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MATH-502In Development

Calculus & University Mathematics

Calculus II

Extend calculus through integration techniques, series, parametric and polar models, and applications of accumulation.

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.

Learning outcomes

By the end, learners will be able to…

  • Evaluate definite and indefinite integrals using appropriate techniques.
  • Apply integration to area, volume, accumulated change, and basic differential-equation models.
  • Determine convergence behavior for sequences and series.
  • Construct and use power-series approximations.
  • Analyze parametric and polar curves with calculus methods.
  • Explain the scope and limitations of an approximation or integration result.

Module outline preview

12 planned modules

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

  1. 01

    Integration Review and the Fundamental Theorem

    Connect antiderivatives, definite integrals, and accumulated change.

    1.75 hours · In Development
  2. 02

    Integration Techniques I

    Use substitution and integration by parts strategically.

    1.75 hours · In Development
  3. 03

    Integration Techniques II

    Apply partial fractions and trigonometric integration methods.

    1.75 hours · In Development
  4. 04

    Improper Integrals and Numerical Approximation

    Evaluate unbounded cases and approximate integrals when needed.

    1.75 hours · In Development
  5. 05

    Applications of Definite Integrals

    Model area, volume, work, and other accumulated quantities.

    1.75 hours · In Development
  6. 06

    Basic Differential-Equation Models

    Use separable models to describe simple change processes.

    1.75 hours · In Development
  7. 07

    Sequences and Convergence

    Determine whether numerical sequences and series converge.

    1.75 hours · In Development
  8. 08

    Power Series

    Build and use power-series representations of functions.

    1.75 hours · In Development
  9. 09

    Taylor and Maclaurin Approximations

    Estimate functions with polynomial approximations and assess error.

    1.5 hours · In Development
  10. 10

    Parametric and Polar Calculus

    Analyze motion and non-rectangular curves with derivatives and integrals.

    1.5 hours · In Development
  11. 11

    Applied Accumulation Models

    Select integration methods for applied problems and interpret units.

    1.5 hours · In Development
  12. 12

    Calculus II Synthesis

    Integrate techniques, series, and applications in cumulative work.

    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.