    Interpret field direction, magnitude, and potential functions.

    1.5 hours · In Development
  10. 10

    Line Integrals and Green’s Theorem

    Connect path-based accumulation with region-based reasoning.

    1.5 hours · In Development
  11. 11

    Surface Integrals and Flux

    Interpret flux across surfaces and major vector-calculus ideas.

    1.5 hours · In Development
  12. 12

    Multivariable Modeling Synthesis

    Select multivariable tools for a cumulative physical or geometric model.

    1.5 hours · In Development

Course status

Course coming soon

This course is not yet open for enrollment and does not include lessons, practice, assessments, or formal credit. You can review the outline while it is developed.

Back to Mathematics

Recommended learning paths

A clear sequence, not a random list.

These paths show a recommended order. Branches identify connected study that can follow once prerequisites are complete.