• Post category:StudyBullet-3
  • Reading time:19 mins read


Learn fast through concise yet contented lectures

What you will 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’HΓ΄pital’s rule

Description

Are you struggling with Mathematics?

Are you anxious about being behind in Maths class?


Get Instant Notification of New Courses on our Telegram channel.


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 BONUS section 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 COMPLETE guide 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!

Tips:

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!

English
language

Content

Introduction
Introduction
Calculus I.1
Calculus I.1: Number Sets
Calculus I.1: Exponents or Powers of Real Numbers
Calculus I.1: Solving Quadratic Equations
Calculus I.1: Proof By Induction Pt.1
Calculus I.1: Proof By Induction Pt.2
Calculus I.1: Functions
Calculus I.2
Calculus I.2: Polynomial Functions
Calculus I.2: Exponential Function
Calculus I.2: Trigonometric Functions Pt.1
Calculus I.2: Trigonometric Functions Pt.2
Calculus I.2: Trigonometric Functions Pt.3
Calculus I.2: Trigonometric Functions Pt.4
Calculus I.2: Trigonometric Functions Pt.5
Calculus I.2: Hyperbolic Functions Pt.1
Calculus I.2: Hyperbolic Functions Pt.2
Exercises I and Solutions I.1
Solutions I.2
Solutions I.3
Solutions I.4
Solutions I.5
Solutions I.6
Solutions I.7
Calculus I.3
Calculus I.3: Inverse Functions
Calculus I.3: Logarithms Pt.1
Calculus I.3: Logarithms Pt.2
Calculus I.3: Complex Numbers Pt.1
Calculus I.3: Complex Numbers Pt.2
Calculus I.3: The Argand Diagram
Calculus I.3: QUIZ!
Exercises II and Solutions II.1
Solutions II.2+3
Solutions II.4
Solutions II.5
Solutions II.6
Calculus I.4
Calculus I.4: Euler’s Formula Pt.1
Calculus I.4: Euler’s Formula Pt.2
Calculus I.4: Multiplication and Division of Complex Numbers
Calculus I.4: Polar Form Pt.1
Calculus I.4: Polar Form Pt.2
Calculus I.4: Double-Angle Formulae
Calculus I.4: de Moivre’s Theorem
Calculus I.4: Roots of Unity
Calculus I.4: Complex Loci Pt.1
Calculus I.4: Complex Loci Pt.2
Calculus I.4: QUIZ!
Exercises III and Solutions III.1+2
Solutions III.3
Solutions III.4
Solutions III.5
Solutions III.6
Solutions III.7 Pt.1
Solutions III.7 Pt.2
Solutions III.8+9
Solutions III.10
Calculus I.5
Calculus I.5: The Limit Pt.1
Calculus I.5: The Limit Pt.2
Calculus I.5: Continuous Functions
Calculus I.5: The Intermediate Value Theorem
Calculus I.5: Limits Involving Infinity
Calculus I.5: Working with Limits
Calculus I.5: Limits of Composite Functions
Calculus I.5: Multiple Limits
Calculus I.5: QUIZ!
Exercises and Solutions IV.1
Solutions IV.2+3
Solutions IV.4+5
Solutions IV.6+7
Solutions IV.8+9
Solutions IV.10
Solutions IV.11 Pt.1
Solutions IV.11 Pt.2
Solutions IV.12
Calculus I.6
Calculus I.6: The Sandwich Theorem Pt.1
Calculus I.6: The Sandwich Theorem Pt.2
Calculus I.6: Logarithmic Vs. Polynomial Vs. Exponential Functions Pt.1
Calculus I.6: Logarithmic Vs. Polynomial Vs. Exponential Functions Pt.2
Calculus I.6: Differentiation From First Principles Pt.1
Calculus I.6: Differentiation From First Principles Pt.2
Calculus I.6: Differentiation From First Principles Pt.3
Calculus I.6: Differentiation From First Principles Pt.4
Calculus I.6: Differentiation From First Principles Pt.5
Calculus I.6: The Chain Rule
Calculus I.6: The Sum Rule Pt.1
Calculus I.6: The Sum Rule Pt.2
Calculus I.6: The Product Rule
Calculus I.6: The Quotient Rule
Calculus I.6: QUIZ!
Exercises and Solutions V.1
Solutions V.2 Pt.1
Solutions V.2 Pt.2
Solutions V.3+4
Solutions V.5+6
Solutions V.7+8
Calculus I.7
Calculus I.7: Derivatives of Inverse Functions
Calculus I.7: Derivatives of Curves
Calculus I.7: Derivatives of Parametric Functions
Calculus I.7: The Mean Value Theorem
Calculus I.7: QUIZ!
Exercises and Solutions VI.1+4
Solutions VI.2
Solutions VI.3
Solutions VI.5
Solutions VI.6
Solutions VI.7
Calculus I.8
Calculus I.8: The Riemann Integral Pt.1
Calculus I.8: The Riemann Integral Pt.2
Calculus I.8: The Riemann Integral Pt.3
Calculus I.8: The Riemann Integral Pt.4
Calculus I.8: The Riemann Integral Pt.5
Calculus I.8: The Riemann Integral Pt.6
Calculus I.8: The Riemann Integral Pt.7
Calculus I.8: The Fundamental Theorem of Calculus Pt.1
Calculus I.8: The Fundamental Theorem of Calculus Pt.2
Calculus I.8: The Fundamental Theorem of Calculus Pt.3
Exercises and Solutions VII.1
Solutions VII.2 Pt.1
Solutions VII.2 Pt.2
Solutions VII.3 Pt.1
Solutions VII.3 Pt.2
Solutions VII.4 Pt.1
Solutions VII.4 Pt.2
Solutions VII.4 Pt.3
Solutions VII.4 Pt.4
Calculus I.9
Calculus I.9: Indefinite and Definite Integrals
Calculus I.9: Properties of Integrals and Techniques for Integration
Calculus I.9: Examples of Integration By Substitution Pt.1
Calculus I.9: Examples of Integration By Substitution Pt.2
Calculus I.9: Examples of Integration By Substitution Pt.3
Calculus I.9: Examples of Integration By Substitution Pt.4
Calculus I.9: Examples of Integration By Substitution Pt.5
Calculus I.9: Examples of Integration By Parts Pt.1
Calculus I.9: Examples of Integration By Parts Pt.2
Calculus I.9: Examples of Integration Using Partial Fractions Pt.1
Calculus I.9: Examples of Integration Using Partial Fractions Pt.2
Calculus I.9: Examples of Integration Using Partial Fractions Pt.3
Calculus I.9: Recursion Relations
Calculus I.9: Surface Areas Pt.1
Calculus I.9: Surface Areas Pt.2
Calculus I.9: QUIZ!
Exercises and Solutions VIII.1
Solutions VIII.2
Solutions VIII.3
Solutions VIII.4
Solutions VIII.5 Pt.1
Solutions VIII.5 Pt.2
Solutions VIII.6 Pt.1
Solutions VIII.6 Pt.2
Solutions VIII.6 Pt.3
Calculus I.10
Calculus I.10: Volumes of Revolution
Calculus I.10: Length of a Curve
Calculus I.10: Infinite Sums Pt.1
Calculus I.10: Infinite Sums Pt.2
Calculus I.10: Convergence Criteria Pt.1
Calculus I.10: Convergence Criteria Pt.2
Calculus I.10: Power Series Pt.1
Calculus I.10: Power Series Pt.2
Calculus I.10: QUIZ!
Exercises and Solutions IX.1
Solutions IX.2 Pt.1
Solutions IX.2 Pt.2
Solutions IX.3
Solutions IX.4
Solutions IX.5 Pt.1
Solutions IX.5 Pt.2
Solutions IX.6
Solutions IX.7 Pt.1
Solutions IX.7 Pt.2
Calculus I.11
Calculus I.11: Taylor’s Theorem Pt.1
Calculus I.11: Taylor’s Theorem Pt.2
Calculus I.11: Examples of Taylor’s Theorem Pt.1
Calculus I.11: Examples of Taylor’s Theorem Pt.2
Calculus I.11: Taylor’s Theorem Pt.3
Calculus I.11: l’HΓ΄pital’s Rule
Calculus I.11: QUIZ!
Exercises and Solutions X.1+6
Solutions X.2
Solutions X.3
Solutions X.4 Pt.1
Solutions X.4 Pt.2
Solutions X.4 Pt.3
Solutions X.5