Calculus 2 - A Complete Course In Integral Calculus

Master the theory, practice and applications of integrals!

What you'll learn

Integral Calculus

Key Integration Techniques

Advanced Integration Techniques

Applications of Integrals

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 YouI 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 collegeTo 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 courses21 hours of instructional video!Whatever your reason this course will help you build key skills quickly. What You'll Take Away From This CourseCalculus 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 sumsCore integration techniques - the Power Rule, Chain Rule and Trigonometric rules Integration by Parts which extends the functions you can integrateAdvanced differentiation techniques such as improper integralsApplications of derivatives such as finding areas under curves and volumes of revolutionParametric and polar function and common applicationsSequences, series, and series convergence tests Power series such as Taylor Series and Maclaurin Series

Overview

Section 1: Integrals

Lecture 1 Antiderivatives

Lecture 2 Antiderivatives and Integration

Lecture 3 Notation for Integration

Lecture 4 The Power Rule

Lecture 5 Integratable Form

Lecture 6 Indefinite and Definite Integrals

Lecture 7 Evaluating Definite Integrals

Lecture 8 Riemann Sums

Lecture 9 Integrals and Riemann Sums

Lecture 10 The Fundamental Theorem of Calculus

Lecture 11 Test Your Knowledge

Section 2: Integration Techniques

Lecture 12 Integration by U-Substitution

Lecture 13 The Reverse Chain Rule

Lecture 14 Integration by Parts

Lecture 15 Integration by Parts for Definite Integrals

Lecture 16 Integration using Partial Fractions

Lecture 17 Example of Integration Using Partial Fractions

Lecture 18 Integrating the Sine and Cosine Functions

Lecture 19 Integrating the Tangent Function

Lecture 20 Improper Integrals

Lecture 21 Example of an Improper Integral

Lecture 22 Evaluating Improper Integrals of the Form [a, infinity)

Lecture 23 Evaluating Improper Integrals of the Form (- infinity, infinity)

Lecture 24 Evaluating Improper Integrals - Discontinuous at ‘a’ or ‘b’

Lecture 25 Improper Integrals – Discontinuous in the interval (a, b)

Lecture 26 Test Your Knowledge

Section 3: Application of Integrals

Lecture 27 Finding the Area Under a Curve

Lecture 28 Finding the Area Between Two Curves

Lecture 29 Volumes of Revolution

Lecture 30 Volumes of Revolution Around the X-Axis

Lecture 31 Volumes of Revolution Around the Y-Axis

Lecture 32 Arc Length Using Integration

Lecture 33 Evaluating Arc Length Using Integration

Lecture 34 Test Your Knowledge

Section 4: Parametric Functions

Lecture 35 Parametric Functions

Lecture 36 Writing Parametric Functions in Cartesian Form

Lecture 37 Differentiating Parametric Functions

Lecture 38 Second Derivatives for Parametric Functions

Lecture 39 Curves of Parametric Functions

Lecture 40 Tangent Lines to Parametric Curves

Lecture 41 The Area Under a Parametric Curve

Lecture 42 The Arc Length of a Parametric Curve

Lecture 43 Volumes of Revolution for Parametric Curves

Lecture 44 Surface Area of Revolution for Parametric Curves

Lecture 45 Test Your Knowledge

Section 5: Polar Functions

Lecture 46 Polar Coordinates

Lecture 47 Switching Between Polar and Cartesian Coordinates

Lecture 48 Graph Sketching for Polar Curves

Lecture 49 Example of Graph Sketching for Polar Curves

Lecture 50 Tangent Lines to Polar Curves

Lecture 51 Example of a Tangent Line to a Polar Curve

Lecture 52 The Intersection of Polar Curves

Lecture 53 The Area Bounded by a Polar Curve

Lecture 54 The Arc Length of a Polar Curve

Lecture 55 The Surface Area of Revolution of a Polar Curve

Lecture 56 Test Your Knowledge

Section 6: Sequences

Lecture 57 Starting Sequences & Series

Lecture 58 Determining the General Term of a Sequence

Lecture 59 The Convergence of a Sequence

Lecture 60 The Limit of a Convergent Sequence

Lecture 61 Types of Sequence

Lecture 62 Bounded Sequences

Lecture 63 Test Your Knowledge

Section 7: Series

Lecture 64 Partial Sums of an Infinite Series

Lecture 65 Sum of an Infinite Series Using Partial Sums

Lecture 66 Geometric Series Convergence Test

Lecture 67 The Sum of a Geometric Series

Lecture 68 Repeating Decimal Problems

Lecture 69 Telescoping Series

Lecture 70 The Sum of a Convergent Telescoping Series

Lecture 71 The Limit and Sum of an Infinite Series

Lecture 72 Common Series Results

Lecture 73 Example of a Telescoping Series

Lecture 74 Test Your Knowledge

Section 8: Series Convergence Tests

Lecture 75 The Integral Convergence Test

Lecture 76 The P-Series Test

Lecture 77 The Nth Term Test

Lecture 78 The Direct Comparison Test

Lecture 79 The Limit Comparison Test

Lecture 80 The Ratio Test

Lecture 81 The Root Test

Lecture 82 Alternating Series Test

Lecture 83 Alternating Series Estimates

Lecture 84 Absolute and Conditional Convergence

Lecture 85 Test Your Knowledge

Section 9: Power Series

Lecture 86 Starting Power Series

Lecture 87 Power Series, Taylor Series and Maclaurin Series

Lecture 88 Interval and Radius of Convergence

Lecture 89 Multiplying Power Series

Lecture 90 Differentiating Power Series

Lecture 91 Evaluating Indefinite Integrals for Power Series

Lecture 92 Evaluating Definite Integrals for Power Series

Lecture 93 Starting Taylor Series

Lecture 94 The Radius and Interval of Convergence of a Taylor Series

Lecture 95 Example of The Radius and Interval of Convergence of a Taylor Series

Lecture 96 Starting Maclaurin Series

Lecture 97 Evaluating the Sum of a Maclaurin Series

Lecture 98 The Radius and Interval of Convergence of a Maclaurin Series

Lecture 99 Example of the Radius and Interval of Convergence of a Maclaurin Series

Lecture 100 Writing Indefinite Integrals as an Infinite Series

Lecture 101 Approximating Definite Integrals Using an Infinite Series

Lecture 102 Example of Approximating Definite Integrals Using an Infinite Series

Lecture 103 Test Your Knowledge

Section 10: Additional Resources

Lecture 104 Calculus 2 Formula List

Lecture 105 Series Convergence Tests

Lecture 106 Trigonometry Formula List

Lecture 107 Trigonometric Function Graphs

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