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


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