Name: Calculus 2 - A Complete Course in Integral Calculus
Rating: 4.9 (34 reviews)

Udemy Business

Teach on Udemy

Turn what you know into an opportunity and reach millions around the world.

Learn More

Your cart is empty.

Keep shopping

Created byGary Thomson

Last updated 9/2024

English

What you'll learn

Integral Calculus
Key Integration Techniques
Advanced Integration Techniques
Applications of Integrals

Course content

10 sections • 107 lectures • 21h 12m total length

Antiderivatives7:42
Students will state what the anti-derivative of a function is and will give examples of antiderivatives.
Antiderivatives and Integration10:10
Students will describe the relationship between the antiderivative of a function and an integral.
Notation for Integration12:19
Students will learn and practice the notation used for integration.
The Power Rule14:39
Students will state the power rule for integration and practice using it on relevant functions.
Integratable Form10:40
Students will state forms of functions which are not differentiable, will change them to an integratable form and evaluate the integral.
Indefinite and Definite Integrals6:46
Students will describe the differences between indefinite and definite integrals.
Evaluating Definite Integrals13:33
Students will state what an definite integral is and practice evaluating definite integrals.
Riemann Sums9:52
Students will state what a Riemann Sum is in general terms and formulaically.
Integrals and Riemann Sums7:42
Students will evaluate definite integrals using Riemann Sums.
The Fundamental Theorem of Calculus13:01
Students will state and describe the two versions of The Fundamental Theorem of Calculus.
Test Your Knowledge0:06
Check how much you've learnt about Integrals by trying these practice questions. Remember to check your work against the step by step solutions provided.

Integration by U-Substitution18:09
Students will describe functions which can be integrated using a substitution method and will practice the technique.
The Reverse Chain Rule11:06
Students will confidently use the reverse chain rule to integrate composite functions.
Integration by Parts17:59
Integration by Parts for Definite Integrals14:49
Students will use the integration by parts technique to evaluate relevant definite integrals.
Integration using Partial Fractions19:03
Students will use partial fractions to change a function to an Integratable form.
Example of Integration Using Partial Fractions16:17
A typical example problem of evaluating an integral using partial fractions.
Integrating the Sine and Cosine Functions8:46
Students will confidently integrate the Sine and Cosine functions.
Integrating the Tangent Function7:49
Students will confidently integrate the Tangent function.
Improper Integrals4:56
Students will state what an improper integral is and give examples of improper integrals.
Example of an Improper Integral11:33
Typical example of an Improper Integral.
Evaluating Improper Integrals of the Form [a, infinity)11:33
Students will evaluate improper integrals of this form using a limit technique.
Evaluating Improper Integrals of the Form (- infinity, infinity)13:46
Students will evaluate improper integrals of this form using a limit technique.
Evaluating Improper Integrals - Discontinuous at ‘a’ or ‘b’10:47
Students will evaluate improper integrals of this form using a limit technique.
Improper Integrals – Discontinuous in the interval (a, b)14:50
Students will evaluate improper integrals of this form using a limit technique.
Test Your Knowledge0:06
Check how much you've learnt about Integration Techniques by trying these practice questions. Remember to check your work against the step by step solutions provided.

Finding the Area Under a Curve16:51
Students will use definite integrals to find the area between a curve and the co-ordinate axes.
Finding the Area Between Two Curves18:59
Students will form and evaluate definite integrals to find the area between two curves.
Volumes of Revolution9:53
Students will state what a volume of revolution is and how it relates to integration.
Volumes of Revolution Around the X-Axis11:57
Students will practice finding volumes of revolution around the X-Axis.
Volumes of Revolution Around the Y-Axis16:44
Students will practice finding volumes of revolution around the Y-Axis.
Arc Length Using Integration9:09
Students will state how integration can be used to find the length of an arc.
Evaluating Arc Length Using Integration19:56
Students will use integration to find the length of an arc.
Test Your Knowledge0:06
Check how much you've learnt about Applications of Integrals by trying these practice questions. Remember to check your work against the step by step solutions provided.

Parametric Functions10:14
Students will state what a parametric function is and give examples of functions defined parametrically.
Writing Parametric Functions in Cartesian Form15:38
Students will practice rewriting parametric functions in Cartesian form by eliminating the parameter.
Differentiating Parametric Functions13:26
Students will practice two methods for differentiating parametric functions.
Second Derivatives for Parametric Functions15:30
Students will practice taking second derivatives of parametric functions.
Curves of Parametric Functions15:52
Students will practice basic sketching of curves of parametric functions.
Tangent Lines to Parametric Curves17:46
Students will find the equation of tangent lines to curves of parametric functions.
The Area Under a Parametric Curve13:42
Students will find the area under the curve of a parametric function.
The Arc Length of a Parametric Curve13:13
Students will find the arc length of curves of a parametric function.
Volumes of Revolution for Parametric Curves13:33
Students will find volumes of revolution for curves of parametric functions.
Surface Area of Revolution for Parametric Curves11:50
Students will find surface areas of revolution for curves of parametric functions.
Test Your Knowledge0:06
Check how much you've learnt about Parametric Functions by trying these practice questions. Remember to check your work against the step by step solutions provided.

Polar Coordinates8:35
Students will describe polar co-ordinates.
Switching Between Polar and Cartesian Coordinates16:34
Students will practice converting polar coordinates to Cartesian coordinates and vice versa.
Graph Sketching for Polar Curves11:09
Students will practice sketching polar curves.
Example of Graph Sketching for Polar Curves21:29
A typical example of Graph Sketching for Polar Curves.
Tangent Lines to Polar Curves11:16
Students will find the equation of tangent lines to polar curves.
Example of a Tangent Line to a Polar Curve16:56
A typical example of a Tangent Line to a Polar Curve.
The Intersection of Polar Curves20:36
Students will find the coordinates of the point where polar curves intersect.
The Area Bounded by a Polar Curve14:43
Students will find the area inside a polar curve.
The Arc Length of a Polar Curve18:48
Students will find the arc length of a polar curve.
The Surface Area of Revolution of a Polar Curve16:07
Students will find the surface area of revolution of a polar curve.
Test Your Knowledge0:06
Check how much you've learnt about Polar Functions by trying these practice questions. Remember to check your work against the step by step solutions provided.

Starting Sequences & Series9:48
Students will describe what a sequence is and how series are constructed from sequences.
Determining the General Term of a Sequence12:30
Students will determine a formula for the Nth term of a sequence.
The Convergence of a Sequence10:23
Students will describe what it means for a sequence to be convergent.
The Limit of a Convergent Sequence11:53
Students will describe what the limit of a sequence is and practice finding the limit of a convergent sequence.
Types of Sequence14:43
Students will describe increasing, decreasing, monotonic and alternating sequences.
Bounded Sequences15:08
Students will describe what a bounded a sequence is and give examples.
Test Your Knowledge0:06
Check how much you've learnt about Sequences by trying these practice questions. Remember to check your work against the step by step solutions provided.

Partial Sums of an Infinite Series11:51
Students will describe what the partial sums of an infinite series are and will calculate partial sums.
Sum of an Infinite Series Using Partial Sums22:26
Students will find the sum of an infinite series using the limit of a series of partial sums.
Geometric Series Convergence Test16:15
Students will check convergence of a geometric series with a simple test.
The Sum of a Geometric Series16:12
Students will practice finding the sum of a geometric series.
Repeating Decimal Problems7:52
Students will practice representing recurring decimals as geometric series and calculating their sum.
Telescoping Series14:17
Students will describe what a telescoping series is and give examples of these types of series.
The Sum of a Convergent Telescoping Series11:34
Students will evaluate the sum of a convergent telescoping series using limits.
The Limit and Sum of an Infinite Series9:28
Students will describe the limit of an infinite series and contrast it with the sum of the same series.
Common Series Results12:50
Students will state results associated with several common series which are important to know for use in other techniques.
Example of a Telescoping Series12:00
A typical example of a Telescoping Series.
Test Your Knowledge0:06
Check how much you've learnt about Series by trying these practice questions. Remember to check your work against the step by step solutions provided.

The Integral Convergence Test17:56
Students will describe what the integral convergence test is and practice using it for various series.
The P-Series Test12:45
Students will describe what a P-Series is and a quick test for whether the series converges or diverges.
The Nth Term Test16:19
Students will describe how to use the Nth term divergence test and practice using the test on various infinite series.
The Direct Comparison Test14:19
Students will describe how the direct comparison test for infinite series work and practice using the test for various series.
The Limit Comparison Test15:44
Students will describe the limit comparison test and practice using it with various series.
The Ratio Test17:49
Students will describe the ratio test and practice using it with various series.
The Root Test17:20
Students will describe the root test and practice using it with various series.
Alternating Series Test20:20
Students will describe what the alternating series test is and practice using the test on various infinite series.
Alternating Series Estimates12:30
Students will estimate the sum of an infinite series by creating upper and lower bounds using partial sums and remainders.
Absolute and Conditional Convergence17:19
Students will describe what it means for a series to converge conditionally and absolutely, and will practice using conditional and absolute convergence.
Test Your Knowledge0:06
Check how much you've learnt about Series Convergence Tests by trying these practice questions. Remember to check your work against the step by step solutions provided.

Starting Power Series16:34
Students will describe what a power series is and, in general terms, what it can be used for.
Power Series, Taylor Series and Maclaurin Series11:09
Students will describe how power series, Taylor series and Maclaurin Series relate.
Interval and Radius of Convergence21:29
Students will describe what the interval and radius of convergence of a power series is and will state examples for a given function.
Multiplying Power Series11:16
Students will practice multiplying power series.
Differentiating Power Series7:43
Students will practice two techniques for differentiating power series.
Evaluating Indefinite Integrals for Power Series10:52
Students will practice integrating power series.
Evaluating Definite Integrals for Power Series10:34
Students will practice evaluating definite integrals of Power Series.
Starting Taylor Series13:52
Students will describe how to represent a function as a Taylor Series and practice writing the Taylor Series for common functions.
The Radius and Interval of Convergence of a Taylor Series8:32
Students will practice finding the radius and interval of convergence of a Taylor Series.
Example of The Radius and Interval of Convergence of a Taylor Series20:11
A typical example of the Radius and Interval of Convergence of a Taylor Series.
Starting Maclaurin Series16:59
Students will describe how to represent a function as a Maclaurin Series and practice writing the Maclaurin Series for common functions.
Evaluating the Sum of a Maclaurin Series8:32
Students will determine the sum of Maclaurin series by comparison with well-known Maclaurin series.
The Radius and Interval of Convergence of a Maclaurin Series8:32
Students will practice finding the radius and interval of convergence of a Maclaurin Series.
Example of the Radius and Interval of Convergence of a Maclaurin Series13:13
Typical examples of the Radius and Interval of Convergence of a Maclaurin Series
Writing Indefinite Integrals as an Infinite Series8:31
Students will practice evaluating indefinite integrals by writing them as an infinite series using common Maclaurin series results.
Approximating Definite Integrals Using an Infinite Series10:42
Students will practice evaluating definite integrals by writing them as an infinite series using common Maclaurin series results.
Example of Approximating Definite Integrals Using an Infinite Series13:20
A typical example of approximating a definite integral using an infinite series.
Test Your Knowledge0:06
Check how much you've learnt about Power Series by trying these practice questions. Remember to check your work against the step by step solutions provided.

Requirements

Differentiation, ideally having completed Calculus 1
Algebra, Trigonometry and knowledge of Mathematical functions

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. We start the Calculus 2 course with some key concepts before moving onto core and advanced integration techniques and applications. We then turn our attention to parametric & polar functions, and sequences & series.

This Course is For You

I created this course to help you master integral Calculus through clear instructional videos and relevant practice questions.

There are many reasons why you might want to take this course:

To learn Calculus 2 from scratch
For additional support if you're taking Calculus 2 in school or college
To help you prep for a Calculus 2 assessment
To review key Integration techniques
To access more than 300 relevant practice questions with full solutions
As prep for taking further Math, engineering or other courses
21 hours of instructional video!

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

What You'll Take Away From This Course

Calculus 2 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 integration - antiderivatives and Riemann sums
Core integration techniques - the Power Rule, Chain Rule and Trigonometric rules
Integration by Parts which extends the functions you can integrate
Advanced differentiation techniques such as improper integrals
Applications of derivatives such as finding areas under curves and volumes of revolution
Parametric and polar function and common applications
Sequences, series, and series convergence tests
Power series such as Taylor Series and Maclaurin Series

Who this course is for:

Students who need to learn Calculus 2
Students who need to learn Integration
Students reviewing key Integration techniques for a test or assignment
Students looking for Calculus 2 practice questions with full step-by-step solutions
Students who want clear instruction on all aspects of Calculus 2

What you'll learn

Explore related topics

Course content

Integrals11 lectures • 1hr 47min

Integration Techniques15 lectures • 3hr 1min

Application of Integrals8 lectures • 1hr 44min

Parametric Functions11 lectures • 2hr 21min

Polar Functions11 lectures • 2hr 36min

Sequences7 lectures • 1hr 15min

Series11 lectures • 2hr 15min

Series Convergence Tests11 lectures • 2hr 42min

Power Series18 lectures • 3hr 32min

Additional Resources4 lectures • 1min

Requirements

Description

Who this course is for: