Calculus 1 - A Complete Course in Differential Calculus

Name: Calculus 1 - A Complete Course in Differential Calculus
Rating: 4.6 (10 reviews)

Master the theory, practice and applications of derivatives!

Created byGary Thomson

Last updated 9/2022

English

What you'll learn

Differential Calculus
Key Differentiation Techniques
Advanced Differentiation Techniques
Applications of Derivatives

Course content

5 sections • 55 lectures • 10h 51m total length

Starting Limits10:30
Students will describe what a limit is informally and give examples of limits with various functions.
Evaluating Limits Graphically11:37
Students will use the graph of a function to evaluate limits.
Evaluating Limits Numerically9:33
Students will evaluate a limit numerically by constructing a table of function values.
Limits that Don’t Exist12:02
Students will give examples of functions where a limit does not exist at a particular point.
One Sided Limits & Existence of a Limit14:58
Students will describe a one-sided limit and will use the definition to explain when a limit exists.
Properties of Limits11:40
Students will state key properties of limits which are useful for evaluating the limits of certain function types.
Formal Definition of a Limit14:20
Students will state the formal definition of a limit and will describe what it means informally.
Evaluating Limits Directly13:58
Students will recognise which limits can be evaluated directly and use the properties of limits to evaluate them.
Functions That Agree at All But One Point9:09
Students will state a key theorem which is helpful in developing a strategy for evaluating limits.
Evaluating Limits Algebraically14:22
Students will use cancellation and rationalisation techniques to evaluate limits which cannot be evaluated directly.
The Squeeze Theorem10:04
Students will evaluate limits using The Squeeze Theorem.
Starting Continuity7:49
Students will describe in general terms what continuous and non-continuous functions are.
Formal Definition of Continuity17:35
Students will state the formal definition of continuity and will describe what it means informally.
Continuity on a Closed Interval13:29
Students will state the definition of continuity on a closed interval using two-sided limits.
Properties of Continuity11:55
Students will state key properties of continuity.
The Intermediate Value Theorem13:15
Students will state The Intermediate Value Theorem and describe how it can be used.
Test Your Knowledge0:06
Check how much you've learnt about Limits & Continuity by trying these practice questions. Remember to check your work against the step by step solutions provided.

Average and Instantaneous Rate of Change15:04
Students will state the difference between average rate of change and instantaneous rate of change, and describe the connection between the two.
The Limit Definition of a Tangent Line Slope14:17
Students will describe how limits can be used to solve the tangent line problem and how the method is generalised to the form the limit definition of a derivative.
Defining The Derivative14:47
Students will state the definition of the derivative of a function and explain what the derivative of a function represents in general terms.
Differentiability15:17
Students will explain what a differentiable function is and the links between differentiability, continuity and limits.
Derivative Notation8:33
Students will use different forms of mathematical notation to represent derivatives.
The Power Rule15:09
Students will master the primary rule for differentiating functions known as The Power Rule.
The Product Rule14:48
Students will state and confidently use The Product Rule for differentiation.
The Quotient Rule12:54
Students will state and confidently use The Quotient Rule for differentiation.
Differentiating Trigonometric Functions10:25
Students will state the derivatives of the trigonometric functions, Sin, Cos & Tan.
Test Your Knowledge0:06
Check how much you've learnt about The Derivative by trying these practice questions. Remember to check your work against the step by step solutions provided.

The Chain Rule17:21
Students will state the conditions in which The Chain Rule can be used and will confidently use The Chain Rule to differentiate composite functions in different scenarios.
The Chain Rule - Examples16:30
Students will practice using The Chain Rule on various types of function.
Implicit Differentiation17:28
Students will state why implicit differentiation is necessary and will confidently use the technique to differentiate appropriate functions.
Second Derivates11:23
Students will explain what second order derivatives are and will confidently find second order derivatives of various types of functions.
Combining Differentiation Rules15:52
Students explore examples where the derivative requires the use of multiple differentiation rules.
Differentiating Exponential Functions14:33
Students will confidently differentiate various forms of exponential function.
Differentiating Logarithmic Functions10:57
Students will state the general derivative of an inverse function and apply it to various functions.
Differentiating Inverse Functions9:07
Students will state the general derivative of an inverse function and apply it to various functions.
Differentiating Inverse Trigonometric Functions9:22
Students will confidently differentiate inverse Trigonometric functions, Arcsin, Arccos, and Acrtan.
L’Hopitals Rule13:08
Students use L’Hopitals Rule to evaluate limits in indeterminate form.
Test Your Knowledge0:07
Check how much you've learnt about The Chain Rule & Advanced Techniques by trying these practice questions. Remember to check your work against the step by step solutions provided.

The Equation of a Tangent to a Curve14:37
Students use derivatives to determine the equation of a tangent to curve.
Determining Whether a Function is Increasing or Decreasing18:50
Students use derivatives to determine whether a function is increasing or decreasing.
Determining Local Extrema of a Function15:20
Students apply derivatives to find local extrema (maximum or minimum) of functions.
2nd Derivative Test15:50
Students use 2nd derivatives to find local extrema of a function.
Points of Inflection14:38
Students use derivatives to find points of inflection of curves.
Concavity10:33
Students use derivatives to determine the concavity of a function.
Concavity Example15:37
Students will consider an example of the concavity of a function.
Determining the Nature of Stationary Points16:28
Students use a nature table to determine stationary point types.
Sketching Curves18:56
Students use information from the derivative and nature tables to sketch curves.
Optimisation Problems14:54
Students apply derivatives to finding optimal solutions to real-world problems.
Optimisation Example12:59
Students will consider an example of optimisation.
Rolle’s Theorem13:26
Students will state Rolle’s Theorem and what it tells us about functions.
The Mean Value Theorem15:15
Students will state The Mean Value Theorem.
Test Your Knowledge0:06
Check how much you've learnt about Applications of Derivatives by trying these practice questions. Remember to check your work against the step by step solutions provided.

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 You

I 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 college
To 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 course
11 hours of instructional video

Whatever your reason this course will help you build key differentiation skills quickly.

What You'll Take Away From This Course

Calculus 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 differentiation
Core differentiation techniques - the Power, Product and Quotient rules
The Chain Rule which allows you to differentiate a wide range of functions
Advanced differentiation techniques and L'Hopital's rule
Applications of derivatives such as local extrema and optimisation

Who this course is for:

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

Calculus 1 - A Complete Course in Differential Calculus

What you'll learn

Explore related topics

Course content

Limits and Continuity17 lectures • 3hr 16min

The Derivative10 lectures • 2hr 1min

The Chain Rule & Advanced Techniques11 lectures • 2hr 16min

Applications of Derivatives14 lectures • 3hr 17min

Additional Resources3 lectures • 1min

Requirements

Description

Who this course is for: