Is calculus 3 hard?: all you need to know about

Is calculus 3 hard or not?

we’re going to respond to this question and also discover what is the hardest subject in calculus 3. So keep reading if you want to discover more about this subject.

I calculus 3 hard?

Calculus 3 is the hardest calculus course among calculus 1 and 2, and it is difficult to understand for most people. It requires to form a student to have a solid basis in mathematics like algebra and the previous calculus courses like calculus 1 and calculus 2. So calculus 3 can be a nightmare for people who have weak mathematics basics in derivatives and integrals.

In calculus 3 students focus on a subject called multivariable, which is studying functions that have multiples variables. So making or finding a derivative or integral of a 3 variable function is very hard compared to single variables.

In addition in calculus 3 there are some difficult mathematics theorems that you have to digest like:

  • theorems of Green
  • stoke’s theorem
  • Lagrange
  • divergence theorem

This is not meaning that calculus 3 is a difficult course that is impossible to complete. But it requires a hell of a lot of work, especially if you fall with a terrible math professor.

So we’re going to talk in detail about the hardest subjects that you will expect to study in calculus 3

The hardest subjects that students study in calculus 3

1 Multivariable Calculus

multivariable calculus is a domain that studies functions with double variables like f(x,y) where you need to study and determine all aspects of these variable such.

As you can see, Multivariable calculus is a subject divided into 5 portions you can click on any portion to find your lesson.

2 – Lagrange

In Lagrange the principal mission is to find or determine the maximum or minimum of functions, this method is very efficacy, especially for functions that have more than one variable.

the Lagrange operation called lambda is a function that you substitute from the principal function to get a result. to put you in the perspective you need to watch this video below

3 – calculating double and triple integrals

Integral is a very interesting part of calculus but in high and advanced levels such as calculus 4, you won’t be using or calculating simple integrals like calculus 1 or 2.

In this step, you will calculate double and even triple integrals, these kinds of integrals are used a lot by physicists to calculate surfaces and volumes. For instance, calculating how much water of liters needs a cartridge to fill it.

fo this topic we have two videos:

one video mentioning or talking about how to calculate double integrals

this video shows an explanation of how to calculate a tripel integral

4- vectors fields

a vector field is a domain where we represent a function in two parts:

  • a real part
  • imaginary part

if we take an example of this kind of function we can write f(x)=X+iY where:

x is called a real part and y is an imaginary part. In other words, anything multiplied by y is called an imaginary part. to understand more about this subject you can watch this video below

5 – line integrals

mathematicians use line integrals to determine the curve of air or surfaces. line integrals normally can be in 2 or 3 dimensions this method is widely used by engineers and physicists.

there is a theorem called a fundamental theorem for line integrals that explain well this subject you can find it in the video below.

6 – theorems of Green

This theorem is specialized in how calculating the integral of a circle. theorems of green allow a mathematician to convert from a line integral to a double integral you can watch more detail in the video below.

7 – curl and vector field

8 – stoke’s theorem

9 – divergence theorem

10 Ordinary differential equations

ordinary differential equations that come with a single variable, to simplify more to solve an ordinary differential equation we use derivatives.

you will learn how to solve the ordinarily differential equation using two technics. general solution and particular solution. In addition, you will also learn what is

  • Leibniz notation
  • Lagrange notation
  • newton notation

11 Partial Differential equations

Partial differential equations are functions that come with more than one single variable like ordinary variables. to be good at a differential equation you have to master the derivative.

for instance, in thermodynamics, a partial differential equation is a domain used to determine how the temperature will going to be exchanged between a warm object and a cold object if you stick them to each other.

in other words, you will learn how the temperature distribution on each point of the object depending on the time.

12 Tensor theorem

it is hard to example what is tensor by written words like university definitions that you can find in the Wikipedia or other education contexts for this reason we let you with this video to discover what is a tensor.

13 Real-analysis

in calculus 5 you learn advanced real analysis subjects that talk about limits, derivatives, and calculus in real analysis you will learn:

  • sequences and limited
  • bounded sequences
  • theorem on limits
  • sandwich theorem
  • supermum and infimum
  • Cauchy sequences and completeness etc

you can find the full course of real analysis at this link.

14 Complex analysis

you will study higher level or complex analysis, in other words, you will use these kinds of equations like in the image below.

in the calculus 5 course and especially complex analysis you will learn:

  • complex diffrenciabilty
  • Complex Derivative
  • Holomorphic and Entire Functions
  • Total Differentiability in ℝ²
  • Cauchy-Riemann Equations
  • Cauchy-Riemann Equations
  • Wirtinger Derivatives
  • Power Series etc

you can find the topic about complex numbers in this link.

15 Extreme Value Theory

extreme value theory is a mathematical method that economists use to predict and manage risk. it is a method that can be used in the banking and endurance industry.

if you are a mathematician and you think of working in ensuring companies or banks you will be using this theory. you can watch this video below to discover what is extreme value theory.


Calculus 3 is the optimum level of calculus in math, but it is not the end. If you think that calculus is the end of math you’re wrong, it is just the beginning of serious math topics.

For this reason, we wrote full article guidance telling what is after calculus 3, you will find this article below.

What comes after calculus: from zero to hero


Yassin ajanif is a physics graduate and electromechanical engineer width more than 5 years in the field. My goal and my team are to share our experience to help you succeed in your career as a stem major. we talk about all tips, problems, and struggle STEM students face in their career and how to overcome them.