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Calculus 1: The Complete Guide

via Udemy


Learn fast through concise yet contented lectures

What you'll learn:
  • Pre-Calculus materials, including number sets, exponents, proof by induction
  • All sorts of functions (polynomial, exponential, trigonometric, hyperbolic)
  • Inverse functions, logarithms, complex numbers, Argand diagrams
  • Euler's formula, multiplication of complex numbers, polar form, double-angle formulae, de Moivre's theorem, roots of unity and complex loci
  • Limits, continuous functions, intermediate value theorem
  • Sandwich theorem, logarithmic vs polynomial vs exponential limits, differentiation from first principles, product rule and chain rule
  • Derivatives of implicit functions, inverse functions, parametric functions, differentiable functions
  • Mean value theorem
  • Integration, the Riemann integral, fundamental theorems of Calculus
  • Indefinite and definite integrals, integration by substitution, integration by parts, recursion relations, partial fractions
  • Volumes of revolution, length of a curve, infinite sums, convergence criteria, power series
  • Taylor's theorem, l'Hôpital's rule

Are you struggling with Mathematics?

Are you anxious about being behind in Maths class?

Or do you just simply want to get ahead of yourself and learn Maths?

Well, let me ask you instead:

How would you feel if Maths weren't something you're afraid of or struggling with anymore?

Instead of having to sit down after class trying to figure out what's going on, what if you no longer have to do that because you clearly understand everything?

I, a newly graduate from Kings's College London with a degree in Mathematics, first honours, will help you with that.

This Calculus I course is packed with videos, no more than 10 minutes each. For those longer videos, I suggest you sit through the whole video in one go, it will definitely be easier to understand, and pause before you move onto the next part unless you've fully understood the materials, otherwise the confusion will pile up. I've also included a bunch of definitions, theorems, quizzes, examples, concise notes for each section, exercises for every topic, and walkthrough of all weekly questions that will help you fully understand Calculus. Most importantly, I've done a BONUSsection for you! It includes some additional questions and a cheat sheet that myself have used to get through the exam.

Calculus is the core of all other topics in Mathematics, and a good understanding of the basics is what is needed to help you get good at the more difficult topics. It's very crucial to learn and understand the basics before you move on to harder materials. Everything has been broken down into simple structure to make learning and understanding easy for you. I will be sharing some of the tips that I have used in solving problems during university as well as my thought process as I approach each question. Feel free to leave questions in the Q&A section. I understand what it's like to have to sit on unanswered questions and confusion for days, or perhaps weeks, so I will try and get back to you ASAP.

This COMPLETEguide is for those of you are looking to get a little bit of extra materials and are ready to fully commit to improving yourself. You've already shown half of your determination by looking at the course, so if this course sounds right for you, boost that up and join me on this journey!


1) It will be very useful if you also take notes of your own as you're watching the lectures, it will help you understand everything better and quicker. Just pause if I move on to other topics too fast or if you haven't fully understood the previous sub-topic before you move on to the next parts.

2) Please ask any questions you may have in the Q&A section if you don't understand. It's one thing to not understand it, but it's a whole new experience and a very important thing to do when learning Maths to be able to discuss it with fellow students who are going through the same thing.

3) Use headphones for better sound.

4) Don't forget you can always slow down or speed up the video!

Taught by

L Sang

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