Calculus 1 - A Complete Course In Differential Calculus

Master the theory, practice and applications of derivatives!

What you'll learn

Differential Calculus

Key Differentiation Techniques

Advanced Differentiation Techniques

Applications of Derivatives

Requirements

Math up to Pre-Calculus, particularly some experience with algebra and knowledge of functions

Experience with Trigonometry would be an advantage

Description

So you’ve made it through Pre-Calculus and are ready for the good stuff! Calculus is the Mathematics of change and used to model and understand many phenomena in the real world – from science and engineering to finance, economics and medicine – it’s difficult to find a field which doesn’t employ Calculus in some way. Although Calculus 1 is largely focused on differentiation techniques and their applications, it's important to set some foundations first. So, we start by looking at the key concepts of limits and continuity, and build upon these to define the derivative. The core of the course then focuses on primary and advanced differentiation techniques, before moving on to answer a range of questions which apply derivatives in some way.This Course is For YouI created this course to help you master differential Calculus through clear instructional videos and relevant practice questions. There are many reasons why you might want to take this course:To learn Calculus 1 from scratch For additional support if you're taking Calculus 1 in school or collegeTo help you prep for a Calculus 1 assessment To review key Differentiation techniques To access more than 200 relevant practice questions with full solutions As prep for taking a Calculus 2 course11 hours of instructional videoWhatever your reason this course will help you build key differentiation skills quickly. What You'll Take Away From This CourseCalculus 1 is a challenging course with a lot of content. But by mastering core techniques you'll be able to answer a wide variety of questions both in class and in the real-world. Each instructional video teaches one technique and mixes a small amount of theory with example problems. You will then practice what you've learnt in the end of section review exercise. I've also included step-by-step solutions so you can check your work as you go. Take this course and you will learn:The foundations of differentiation - limits and continuity The first principles of differentiationCore differentiation techniques - the Power, Product and Quotient rules The Chain Rule which allows you to differentiate a wide range of functionsAdvanced differentiation techniques and L'Hopital's ruleApplications of derivatives such as local extrema and optimisation

Overview

Section 1: Limits and Continuity

Lecture 1 Starting Limits

Lecture 2 Evaluating Limits Graphically

Lecture 3 Evaluating Limits Numerically

Lecture 4 Limits that Don’t Exist

Lecture 5 One Sided Limits & Existence of a Limit

Lecture 6 Properties of Limits

Lecture 7 Formal Definition of a Limit

Lecture 8 Evaluating Limits Directly

Lecture 9 Functions That Agree at All But One Point

Lecture 10 Evaluating Limits Algebraically

Lecture 11 The Squeeze Theorem

Lecture 12 Starting Continuity

Lecture 13 Formal Definition of Continuity

Lecture 14 Continuity on a Closed Interval

Lecture 15 Properties of Continuity

Lecture 16 The Intermediate Value Theorem

Lecture 17 Test Your Knowledge

Section 2: The Derivative

Lecture 18 Average and Instantaneous Rate of Change

Lecture 19 The Limit Definition of a Tangent Line Slope

Lecture 20 Defining The Derivative

Lecture 21 Differentiability

Lecture 22 Derivative Notation

Lecture 23 The Power Rule

Lecture 24 The Product Rule

Lecture 25 The Quotient Rule

Lecture 26 Differentiating Trigonometric Functions

Lecture 27 Test Your Knowledge

Section 3: The Chain Rule & Advanced Techniques

Lecture 28 The Chain Rule

Lecture 29 The Chain Rule - Examples

Lecture 30 Implicit Differentiation

Lecture 31 Second Derivates

Lecture 32 Combining Differentiation Rules

Lecture 33 Differentiating Exponential Functions

Lecture 34 Differentiating Logarithmic Functions

Lecture 35 Differentiating Inverse Functions

Lecture 36 Differentiating Inverse Trigonometric Functions

Lecture 37 L’Hopitals Rule

Lecture 38 Test Your Knowledge

Section 4: Applications of Derivatives

Lecture 39 The Equation of a Tangent to a Curve

Lecture 40 Determining Whether a Function is Increasing or Decreasing

Lecture 41 Determining Local Extrema of a Function

Lecture 42 2nd Derivative Test

Lecture 43 Points of Inflection

Lecture 44 Concavity

Lecture 45 Concavity Example

Lecture 46 Determining the Nature of Stationary Points

Lecture 47 Sketching Curves

Lecture 48 Optimisation Problems

Lecture 49 Optimisation Example

Lecture 50 Rolle’s Theorem

Lecture 51 The Mean Value Theorem

Lecture 52 Test Your Knowledge

Section 5: Additional Resources

Lecture 53 Calculus 1 Formula Sheet

Lecture 54 Trigonometry Formula Sheet

Lecture 55 Trigonometric Functions Graphs

Students who need to learn Calculus 1,Students who need to learn Differentiation,Students reviewing key Differentiation techniques for a test or assignment,Students looking for Calculus 1 practice questions with full step-by-step solutions,Students who want clear instruction on all aspects of Calculus 1