Ace Calculus 2 In 13 Hours (the Complete Course)
 

| Duration: 13h 7m
To apply the methods of integral calculus to the study of functions and problem solving
What you'll learn
Study the definite integral
Determine the antiderivative (indefinite integral) of a function
Solve problems involving applications of the definite integral
Apply the methods of integration to problems on rectilinear motion and exponential and logistic growth
Evaluate improper integrals
Begin the study of infinite sequences and series
Requirements
Precalculus (algebra, trigonometry, and functions)
Calculus 1 (limits, continuity, derivatives, and their applications)
Description
HOW THIS COURSE WORK
This course, Ace Calculus 2 in 13 Hours (The Complete Course), has everything you need to know for Calculus 2, including video and notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and derivations of rules and theorems. The course is organized into the following sections
Riemann Sums
Fundamental Theorem of Calculus
Antiderivatives
Techniques of Integration
Applications of Integration
Improper Integrals
Differential Equations
Sequences
Series
CONTENT YOU WILL GET INSIDE EACH SECTION
Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.
Notes: In this section, you will find my notes that I wrote during lecture. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).
Extra notes: I provide some extra notes, including formula sheets and some other useful study guidance.
Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.
THINGS THAT ARE INCLUDED IN THE COURSE
An instructor who truly cares about your success
Lifetime access to Ace Calculus 2 in 13 Hours (The Complete Course)
Friendly support in the Q&A section
Udemy Certificate of Completion available for download
BONUS #1: Downloadable lectures so you can watch whenever and wherever you are.
BONUS #2: Downloadable lecture notes and some extra notes so you can review the lectures without having a device to watch/listen to the recordings.
BONUS #3: 9 assignments with solutions (one assignment per section) to make you productive while taking the course.
BONUS #4: Step-by-step guide to help you solve problems.
See you inside the course!
Overview
Section 1: Introduction
Lecture 1 Overview
Lecture 2 Welcome and How It Works
Lecture 3 Tips to Maximize Your Learning
Section 2: Riemann Sums
Lecture 4 Downloadable Notes
Lecture 5 Area Estimation
Lecture 6 Example 2: Area Estimation of Sine Function
Lecture 7 Example 3: Area Estimation Physical Context
Lecture 8 Sigma Notation
Lecture 9 Summation Rules and Formulas
Lecture 10 Examples: Evaluate Summation
Lecture 11 Limit of a Riemann Sum
Lecture 12 Example 1: Evaluate Signed Area
Lecture 13 Example 2: Evaluate Signed Area
Lecture 14 Example 3: Evaluate Signed Area
Lecture 15 Example 4: Evaluate Signed Area
Section 3: Fundamental Theorem of Calculus (FTC)
Lecture 16 Downloadable Notes
Lecture 17 Fundamental Theorem of Calculus (Part II)
Lecture 18 Basic Antiderivatives
Lecture 19 Proof of FTC (Part II)
Lecture 20 Properties of the Definite Integral
Lecture 21 Examples: Evaluate Definite Integral
Lecture 22 Fundamental Theorem of Calculus (Part I)
Lecture 23 Proof of FTC (Part I)
Lecture 24 Examples: FTC (Part I)
Section 4: Antiderivatives
Lecture 25 Downloadable Notes
Lecture 26 Antiderivatives
Lecture 27 Examples: Antiderivatives in Physics
Lecture 28 Solving Non Basic Antiderivatives
Lecture 29 Substitution Method
Lecture 30 More Examples of u-Sub
Lecture 31 Algebraic Method
Lecture 32 Three "New" Basic Rules
Lecture 33 Algebraic Method: Completion of Square
Lecture 34 Long Division
Section 5: Techniques of Integration
Lecture 35 Downloadable Notes
Lecture 36 Techniques of Integration
Lecture 37 Integration by Parts (IBP)
Lecture 38 Examples: IBP
Lecture 39 Priority List for the Choice of f(x)
Lecture 40 More Examples of IBP
Lecture 41 Reduction Formula
Lecture 42 IBP Involving Bounds
Lecture 43 Integrating Trigonometric Powers
Lecture 44 Case 1: Odd Powers of cos( )
Lecture 45 Case 2: Odd Powers of sin( )
Lecture 46 Case 3: Even Powers of sin( ) and cos( )
Lecture 47 Case 4: Odd Powers of tan( ) with some sec( )
Lecture 48 Case 5: Even Powers of sec( )
Lecture 49 Case 6: Trig. Identity/Cheat/Guess
Lecture 50 Trigonometric Substitution
Lecture 51 Case 1: "a^2-x^2" form
Lecture 52 Case 2: "a^2+x^2" form
Lecture 53 Case 3: "x^2-a^2" form
Lecture 54 Partial Fractions
Lecture 55 Case 1: Distinct Linear Factors
Lecture 56 Case 2: Repeated Linear Factor
Lecture 57 Case 3: Quadratic (non reducible) Factors
Lecture 58 More Examples on Partial Fractions
Lecture 59 Recap of Integration Techniques
Section 6: Applications of Integration
Lecture 60 Downloadable Notes
Lecture 61 Applications of Integration
Lecture 62 Average Value of a Function
Lecture 63 Mean Value Theorem for Integrals
Lecture 64 Proof of the MVT
Lecture 65 Revisited Examples: MVT
Lecture 66 Examples: MVT
Lecture 67 Area Between Curves
Lecture 68 Examples: Area Between Curves
Lecture 69 Example: Area Between Curves (Physics)
Lecture 70 Antoinette's Theorem
Lecture 71 Area Bounded by More Than 2 Curves
Lecture 72 Horizontal Rectangle Representation
Lecture 73 Examples: Horizontal Rectangle Representation
Lecture 74 Volume of Rotation
Lecture 75 Examples: Volume of Rotation
Lecture 76 Washer Method Involving Horizontal Rectangles
Lecture 77 The Shell Method
Lecture 78 Examples: The Shell Method
Lecture 79 Arc Length of a Curve
Lecture 80 Examples 1-3: Arc Length
Lecture 81 Examples 4-5: Arc Length
Section 7: Improper Integrals
Lecture 82 Downloadable Notes
Lecture 83 Improper (Unbounded) Integrals
Lecture 84 Infinite Bound
Lecture 85 p-Integral
Lecture 86 Examples: Infinite Bound
Lecture 87 Improper due to Discontinuities
Lecture 88 Discontinuity at the Bound
Lecture 89 Discontinuity Within the Bounds
Section 8: Differential Equations
Lecture 90 Downloadable Notes
Lecture 91 Differential Equation (DE)
Lecture 92 Separable Differential Equations
Lecture 93 Examples: Separable DE
Lecture 94 Recap and More Examples: Separable DE
Section 9: Sequences
Lecture 95 Downloadable Notes
Lecture 96 Introduction to Sequences
Lecture 97 Examples: Sequences
Lecture 98 Characteristics of Sequence
Lecture 99 Monotonic Behavior
Lecture 100 Examples: Monotonic Behavior
Lecture 101 Boundedness
Lecture 102 Bounded Monotonic Sequence Theorem
Lecture 103 Examples: Limit of a Sequence
Lecture 104 Relative Rates of Growth
Section 10: Series
Lecture 105 Downloadable Notes
Lecture 106 Partial Sum of a Series
Lecture 107 Infinite Series
Lecture 108 Two Special Series
Lecture 109 Geometric Series
Lecture 110 Telescoping Series
Lecture 111 Convergence Tests on Series
Lecture 112 Nth Term Test for Divergence
Lecture 113 Integral Test
Lecture 114 p-Series
Lecture 115 Example: Integral Test
Lecture 116 Comparison Test
Lecture 117 Examples: Limit Comparison Test
Lecture 118 Ratio Test
Lecture 119 Nth Root Test
Lecture 120 Review on Convergence Tests
Section 11: Conclusion
Lecture 121 Thank You & Good Luck & Next Step
Lecture 122 BONUS: Let's Keep Learning!