Calculus I (Limits, Derivative, Integrals) **Full Course**
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Course content
1 modules • 61 lessons • 7.3 hours of video
Calculus I (Limits, Derivative, Integrals) **Full Course**
61 lessons
• 7.3 hours
Calculus I (Limits, Derivative, Integrals) **Full Course**
61 lessons
• 7.3 hours
- The Velocity Problem | Part I: Numerically 07:52
- The Velocity Problem | Part II: Graphically 07:14
- A Tale of Three Functions | Intro to Limits Part I 04:16
- A Tale of Three Functions | Intro to Limits Part II 08:05
- What is an infinite limit? 04:26
- Limit Laws | Breaking Up Complicated Limits Into Simpler Ones 06:16
- Building up to computing limits of rational functions 03:36
- Limits of Oscillating Functions and the Squeeze Theorem 06:59
- Top 4 Algebraic Tricks for Computing Limits 07:10
- A Limit Example Combining Multiple Algebraic Tricks 07:23
- Limits are simple for continuous functions 07:21
- Were you ever exactly 3 feet tall? The Intermediate Value Theorem 04:00
- Example: When is a Piecewise Function Continuous? 03:18
- Limits "at" infinity 06:36
- Computing Limits at Infinity for Rational Functions 07:08
- Infinite Limit vs Limits at Infinity of a Composite Function 09:50
- The most important limit in Calculus // Geometric Proof & Applications 11:54
- Definition of the Derivative | Part I 06:01
- Applying the Definition of the Derivative to 1/x 05:46
- Definition of Derivative Example: f(x) = x + 1/(x+1) 06:37
- The derivative of a constant and of x^2 from the definition 05:20
- Derivative Rules: Power Rule, Additivity, and Scalar Multiplication 07:26
- How to Find the Equation of a Tangent Line 05:15
- The derivative of e^x. 02:10
- The product and quotient rules 05:43
- The derivative of Trigonometric Functions 05:39
- Chain Rule: the Derivative of a Composition 05:28
- Interpreting the Chain Rule Graphically 05:14
- The Chain Rule using Leibniz notation 05:37
- Implicit Differentiation | Differentiation when you only have an equation, not an explicit function 07:09
- Derivative of Inverse Trig Functions via Implicit Differentiation 04:42
- The Derivative of ln(x) via Implicit Differentiation 04:59
- Logarithmic Differentiation | Example: x^sinx 03:37
- Intro to Related Rates 06:35
- Linear Approximations | Using Tangent Lines to Approximate Functions 09:49
- The MEAN Value Theorem is Actually Very Nice 07:37
- Relative and Absolute Maximums and Minimums | Part I 04:38
- Relative and Absolute Maximums and Minimums | Part II 07:23
- Using L'Hopital's Rule to show that exponentials dominate polynomials 09:25
- Applying L'Hopital's Rule to Exponential Indeterminate Forms 07:59
- Ex: Optimizing the Volume of a Box With Fixed Surface Area 11:36
- Folding a wire into the largest rectangle | Optimization example 06:59
- Optimization Example: Minimizing Surface Area Given a Fixed Volume 09:37
- Tips for Success in Flipped Classrooms + OMG BABY!!! 08:34
- What's an anti-derivative? 06:07
- Solving for the constant in the general anti-derivative 04:11
- The Definite Integral Part I: Approximating Areas with rectangles 05:38
- The Definite Integral Part II: Using Summation Notation to Define the Definite Integral 09:17
- The Definite Integral Part III: Evaluating From The Definition 06:55
- "Reverse" Riemann Sums | Finding the Definite Integral Given a Sum 10:13
- Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example 11:04
- Fundamental Theorem of Calculus II 05:03
- Intro to Substitution - Undoing the Chain Rule 06:35
- Adjusting the Constant in Integration by Substitution 03:23
- Substitution Method for Definite Integrals **careful!** 04:51
- Back Substitution - When a u-sub doesn't match cleanly! 08:27
- Average Value of a Continuous Function on an Interval 08:03
- Exam Walkthrough | Calc 1, Test 3 | Integration, FTC I/II, Optimization, u-subs, Graphing 34:29
- ♥♥♥ Thank you Calc Students♥♥♥ Some final thoughts. 04:05
- CALCULUS SPEEDRUN || Limits || Episode 1 12:42
- 5 counterexamples every calculus student should know 15:51
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