Intro To Calculus 1

Name: Intro To Calculus 1
Rating: 4.4 (5 reviews)

Calculus 1

Created byLonzo Fulwider

Last updated 4/2026

English

What you'll learn

Learn all the different techniques for finding limits including: 4 types of discontinuities, limits at infinity, limits with radicals, trig limits, l'hopital
Learn all different techniques for finding derivatives including: power rule, product rule, quotient, chain rule, logarithmic, rolles theorem, mean value thm
Applying derivatives in real world such as max and min problems, related rates problem, and extremas
Finally introduce the basics of what a limit is? Including u-substitution, definite, and indefinite integrals
Learn Riemann Sum
Learn Sigma Notation
Learn Integral Of Exponential Function
Learn Trig Integrals
Learn Fundamental Theorem Of Calculus
Learn Separable Differential Equations
Learn Integrating powers of sines, cosines, tangents, and secants
Learn integration by parts
Learn tabular method
Learn integration by parts with LIATE

Course content

5 sections • 115 lectures • 39h 36m total length

Deriving Using Definition Of Derivative23:06
Quiz On Deriving Using Definition Of Derivative9:05
Deriving Using Power Rule15:25
Quiz On Deriving Using Power Rule4:17
Deriving Using Product Rule14:30
Quiz On Product Rule6:46
Deriving Using Quotient Rule19:47
Quiz On Quotient Rule8:11
Deriving Using Chain Rule23:21
Part 2 Of Deriving Using Chain Rule10:53
Quiz On Chain Rule6:04
Implicit Differentiation10:33
Implicit Differentiation Part 215:47
Quiz On Implicit Differentiation5:14
Implicit Differentiation Twice17:57
Part 2 Of Implicit Differentiation Twice5:21
Quiz On Implicit Differentiation Twice3:35
Deriving Using Logarithmic Differentiation15:47
Part 2 Of Logarithmic Differentiation9:22
Quiz On Logarithmic Differention7:04
Deriving Of Natural Exponential Function9:40
Part 2 Of Deriving Of Natural Exponential Function11:56
Quiz On Deriving Of Natural Exponetial Function8:43
Derivative Of Natural Logarithmic Function8:43
Part 2 Of Deriving Of Natural Logarithmic Function6:23
Quiz On Natural Logarithmic Function4:33
Implicit Differentiation30:31
In this section I will derive implicitly. I will find the slope of the tangent line of a graph, then I will find the tangent line when given the explcit formula and a given point. Finally, I will find the second derivative implicitly.
Deriving Chain Rule29:28
In this section, I will derive using chain rule and product rule.
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Derivative Practice Problems Part 425:03
This is part 4 of derivative practice problems.
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Derivative Practice Problems Part 324:27
This is part 3 of derivative practice problems.
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Derivative Practice Problems Part 235:39
This is part 2 of derivative practice problems
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Derivative practice problems part 132:54
This is part 1 of practice problems involving derivatives.
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Increasing and decreasing using first derivative.20:44
In this section, I will determine where a function increase or decrease using first derivative.
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Concavity and point of inflection using second derivative28:57
In this section, I will determine where the graph is concave up or concave down and point of inflection using second derivative.
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Extremas15:42
In this section, I will go over the difference between a relative extrema( local min, and local max), and absolute extrema(absolute max and absolute min). Then I will show you how to find them.
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More on derivative of logarithmic functions.14:10
In this section, I will do few more problems involving logarithmic functions, chain rule and power rule
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Rolle's Theorem25:43
In this section, I will go over rolle's theorem, and determine the c-value if rolle's theorem can actually be applied.
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Mean-Value Theorem15:24
In this section, I will apply and demonstrate the mean-value theorem.
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Logarithmic Differentiation25:18
In this section, I will derive using logarithmic differentiation
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Derivatives Using Charts24:57
In this video, I will explain how to find derivative when only given table, charts or a graph.
Ex) 2: Finding Derivatives Using Charts12:11
In this video, I will do example 2 of finding derivatives using charts.
Ex) 3: Finding Derivatives Using A Graph6:14
In this video, I will do example 3 of finding derivatives using a graph.
Equation Of Tangent Line17:53
In this video, I will introduce the equation of tangent line, and go over all the steps of finding equation of tangent line.
Part 2 Of Finding Equation Tangent And Normal To The Curve27:28
This is part 2 of writing equation of the line tangent and normal to the curve.
Quiz On Finding Equation Tangent And Normal To The Curve6:11
In this video, I will do a quiz of finding the equation of tangent and normal to the curve.
Test Your Knowledge On Derivatives Part 136:04
Test Your Knowledge On Derivatives Part 241:11

Average Rate Of Change16:52
In this video, I will introduce average rate of change, and explain how to find average rate of change when given pieces of information.
Intro To Demand Function10:15
In this video, I will introduce the demand function and go over the formulas that is related to the demand function.
Ex)2 Demand Function14:14
In this video, I will do example 2 of demand function.
Ex)3 Demand Function7:31
In this video, I will do example 3 of demand function.
Ex) 4 Demand Function6:16
In this video, I will do example 4 of demand function.
Ex) 5 Demand Function6:17
In this video, I will do example 5 of demand function.
Ex) 6 Demand Function9:58
In this video, I will do example 6 of demand function word problem.
In this video, I will do example 6 of demand function word problem.9:58
Ex) 7 Demand Function10:29
In this video, I will do example 7 demand function word problem.
Ex) 8 Demand Function12:38
In this video, I will do example 8 of demand function word problem.
Ex) 9 Demand Function5:51
In this video, I will do example 9 of demand function word problem.
Intro To Related Rate Word Problems32:57
In this video, I will introduce related rates word problems, and all the step to solve related rates problems. I will do three examples of related rates word problems.
Ex)4 Related Rate Word Problem15:51
In this video, I will do example 4 of related rate word problem.
Ex)5 Related Rate Word Problem17:45
In this video, I will do example 5 of related rate word problem.
Ex) 6 Related Rate Word Problem11:59
In this video, I will do example 6 of related rate word problem.
Ex)7 Related Rate Word Problem12:45
In this video, I will do example 7 of related rate word problem.
Ex)8 Related Rate Word Problem13:57
In this video, I will do example 8 of related rate word problem.
Quiz On Related Rate Word Problem15:58
In this video, I will do a quiz on related rate word problem.
Intro To Optimization In Calculus13:15
In this video, I will introduce how to solve optimization word problems in calculus 1. I will go over all the steps for solving optimization problems.
Ex) 2 Optimization Word Problem9:12
In this video, I will do an optimization word problems involving fencing.
Ex) 3 Optimization Word Problem12:35
In this video, I will do an optimization word problem involving an open box.
Ex) 4 Optimization Word Problem10:45
In this video, I will do example 4 optimization word problem.
Ex) 5 Optimization Word Problem10:01
In this video, I will do example 5 of optimization word problem involving two adjacent rectangular corrals.
Ex)6 Optimization Word Problem13:04
In this video, I will do example 6 of optimization word problem involving rectangular page.
Quiz On Optimization Word Problem12:52
In this video, I will do a quiz on optimization word problem.

What is a limit?4:02
In this course, I will go over all the different techniques and the proper graphing for finding a limit for certain functions.
Does The Limit Exist?20:27
In this video, I will go over 3 step continuity test and determine if the limit exist and if it continuous at a certain x-value.
Intro To Limits34:28
In this video, I will briefly go over some common techniques for finding limits. I will introduce one sided limits, limits at infinity, conjugate method, and l'hopital rule.
Continuity and Limits9:21
In this video, I will explain and show how to tell if a function is continuous by using the definition of continuity.
4 types of discontinuities10:04
In this section, I will go over the four main types of discontinuity.
Limit At Infinity56:58
Limits at infinity and with radicals27:02
In this section, I will go over the rules for finding the limit to positive and negative infinity. I will also go over limits involving radicals.
Trig Limits35:07
In this section, I will go over some basic limits involving trig, and I will go over special trig limits.
Basic Limit Problems28:07
In this section, I will do some common limit problems
L'hopital Rule13:50
In this section, I will go over l'hopital rule and how to apply the rule.
Limit Practice Problems Part 131:27
This is part 1 of limit practice problems.

Riemann Sum Part 130:29
In this video, I will introduce the Riemann Sum which is basically estimating the area under a curve by making small rectangles finding the area of each rectangles and then adding them up. I'll go over the different techniques of estimating area under the curve such as: right, left, midpoint, and trapezoidal method of riemann sum.
Part 2 Of Riemann Sum40:45
This is part 2 of riemann sum.
Part 3 Of Riemann Sum50:47
This is part 3 of riemann sum.
Sigma Notation1:09:03
In this video, I will introduce sigma notation and limits of finite sums which is basically the formal definition of a Riemann Sum and definite integral. In this video, you will solve limit problems by taking a function and express it as the limit of a sequence of Riemann Sums over an interval.
Integration Rules39:56
In this video, I will go over some common integration rules, and go over the difference between definite and indefinite integral.
Integral Of Exponential Function44:12
In this video, I will go over the common derivative rules of an exponential function. I will do examples both bounded and unbounded integral.
Trig Integrals43:55
In this video, I will go over some common basic integration rules both indefinite and definite integrals. We will review trigonometric identities such as pythagorean identities to simplify integrals.
Fundamental Theorem Of Calculus1:06:40
In this video, I will go over fundamental theorem of calculus part 1 and part 2. I will also review integration rules and properties.
Separable Differential Equations42:51
In this video, I will go over how to solve first- order differential equations when given initial value. I will go over the steps for solving a separable equation, and solve for the general solution when given an initial constraint.
More Difficult Separable Differential Equations46:20
In this video, I will do three examples of more difficult separable differential equations.
Separable Differential Equation Example With Application In Geometry5:08
In this video, I will solve a separable differential equation involving application in geometry.
Quiz On Separable Differential Equation6:16
In this video, I will do a quiz on separable differential equation.
Integrals and Indefinite Integration21:54
In this section, I will introduce what is an integral and indefinite integral. Also I will explain how you can get f''(x), f'(x) to regular f(x) with the help of integrals.
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Integration by u-substitution28:00
In this section, I will integrate using u-substitution. I will use change of variables to evaluate a definite integral, and evaluate a definite integral involving an even or odd function.
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U-Substitution (Medium-Hard Examples)29:05
In this video, I will integrate using u substitution using medium-hard examples.
Ex)1 Harder Example Of U-Substitution10:52
In this video, I will do example 1 of a harder example of u-substitution.
Ex) 2 U-Substitution Of Harder Example3:36
This is example 2 of a harder example of u-substitution that requires back substitution.
Ex) 3 U-Substitution Of Harder Example6:32
In this video, I will do example 3 of a harder u-substitution that requires double substitution.
Integrating Powers Of Sines And Cosines19:45
In this video, I will go over integrating powers of sines and cosines. This is not integrating with trig substitution.
Integrating Powers Of Tangents And Secants16:17
In this video, I will go over how to integrate powers of tangents and secants.
Intro To Integration By Parts9:14
In this video, I will go over integration by parts.
Integration By Parts Involving ln(x)4:12
In this video, I will do example two of integration by parts involving ln(x).
Integration By Parts More Than Once14:08
This is example 3 of integration by parts more than once.
Integration By Parts Tabular Method10:55
In this video, I will introduce the tabular method for integration by parts.
Integration By Parts For Definite Integrals10:03
In this video, I will do integration by parts with definite integral.
Integration By Parts With LIATE9:06
In this video, I will integrate by parts with the help of LIATE.
Quiz On Integration By Parts11:14
In this video, I will go over the quiz on integration by parts.

Requirements

You need a good foundation of algebra 2, and Trigonometry

Description

This course is broken in three section: limits, derivatives, and integrals. You will understand the meaning of what a limit is, and the different techniques for finding limits including: 4 types of discontinuities, limits at infinity, limits with radicals, trig limits, l'hopital rule, and basic limits problems. You will learn what is a derivative, and all the different techniques for finding a derivative including: power rule, product rule, quotient rule, implicit differentiation, chain rule, logarithmic derivatives, rolles theorem, mean-value theorem, extremas. Also you will apply derivatives in the real world such as max and min problems, related rate problems. Finally you will be introduced to limits such as u-substitution, indefinite, and definite integrals, fundamental theorem of calculus. Everything is video based lecture there's no unnecessary downloads. I recommend getting a large notebook, and writing down good as we go along as if you were in a real university. All the practice problems are video based with step by step guide in solving the problems. You can work on your own paste, and pause any time. After completing this course you will be good at finding any limit, finding any type of derivative with a good foundation of solving a word problem involving derivatives. Also you will have a good foundation of what a limit is and using using u-substitution, definite, indefinite integral, and fundamental theorem calculus which will come in handy in calculus 2.

Who this course is for:

This course is perfect for business calculus, AP calculus AB, Calculus 1, and first semester college students

Intro To Calculus 1

What you'll learn

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Course content

Derivatives47 lectures • 12hr 58min

Application Problems Using Your Derivative Rules25 lectures • 5hr 13min

Limits11 lectures • 4hr 31min

Integrals27 lectures • 11hr 31min

Final Exam5 lectures • 5hr 23min

Requirements

Description

Who this course is for: