Calculus 2 – A Complete Course In Integral Calculus

Published 2/2023
MP4 | Video: h264, 1280×720 | Audio: AAC, 44.1 KHz
Language: English | Size: 27.84 GB | Duration: 21h 19m
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 KnowledgeSection 3: Application of IntegralsLecture 27 Finding the Area Under a CurveLecture 28 Finding the Area Between Two CurvesLecture 29 Volumes of RevolutionLecture 30 Volumes of Revolution Around the X-AxisLecture 31 Volumes of Revolution Around the Y-AxisLecture 32 Arc Length Using IntegrationLecture 33 Evaluating Arc Length Using IntegrationLecture 34 Test Your KnowledgeSection 4: Parametric FunctionsLecture 35 Parametric FunctionsLecture 36 Writing Parametric Functions in Cartesian FormLecture 37 Differentiating Parametric FunctionsLecture 38 Second Derivatives for Parametric FunctionsLecture 39 Curves of Parametric FunctionsLecture 40 Tangent Lines to Parametric CurvesLecture 41 The Area Under a Parametric CurveLecture 42 The Arc Length of a Parametric CurveLecture 43 Volumes of Revolution for Parametric CurvesLecture 44 Surface Area of Revolution for Parametric CurvesLecture 45 Test Your KnowledgeSection 5: Polar FunctionsLecture 46 Polar CoordinatesLecture 47 Switching Between Polar and Cartesian CoordinatesLecture 48 Graph Sketching for Polar CurvesLecture 49 Example of Graph Sketching for Polar CurvesLecture 50 Tangent Lines to Polar CurvesLecture 51 Example of a Tangent Line to a Polar CurveLecture 52 The Intersection of Polar CurvesLecture 53 The Area Bounded by a Polar CurveLecture 54 The Arc Length of a Polar CurveLecture 55 The Surface Area of Revolution of a Polar CurveLecture 56 Test Your KnowledgeSection 6: SequencesLecture 57 Starting Sequences & SeriesLecture 58 Determining the General Term of a SequenceLecture 59 The Convergence of a SequenceLecture 60 The Limit of a Convergent SequenceLecture 61 Types of SequenceLecture 62 Bounded SequencesLecture 63 Test Your KnowledgeSection 7: SeriesLecture 64 Partial Sums of an Infinite SeriesLecture 65 Sum of an Infinite Series Using Partial SumsLecture 66 Geometric Series Convergence TestLecture 67 The Sum of a Geometric SeriesLecture 68 Repeating Decimal ProblemsLecture 69 Telescoping SeriesLecture 70 The Sum of a Convergent Telescoping SeriesLecture 71 The Limit and Sum of an Infinite SeriesLecture 72 Common Series ResultsLecture 73 Example of a Telescoping SeriesLecture 74 Test Your KnowledgeSection 8: Series Convergence TestsLecture 75 The Integral Convergence TestLecture 76 The P-Series TestLecture 77 The Nth Term TestLecture 78 The Direct Comparison TestLecture 79 The Limit Comparison TestLecture 80 The Ratio TestLecture 81 The Root TestLecture 82 Alternating Series TestLecture 83 Alternating Series EstimatesLecture 84 Absolute and Conditional ConvergenceLecture 85 Test Your KnowledgeSection 9: Power SeriesLecture 86 Starting Power SeriesLecture 87 Power Series, Taylor Series and Maclaurin SeriesLecture 88 Interval and Radius of ConvergenceLecture 89 Multiplying Power SeriesLecture 90 Differentiating Power SeriesLecture 91 Evaluating Indefinite Integrals for Power SeriesLecture 92 Evaluating Definite Integrals for Power SeriesLecture 93 Starting Taylor SeriesLecture 94 The Radius and Interval of Convergence of a Taylor SeriesLecture 95 Example of The Radius and Interval of Convergence of a Taylor SeriesLecture 96 Starting Maclaurin SeriesLecture 97 Evaluating the Sum of a Maclaurin SeriesLecture 98 The Radius and Interval of Convergence of a Maclaurin SeriesLecture 99 Example of the Radius and Interval of Convergence of a Maclaurin SeriesLecture 100 Writing Indefinite Integrals as an Infinite SeriesLecture 101 Approximating Definite Integrals Using an Infinite SeriesLecture 102 Example of Approximating Definite Integrals Using an Infinite SeriesLecture 103 Test Your KnowledgeSection 10: Additional ResourcesLecture 104 Calculus 2 Formula ListLecture 105 Series Convergence TestsLecture 106 Trigonometry Formula ListLecture 107 Trigonometric Function GraphsStudents 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 2Homepage[code]https://www.udemy.com/course/calculus-2-complete/[/code]