Here are many **free Calculus learning materials and teaching resources**, covering all major areas of calculus.

#### Quick Links to Calculus Learning Materials in this article:

**Calculus Learning Materials and Resources****Calculus Handouts & Presentations from UMass OpenCourseware****Online Calculus Learning Materials and Resources****Math 148 Business Calculus Course**

Calculus is all about **understanding change**. It’s like having a magnifying glass for motion, letting you see not just where things are but **how fast they’re getting there and how much stuff accumulates along the wa**y. It’s like the language of change!

Here’s a breakdown of the **key concepts**:

**Functions:**Imagine a machine that takes in numbers (inputs) and spits out other numbers (outputs). That’s a function! Calculus helps us analyze how these outputs change as the inputs do.**Derivatives:**Think of them as the “instantaneous change rates” of functions. They tell you how fast something is moving up or down at any given moment, like the slope of a hill at a specific point.**Differentiation:**This is the process of finding derivatives. It’s like figuring out the “gears and levers” inside the machine that control how the outputs change with the inputs.**Integrals:**These are the opposite of derivatives. They add up “infinitesimal slices” of a function (imagine tiny rectangles under a curve) to tell you the total “stuff” it represents. Think of it like calculating the area under a curve.**Integration:**This is the process of finding integrals. It’s like collecting all the tiny pieces and putting them together to get the whole picture.

**Why Learn Calculus?**

Calculus isn’t just about fancy math tricks. It’s a powerful tool used in countless fields:

**Physics:**Calculating motion, forces, and energy**Engineering:**Designing bridges, buildings, and machines**Economics:**Modeling markets, investments, and growth**Computer Science:**Optimizing algorithms and graphics**Medicine:**Understanding blood flow, drug dosage, and disease progression

Calculus trains your brain to think critically about change, solve complex problems, and make sense of real-world phenomena. It’s like a mental superpower that unlocks doors in various fields.

**Benefits in Life and Career:**

**Stronger problem-solving skills:**Apply analytical thinking to everyday challenges.**Improved quantitative reasoning:**Make informed decisions based on data and trends.**Deeper understanding of the world:**See the “hidden math” behind everything from rocket launches to weather patterns.**Competitive edge in STEM careers:**Open doors to high-demand jobs in various fields.**Boosted critical thinking and creativity:**Develop skills valuable in any profession.

Remember, calculus might seem daunting at first, but it’s like climbing a mountain: the view from the top is worth the effort. With dedication and practice, you can unlock the power of change and see the world in a whole new light. **For more calculus content, please visit 78 Calculus Cheat Sheets, Reviews, Formulas and Textbooks**.

### Calculus Learning Materials and Resources (pdf)

- A Brief Guide to Calculus 2
- A Reform Approach to Business Calculus
- Active Calculus Textbook
- An Introduction to Calculus – Limits, Derivatives, and Integrals
- Antiderivatives and Indefinite Integrals Notebook
- Antiderivatives and the Indefinite Integral
- AP Calculus AB Multiple Choice Test with Solutions
- AP Calculus AB Pre-Exam with Answers
- AP Calculus AB Worksheets with Answers
- AP Calculus Cheat Sheet
- AP Calculus Problem Book, with Answers
- Study Guide for the AP Calculus AB Examination
- Apex Calculus Textbook with Answers to Odd-Numbered Problems
- Applications of Integration
- Applied Calculus Textbook
- Basic Calculus Refresher
- Basic Differentiation – A Refresher
- Business Calculus Problems with Solutions
- Calculus 1 Review Problems with Answers
- Calculus 1 Review with Solutions
- Calculus 1 Second Semester Textbook
- Calculus 1 Test Review and Solutions
- Calculus 2 Examples and Solutions
- Calculus 2 Examples, Problems and Solutions
- Calculus 2 Final Exam with Answers & Solutions
- Calculus 2 for Engineers
- Calculus 2 Integal Calculus
- Calculus 2 Midterm Exam with Solutions
- Calculus 2 Problems with Answers
- Calculus 2 Problems with Solutions
- Calculus 2 Review with Solutions
- Calculus 2 Textbook
- Calculus 2 with Analytic Geometry Textbook
- Calculus 2 Workbook with Answers
- Calculus Applied to Probability and Statistics
- Calculus Cheat Sheet
- Calculus Lecture Notes, First Semester
- Calculus Lecture Notes, Second Semester
- Calculus on the Number e
- Calculus Refresher
- Calculus Textbook
- Calculus with Parametric Equations
- Common Derivatives and Integrals
- Conics and Calculus
- Derivatives Cheat Sheet
- Derivatives of ln and e
- Derivatives of Polynomial, Exponential, Trig & Log Functions
- Derivatives of Trig Functions
- Detailed Review for Calculus 1A
- Detailed Review for Calculus 1B
- Differential Calculus from Khan Academy.zip (504mb)
- Differential Equations
- Differentiation and Integration Formulas
- Fourier Series
- Functionals and the Functional Derivative
- Fundamentals of Calculus Textbook
- Geometric Series Problems with Solutions
- Implicit Differentiation and Logarithmic Differentiation
- Improper Integrals
- Infinite Sequences and Series
- Infinite Series
- Integral Calculus Exercises with Examples and Answers
- Integral Calculus Formula Sheet
- Integral of the Natural Log
- Integral Problems and Solutions
- Integrated Calculus 2 Exam and Solutions
- Integration by Parts
- Integration Formulas and the Substitution Rule
- Integration Review Sheet
- Integration Substitution Method Worksheet with Solutions
- Integration-Worked Examples
- Logarithmic Differentiation
- Logarithms and Calculus
- Matrix Calculus – Derivation and Simple Application
- Multiple Integrals and Vector Calculus
- Multivariable Calculus Formula and Theorem Review
- Multivariable Calculus Lecture Notes
- Multivariable Calculus Problems and Solutions
- Multivariable Calculus, Early Transcendentals Textbook, with Answers
- Multivariable Calculus, Late Transcendentals Textbook, with Answers
- Multivariate Calculus Final Exam with Solutions
- Numerical Approximations of Definite Integrals
- Parametric Integration Techniques
- Partial Derivatives and Differentials: Explanations with Examples
- Partial Fractions for Quotient of Polynomials
- Partial Fractions Worksheet
- Polar Coordinates
- Power Series
- Power, Taylor, and Maclaurin Series Survival Guide
- Related Rates of Change Problems with Solutions
- Review of Differentiation and Integration
- Second-Order Linear Differential Equations, with Solutions
- Series Convergence-Divergence Flow Chart
- Short Introduction to Calculus for Business
- Single Variable Calculus Problems with Detailed Solutions
- Single Variable Calculus, Early Transcendentals Textbook, with Answers
- Single Variable Calculus, Late Transcendentals Textbook, with Answers
- Strategy for Integration, with Solutions
- Substitution Techniques
- Taylor Series Formulas
- Techniques of Integration
- The Calculus of Several Variables Textbook
- The Fundamental Theorem of Calculus Problems with Solutions
- The Second Derivative Test
- The Two Fundamental Theorems of Calculus
- Things You Should Know Before Beginning Calculus 2
- Trigonometric Integrals with Solutions
- Understanding Basic Calculus with Solutions & Answers
- Vector Calculus Textbook
- Vector Calculus Useful Stuff
- Vector Calculus

#### Calculus Handouts & Presentations from UMass OpenCourseware:

Copyright 2014, Catalin Zara. This work is licensed under a Creative Commons License by UMass Boston OpenCourseWare, no changes were made. All files are in pdf format.

- Chain Rule
- Conservative Fields
- Constrained Optimization
- Continuity
- Cross Product
- Curl Theorem
- Curvilinear Coordinates
- Derivative as a Function
- Derivative at a Point
- Differentiation Formulas
- Directional Derivatives
- Divergence Theorem
- Dot Product
- Double Integrals in Polar Coordinates
- Double Integrals
- Functions
- Fundamental Theorems
- Geometry of Lines and Planes
- Green’s Theorem
- Implicit Functions
- Limit Laws
- Limits and Continuity
- Limits
- Line Integrals
- Linearizations
- Lines and Planes
- More about Limits
- Numbers and Functions
- Operations with Functions
- Optimization
- Parametric Curves
- Parametrized Surfaces
- Partial Derivatives
- Rectangular Coordinates
- Surface Integrals
- Vectors

### Online Calculus Learning Materials and Resources

- The Calculus Page Problems List, with Explanations and Solutions
- CLEP Calculus Exam Guide, with Answer Key (pdf)
- AP Calculus Practice Exam, with Answer Key (pdf)
- AP Calculus AB Past Exam Questions, with Answers
- Preparing for the AP Calculus AB Exam – Part 1: Derivatives, Free Course from Edx.org
- Challenging Concepts from Calculus AB & Calculus BC, Free Course from Edx.org
- Calculus 1 Lesson Units from Khan Academy
- All Calculus Courses and Lessons from Khan Academy
- Calculus Videos from Professor Dave: These videos will provide you with a solid grounding in the concepts of differentiation and integration, along with a lot of practice.
- Calculus Videos from Professor Leonard
- Calculus 1 Videos: Differential Calculus, from Mathispower4u
- Calculus 2 Videos: Integral Calculus, from Mathispower4u
- Calculus 3 Videos: Multi Variable Calculus, from Mathispower4u
- Single Variable Calculus Course from MIT: This calculus course teaches differentiation and integration of one-variable functions, as well as applications. Included are: a Course Reader, Lecture Notes, Video Lectures, Assignments, and Exams with Solutions.
- 100 Calculus Skills to investigate and learn from examples
- Differentiation Interactive Practice with Answers, from drfrostmaths.com
- Differentiation Downloads, from drfrostmaths.com
- Complete Calculus Cheat Sheet: Full and Reduced in size
- Limits Calculus Cheat Sheet: Full and Reduced in size
- Derivatives Calculus Cheat Sheet: Full and Reduced in size
- Integrals Calculus Cheat Sheet: Full and Reduced in size
- Common Derivatives and Integrals: Full and Reduced in size
- Table of Laplace Transforms
- Calculus 1 Notes and Practice Problems with Solutions
- Calculus 2 Notes and Practice Problems with Solutions
- Calculus 3 Notes and Practice Problems with Solutions
- Differential Equations Notes
- Differentiation Practice with Answers: Power Rule and Trig Functions and Quiz with Answers
- Differentiation Practice with Answers: Addition, Product and Quotient Rules and Quiz with Answers
- The Chain Rule Practice with Answers and Quiz with Answers
- Free Calculus Courses from Modern States (registration required):
- Excellent Calculus Notes by Ken Kuniyuki, Professor at San Diego Mesa College:
- Calculus Guides, Practices and Videos from Mathcenter.ac.uk:
- Differential Equations
- First order differential equations
- Second order differential equations
- Applications to finding tangents and normals
- Chain rule
- Differentiation by taking logs
- Differentiation from first principles
- Differentiation of functions defined parametrically
- Implicit differentiation
- Maxima & minima
- Partial differentiation
- Product rule
- Quotient rule
- Use of a table of derivatives and standard rules
- Integration as a summation
- Integration as the reverse of differentiation
- Integration by parts
- Integration by substitution
- Integration requiring use of trigonometric identities
- Integration that leads to log functions
- Integration using partial fractions
- Simple applications e.g. finding areas and volumes

#### Math 148 Business Calculus Course

Shana Calaway.. Open Course Library: MATH&148 Business Calculus. The Open Course Library. Washington State Board for Community & Technical Colleges, March 2013. All files are in pdf format.

- Business Calculus Full Textbook
- Chapter 0: Introduction
- Chapter 1: Review
- Chapter 1 Answers
- Chapter 2: The Derivative
- Chapter 2 Answers
- Chapter 3: The Integral
- Chapter 3 Answers
- Chapter 4: Functions of Two Variables
- Chapter 4 Answers
- Car Ride Activity 1
- Car Ride Activity 2
- Clipping Project 1
- Clipping Project 2
- Clipping Project 3
- Course Objectives
- Module level Objectives
- Video Playlist
- Written Homework
- Written Homework – Solutions
- Test Problems (no answers)

*– love learning -your best ed lessons guide, Scott*