Ace Calculus 2 in 13 Hours (The Complete Course)

To apply the methods of integral calculus to the study of functions and problem solving

4.25 (20 reviews)
Udemy
platform
English
language
Math
category
instructor
193
students
13 hours
content
Sep 2023
last update
$64.99
regular price

What you will 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

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!

- Gina :)

Content

Introduction

Overview
Welcome and How It Works
Tips to Maximize Your Learning

Riemann Sums

Downloadable Notes
Area Estimation
Example 2: Area Estimation of Sin Function
Example 3: Area Estimation Physical Context
Sigma Notation
Summation Rules and Formulas
Examples: Evaluate Summation
Limit of a Riemann Sum
Example 1: Evaluate Signed Area
Example 2: Evaluate Signed Area
Example 3: Evaluate Signed Area
Example 4: Evaluate Signed Area

Fundamental Theorem of Calculus (FTC)

Downloadable Notes
Fundamental Theorem of Calculus (Part II)
Basic Antiderivatives
Proof of FTC (Part II)
Properties of the Definite Integral
Examples: Evaluate Definite Integral
Fundamental Theorem of Calculus (Part I)
Proof of FTC (Part I)
Examples: FTC (Part I)

Antiderivatives

Downloadable Notes
Antiderivatives
Examples: Antiderivatives in Physics
Solving Non Basic Antiderivatives
Substitution Method
More Examples on u-Sub
Algebraic Method
Three "New" Basic Rules
Algebraic Method: Completion of Square
Long Division

Techniques of Integration

Downloadable Notes
Techniques of Integration
Integration by Parts (IBP)
Examples: IBP
Priority List for the Choice of f(x)
More Examples on IBP
Reduction Formula
IBP Involving Bounds
Integrating Trigonometric Powers
Case 1: Odd Powers of cos( )
Case 2: Odd Powers of sin( )
Case 3: Even Powers of sin( ) and cos( )
Case 4: Odd Powers of tan( ) with some sec( )
Case 5: Even Powers of sec( )
Case 6: Trig. Identity/Cheat/Guess
Trigonometric Substitution
Case 1: "a^2-x^2" form
Case 2: "a^2+x^2" form
Case 3: "x^2-a^2" form
Partial Fractions
Case 1: Distinct Linear Factors
Case 2: Repeated Linear Factor
Case 3: Quadratic (non reducible) Factors
More Examples on Partial Fractions
Recap of Integration Techniques

Applications of Integration

Downloadable Notes
Applications of Integration
Average Value of a Function
Mean Value Theorem for Integrals
Proof of the MVT
Revisited Examples: MVT
Examples: MVT
Area Between Curves
Examples: Area Between Curves
Example: Area Between Curves (Physics)
Antoinette's Theorem
Area Bounded by More Than 2 Curves
Horizontal Rectangle Representation
Examples: Horizontal Rectangle Representation
Volume of Rotation
Examples: Volume of Rotation
Washer Method Involving Horizontal Rectangles
The Shell Method
Examples: The Shell Method
Arc Length of a Curve
Examples 1-3: Arc Length
Examples 4-5: Arc Length

Improper Integrals

Downloadable Notes
Improper (Unbounded) Integrals
Infinite Bound
p-Integral
Examples: Infinite Bound
Improper due to Discontinuities
Discontinuity at the Bound
Discontinuity Within the Bounds

Differential Equations

Downloadable Notes
Differential Equation (DE)
Separable Differential Equations
Examples: Separable DE
Recap and More Examples: Separable DE

Sequences

Downloadable Notes
Introduction to Sequences
Examples: Sequences
Characteristics of Sequence
Monotonic Behavior
Examples: Monotonic Behavior
Boundedness
Bounded Monotonic Sequence Theorem
Examples: Limit of a Sequence
Relative Rates of Growth

Series

Downloadable Notes
Partial Sum of a Series
Infinite Series
Two Special Series
Geometric Series
Telescoping Series
Convergence Tests on Series
Nth Term Test for Divergence
Integral Test
p-Series
Example: Integral Test
Comparison Test
Examples: Limit Comparison Test
Ratio Test
Nth Root Test
Review on Convergence Tests

Conclusion

Thank You & Good Luck & Next Step

Screenshots

Ace Calculus 2 in 13 Hours (The Complete Course) - Screenshot_01Ace Calculus 2 in 13 Hours (The Complete Course) - Screenshot_02Ace Calculus 2 in 13 Hours (The Complete Course) - Screenshot_03Ace Calculus 2 in 13 Hours (The Complete Course) - Screenshot_04

Reviews

Nam
March 16, 2023
I suddenly understood the main concept of Integral Calculus of Area Estimation under the Curve, that had been confusing to me before. Very clear and concise.

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Related Topics

4000758
udemy ID
4/23/2021
course created date
7/11/2021
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