Summer is one of the best times to prepare for math courses, especially the courses that you have a problem or struggle with like algebra or calculus.

In this, post we’re going to give you 7 steps to prepare for calculus during the summer.

you would be preparing the necessary calculus subjects on your own without investing in online courses or personal internships just from the free sources that will mention in this article.

but you have to respect the timeline of each subject and give it enough time to Absorb.

This program is going to be accelerated meaning it would have to complete in just two months or 8 weeks. so it will require additional dedication and hard work, by spending at least 5 hours a day to succeed at this preparation.

This is the timeline and subjects you need to prepare for calculus.

- Trigonometry ==> 2 weeks
- Complex numbers ==> 1 week
- Rational functions ==> 1 week
- Vectors ==> 1 week
- Series ==> 1 week:
- Limits and continuity ==> 2 week

## 1 – trigonometry 2 weeks

The first subject you have to begin during the first two weeks is trigonometry. you have to learn the all basics of trigonometry subject that we would list below:

- Trigonometric identities on the unit circle
- Inverse trigonometric functions
- law of sine
- law of cosine
- trigonometric funtions

The first thing that you will begin within the first week is how to transform the angle From degrees to radians. first of all, you have to learn how to represent angles in circles like this form below.

For instance, you would be learning where you should point **π/4 or π/3** in a circle. The unit and circle subject is interesting also in representing trigonometric functions.

the next step is to learn how to discover trigonometric functions like sine and cosine and learn how to inverse them for instance:

you should know:

- what is the law of cosine
- what is the law of sine
- The inverse of cos is arccos
- The inverse of sin is arcsin

theses operations are easy to complete they are not complicated once you understand them they won’t take you so much to complete.

The last thing is will be learning how to solve trigonometric equations like in the example below:

- cos(x)² + sin(x)²= 1
- tang(x) = sin(x)/cos(x)
- cos(π+π/4)

this is the hardest part you will face in trigonometry, to not struggle in these equations you have to respect the order by restudying the all previous topics we mentioned in the paragraph.

## 2 Complex numbers 1 week

complex numbers will be your next subject to study after trigonometry, in complex numbers you will be studying functions like the example below:

if you haven’t heard or studied complex numbers. you will discover your first time the wired sing or “ i “ as you have seen multiplied by Y in the example above.

complex numbers are not a complicated subject, if you dedicated 5 hours a day you could finish it in just 1 week. 1 Week is not enough to solve many problems to gain enough experience. but 2 months of summer is enough to have an idea about getting you on the right track to finish your calculus summer preparation.

in complex numbers you’ll be discovering :

- The complex plane
- Distance and midpoint of complex numbers
- Complex conjugates and dividing complex numbers
- Identities with complex numbers
- Modulus (absolute value) and argument (angle) of complex numbers
- The polar form of complex numbers
- Graphically multiplying complex numbers
- Multiplying and dividing complex numbers in polar form

for instance, we’re going to give an example of how to multiply complex :

*in complex number i²=-1*

This was an example that indicates that complex numbers are a topic that requires having a solid background in algebra. So if you struggle in algebra as you will struggle you will not be doing well in complete numbers.

## 3 Rational functions 1 week

rational functions is not a complex subject, you could study it and complete it easily in just 3 or 4 days if you are very good and have a solid background in a fraction a subject you alrady took in algebra 1.

Typically fractional numbers are functions that can be written in the following form.

so it is a mix or any function that is written as a fraction. In ration fractions, you will be learning how to:

- Reducing rational expressions to the lowest terms
- End behavior of rational functions
- Discontinuities of rational functions
- Graphs of rational functions
- Modeling with rational functions
- Multiplying and dividing rational expressions
- Adding and subtracting rational expressions

## 4 Vectors 1 week

vectors is not a complex subejcts, you could finish it in 3 days if you have solid basics in geometry courses that you should normally have taken between algebra 1 and algebra 2 courses.

- Vector components
- Magnitude of vectors
- Scalar multiplication
- Vector addition and subtraction
- Direction of vectors
- Vector components from magnitude and direction
- Adding vectors in magnitude and direction form
- Vectors word problems

## 5 series 1 week

Serie and sequences are one of the primordial topics you should focus on preparing for calculus in the summer. You will be needing to have solid basics in series to study calculus 1, and calculus 2 but frequently in multivariable calculus and differential equations.

you should focus on learning the two types of series:

- Geometric series
- Arithmetic series

In addtion have a look at a theorem called The binomial theorem.

in general, this is an easy subejcts compared to the last and next important subject you should focus on we’ll mention in the next paragraph.

## 6 limits and continuity 2 weeks

limits and continuity are the second and most interesting topics you should focus on if you want to succeed in your summer calculus preparation. This is the first subject you will be studying in your first calculus course at college which is calculus 1.

limits and continuity are a little bit difficult it memorization and a lot of hard work, you will find all subjects that you should completely take to prepare for calculus in this link.

## 7 use the right method of studying

the last step is to work hard but not forget to work smart. What do I mean by that?

you must first take your tile to understand all parts of the lecture and not jump between courses. For instance, when you take trigonometry you must ensure to understand all its parts before jumping to solving exercises.

In the second step after finishing the course, you have to solve the highest number of exercises possible. understanding a lecture without practice will be a loss of time.

good luck