Take free online calculus courses to build your math skills and improve your performance in school and at work. Here are the top 10 online courses to supplement your calculus skills:

**1.** **Calculus 1C: Coordinate Systems & Infinite Series**

**About this course**

How did Newton describe the orbits of the planets? To do this, he created calculus. But he used a different coordinate system more appropriate for planetary motion. We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions.

How does a computer make accurate computations? Absolute precision does not exist in the real world, and computers cannot handle infinitesimals or infinity. Fortunately, just as we approximate numbers using the decimal system, we can approximate functions using series of much simpler functions. These approximations provide a powerful framework for scientific computing and still give highly accurate results. They allow us to solve all sorts of engineering problems based on models of our world represented in the language of calculus.

- Changing Perspectives
- Parametric Equations
- Polar Coordinates

- Series and Polynomial Approximations
- Series and Convergence
- Taylor Series and Power Series

This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum.

##### What you’ll learn

- To compute arc length
- Methods for parameterizing curves
- To do calculus in polar coordinates
- How to approximate functions with Taylor polynomials
- To determine convergence properties of infinite series

**Length:** 13 weeks

**Level:** Intermediate

**2. Precalculus**

**About this course**

This course is part of Global Freshman Academy (GFA), which means you can earn transferable ASU credit toward your college degree.

In this college-level Precalculus course, you will prepare for calculus by focusing on quantitative reasoning and functions. You’ll develop the skills to describe the behavior and properties of linear, exponential, logarithmic, polynomial, rational, and trigonometric functions.

Content in this course will be adaptive, allowing you to achieve mastery in a certain concept before moving on to the next. Utilizing the ALEKS learning system, students in this personalized, self-paced course will be instructed on the topics they are most ready to learn while also providing individualized coaching as you move through each topic.

Before taking this course, you should already have a strong understanding of algebraic skills such as factoring, basic equation solving, and the rules of exponents and radicals.

**What you’ll learn**

- How to describe the behavior and properties of linear, exponential, logarithmic, polynomial, rational, and trigonometric functions
- How to apply your understanding of these functions to real-world problems
- Skills required for success in future studies in calculus

**Length: **15 weeks

**Level:** Intermediate

**3. Calculus Applied**

**About this course**

In this course, we go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand how calculus and mathematical models play a role in their work.

This is a course to learn applications of calculus to other fields, and NOT a course to learn the basics of calculus. Whether you’re a student who has just finished an introductory Calculus course or a teacher looking for more authentic examples for your classroom, there is something for you to learn here, and we hope you’ll join us!

**What you’ll learn**

- Authentic examples and case studies of how calculus is applied to problems in other fields
- How to analyze mathematical models, including variables, constants, and parameters
- Appreciation for the assumptions and complications that go into modeling real world situations with mathematics

**Length: **10 weeks

**Level:** Intermediate

**4. Engineering Calculus and Differential Equations**

**About this course**

How do electrical engineers find out all the currents and voltages in a network of connected components? How do civil engineers calculate the materials necessary to construct a curved dome over a new sports arena? How do space flight engineers launch an exploratory probe? If questions like these pique your interest, this course is for you!

This course will enable you to develop a more profound understanding of engineering concepts and enhance your skills in solving engineering problems. In other words, youwill be able to construct relatively simple models of change and deduce their consequences. By studying these, youwill learn how to monitor and even controla given system to do what you want it to do.

Techniques widely used in engineering will be illustrated; such as Laplace transform for solving problems in vibrations and signal processing. We have designed animations and interactive visualizations to supplement complex mathematical theories and facilitate understanding of the dynamic nature of topics involving calculus.

**What you’ll learn**

- Limits, Continuity, and Differentiation in Engineering Calculus
- Applications of Derivatives
- Parametric Equations and Polar Coordinates
- Techniques of Integration
- Applications of Definite Integrals
- Engineering Differential Equations and First Order Equations
- Homogeneous, Inhomogeneous Equations, and Exact Equations
- Homogeneous Linear Equations with Constant Coefficients
- Cauchy-Euler Equations and Laplace Transforms
- How to analyze a given engineering problem
- Ways to identify appropriate calculus and ordinary differential equations (ODE) skills
- How to formulate the mathematical problem
- How to find the solutions for engineering problems

**Length: **6 weeks

**Level:** Introductory

**5.** **Introduction to Calculus**

**About this Course**

The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. The course emphasizes the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics.

**Students taking Introduction to Calculus will:**

• gain familiarity with key ideas of precalculus, including the manipulation of equations and elementary functions (first two weeks),

• develop fluency with the preliminary methodology of tangents and limits, and the definition of a derivative (third week),

• develop and practice methods of differential calculus with applications (fourth week),

• develop and practice methods of the integral calculus (fifth week).

**Length: **5 weeks

**Level:** Intermediate

**6. Calculus: Single Variable Part 1 – Functions**

**About this Course**

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.

In this first part–part one of five–you will extend your understanding of Taylor series, review limits, learn the *why* behind l’Hopital’s rule, and, most importantly, learn a new language for describing growth and decay of functions: the BIG O.

**Length:** 4 weeks

**Level: **Introductory

**7. Calculus: Single Variable Part 2 – Differentiation**

**About this course**

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.

In this second part–part two of five–we cover derivatives, differentiation rules, linearization, higher derivatives, optimization, differentials, and differentiation operators.

**Length: **3 weeks

**8.** **Precalculus: the Mathematics of Numbers, Functions and Equations**

**About this course**

This course is the first of two precalculus courses from the University of Padova that will provide you with an introduction to the fundamental mathematical skills required to complete your first course in calculus.

You will learn the basic precalculus required for college or undergraduate-level studies, including factoring and division, sets and set operations, reasoning and proofs, functions and graphs, and equations and inequalities.

On this online precalculus course, you will gain the foundation to support further mathematical studies and improve your use of maths in everyday life.

**What you’ll learn**

- Describe the basic arithmetic of numbers, including absolute value and radicals
- Explain the elements of mathematical reasoning and proofs
- Solve polynomials: roots, factoring, and division
- Identify the standard notation for sets and set operation
- Classify the type of functions and their graph
- Solve equations and inequalities

**Length:** 5 weeks

**9. Advanced Precalculus: Geometry, Trigonometry and Exponentials**

**About this course**

This course is the second of two precalculus courses from the University of Padova, providing you with the advanced mathematical skills required to complete a first course in calculus.

You’ll get to grips with more challenging precalculus topics: plane and solid geometry; logarithms and exponentials; equalities and inequalities; and trigonometric functions and identities.

By the end of this course you’ll have gained the skills to support further mathematical studies.

What topics will you cover?

- Plane and solid geometry
- Logarithms and exponentials
- Trigonometric functions and identities
- Equalities and inequalities involving exponential and trigonometric functions

**What you’ll learn**

- Solve problems using properties of the basic transcendental functions: exponential, logarithmic, and trigonometric
- Solve equalities and inequalities in terms of transcendental functions
- Apply elements of mathematical reasoning and proofs
- Apply elements of mathematical reasoning and proofs
- Calculate expressions involving transcendental functions
- Calculate areas and volumes of basic geometric plane figures and spatial solids
- Compare exponentials and logarithms

**Length:** 4 weeks

**10. Differential Equations for Engineers**

**About this course**

This course is about differential equations and covers material that all engineers should know. Both basic theory and applications are taught. In the first five weeks we will learn about ordinary differential equations, and in the final week, partial differential equations.

The course is composed of 56 short lecture videos, with a few simple problems to solve following each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of six weeks in the course, and at the end of each week there is an assessed quiz.

**Length: **6 weeks

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