Calculus II β€” Online Calculus Course

Calculus 2 | Maths 265 Β· 4 College Credits | UPI Study
Maths 265 4 College Credits NCCRS Recommended + Intro to a Calc 3 Topic

Calculus
2

A continuation of Calculus 1 covering advanced integration, infinite series, and differential equations β€” with a short introduction to parametric, polar, and vector topics that some universities like to see before Calculus 3.

Calculus 2 Course
$250 per course
One-time Β· Lifetime access Β· No subscription
Enroll & Start Today β†’
NCCRS Recommended 4 Credit Hours + Intro to a Calc 3 Topic Self-Paced
$250 PER COURSE or UPI Study Pro subscription
97% Completion Rate Course completion rate
28–30 Days Average course completion
Save $650+ vs. avg. community college cost for 4 credits
Self-Paced Β· Final Exam Β· NCCRS Recommended

What You'll Learn

A complete Calculus 2 course β€” advanced integration, series, and differential equations β€” plus a short introduction to a few Calculus 3 topics, completed at your own pace.

πŸ“˜
This is a Calculus 2 course β€” with a short intro to a few Calculus 3 topics. The NCCRS-recommended Maths 265 syllabus is built around the standard Calculus 2 sequence. It also includes a brief introduction to parametric equations, polar coordinates, and vectors β€” early Calculus 3 material that some universities like to see covered here. It's an introduction only; if you want the full treatment of these topics, that's covered properly in our Calculus 3 course.
Learning Outcomes

What You'll Be Able to Do

  • Analyze an integrand and select and justify the most efficient integration technique β€” substitution, integration by parts, trigonometric methods, or partial fractions β€” then carry out the evaluation
  • Evaluate limits of indeterminate forms using L'HΓ΄pital's Rule, and determine the convergence or divergence of improper integrals, justifying the method including comparison
  • Analyze problems involving hyperbolic and inverse hyperbolic functions β€” including applications such as the catenary β€” and apply appropriate identities, derivatives, and integration techniques
  • Formulate and solve definite integrals to compute areas, volumes, arc length, surface area, and work, selecting the disk, washer, or shell method best suited to the solid
  • Construct and solve separable first-order differential equations to model exponential, logistic, and growth-and-decay phenomena, and interpret the solutions in context
  • Differentiate among the convergence tests, choose the most efficient one for a given series, and distinguish absolute from conditional convergence
  • Determine the radius and interval of convergence of a power series and generate Taylor and Maclaurin series, applying them to approximate values and integrals and assessing error with Taylor's Inequality
  • Analyze parametric, polar, and vector representations β€” graphing curves, computing slopes, arc length, and area, converting between coordinate systems, and applying dot and cross products in two and three dimensions
Topics Covered

Major Course Topics

Review of substitution & advanced integration
Integration by parts & the LIATE strategy
Trigonometric integrals & substitution
Partial fraction decomposition
Numerical integration (Midpoint, Trapezoidal, Simpson's)
L'HΓ΄pital's Rule & indeterminate forms
Improper integrals (Type I & II) & comparison
Hyperbolic & inverse hyperbolic functions
Areas between curves
Volumes: disk, washer & shell methods
Arc length & surface area of revolution
Work & physical applications (Hooke's Law)
Differential equations & slope fields
Euler's method & the logistic model
Sequences & infinite series
Geometric & telescoping series
Convergence tests (integral, ratio, root, comparison)
Alternating series & absolute convergence
Power series: radius & interval of convergence
Taylor & Maclaurin series & error analysis
Parametric curves & parametric calculus
Polar coordinates: curves, areas & arc length
Vectors in RΒ² & RΒ³: dot & cross products
Simple Process

How It Works

Three steps from enrollment to transferable college credit β€” no campus visits, no application required.

01
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Pick & Enroll

Start one or more courses covering lower or upper division requirements β€” instantly, today.

02
🎯

Earn College Credit

Watch short video lessons, take quizzes and the final exam β€” all from home, on your schedule.

03
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Transfer Your Credits

Send earned credits to your school and graduate sooner, at a fraction of the cost.

Does My School Accept This Course?

UPI Study courses carry NCCRS recommendations β€” the same standard recognized by hundreds of cooperating colleges and universities. Check if your school is on our list and move forward with confidence β€” or schedule a call with our team.

Accepted at cooperating universities

UPI Study Courses Include

⏱️Self-paced, flexible learning
πŸŽ₯Video-based lessons
πŸ“˜Digital study materials
🧩Interactive quizzes & assessments
πŸ“„ACE & NCCRS-recommended transcripts
πŸ’¬Academic support & guidance
πŸ“ˆGrade improvement opportunities
πŸ’»Access on desktop & mobile

Build analytical strength with Calculus 2.

Go deeper into the mathematics of the physical world. Advanced integration, infinite series, and differential equations β€” with a short introduction to parametric, polar, and vector topics β€” power everything from engineering to economics.

🎯 Why It Matters

  • Develop rigorous quantitative and analytical thinking
  • Build a foundation for advanced STEM coursework
  • Apply scientific and mathematical reasoning to real problems
  • Strengthen skills valued across engineering, research, and data fields

πŸ’Ό In-Demand Careers

  • Research Assistant
  • Lab Technician
  • Data Analyst
  • Engineering Technician
  • Science Educator
  • Technical Writer

πŸš€ How This Sets You Up

  • Complete structured lessons and a comprehensive final exam
  • Earn 4 transferable college credit hours
  • Recognized by NCCRS cooperating universities globally
  • Self-paced β€” no deadlines, no campus visits required
Student Reviews

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Real Results.

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FAQ

Common Questions Answered.

Everything you need to know about Calculus 2 β€” credits, grading, transfer, and how it compares to traditional options.

What is Calculus 2?
Calculus 2 (Maths 265) is a college-level STEM course worth 4 credit hours and carrying an NCCRS recommendation. It continues single-variable calculus with advanced integration techniques, improper integrals, hyperbolic functions, applications of integration, differential equations, and infinite sequences and series. It also includes a short introduction to a few Calculus 3 topics β€” parametric equations, polar coordinates, and vectors β€” which some universities like to see covered at this stage.
Does this course cover Calculus 3?
Only as a brief introduction. The Maths 265 syllabus includes a short intro to parametric equations, polar coordinates, and vectors β€” early Calculus 3 material that some universities like to see covered in Calculus 2. This is a Calculus 2 course at its core; it is not a substitute for a full Calculus 3 course. If you need the complete treatment of those topics, take our Calculus 3 course.
Is this course difficult?
The course is designed to be rigorous but accessible. It is self-paced, so you can take the time you need on more difficult concepts like convergence tests or Taylor series. Most students complete it in 28–30 days with consistent effort.
Is this course self-paced?
Yes. The course is fully self-paced with no deadlines or fixed class times. Most students complete it in 28–30 days, but you can move faster or slower depending on your schedule.
How many college credits is this course worth?
This course carries an NCCRS recommendation for 4 semester credit hours in Calculus, Mathematics, or Computer Science β€” in both the lower division/associate degree category and the upper division baccalaureate degree category.
Are there exams? How is grading done?
Yes β€” the course includes quizzes, an assignment, and a final exam of 100 multiple-choice questions. Your grade is equally weighted: 25% Attendance Β· 25% Quizzes Β· 25% Assignment Β· 25% Final Exam. A score of 70 or above is required to pass.
How do I check if my university accepts UPI Study credits?
Check our Find My College directory. If your university recognizes NCCRS credit recommendations, UPI Study courses qualify. You can also book a free call with our team.
How does UPI Study compare to a traditional university course?
A traditional university course in this subject typically costs $500–$1,500+ per credit hour and requires fixed schedules, campus attendance, and semester timelines. UPI Study covers the same NCCRS-recommended content at $250 total, with no deadlines and no campus requirement.
Can international students take this course?
Yes. UPI Study courses carry an NCCRS recommendation β€” recognized by cooperating institutions in the U.S., Canada, the UK, and other countries. Students have submitted credits across 26+ countries.

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Why It Matters

Why Take College Credits?

Quick answers about transferable online credits, test-out style learning, and ACE & NCCRS-recommended options through UPI Study.

🏫

Which universities accept these credits?

UPI Study courses carry NCCRS recommendations recognized by many cooperating colleges and universities across the U.S., Canada, and UK.

1,733+ verified schools β†’
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Who can take self-paced college courses?

Anyone can enroll β€” including high school students, incoming college students, adult learners, and students trying to test out of traditional courses.

No prerequisites required β†’
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Why choose this over traditional classes?

Save time and reduce tuition costs. Many students complete prerequisites faster and shorten their time to graduation β€” at a fraction of the cost.

$60M+ saved by students β†’
πŸ“œ

How many credits can I earn?

This course is NCCRS-recommended for 4 semester credit hours. Transfer as many credits as your university allows β€” students have transferred anywhere from 3 to 90+ credits depending on their school's policy.

4 credits this course β†’
What's Included

Everything You Need to Succeed

πŸŽ₯

Video-Based Lessons

HD video lectures broken into short, focused modules. Watch at your own pace β€” pause, rewind, replay any time.

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Quizzes & Final Exam

Evaluate your understanding after every section with quizzes and a comprehensive final exam that mirrors real college assessment.

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Structured College-Level Course

Structured lessons covering the full Calculus 2 sequence, with a short intro to a few Calculus 3 topics β€” a complete college-level Calculus 2 course.

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Official Transcript

Complete the course, request your transcript, and transfer 4 credit hours to cooperating universities. No separate exam required.

Ready to Start?

Earn 4 College Credits
for $250.

Self-paced. No deadlines. NCCRS-recommended, recognized by cooperating universities. Join 135,000+ learners on the UPI Study platform.