Calculus

The course objective of Math 104: Calculus is to master the basics of calculus with an emphasis on limits, derivatives, and integrals. This course is taught in detail with 843 lessons, and you'll receive a transcript with a college certificate.

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Course curriculum

1. Course Overview and Learning Outcomes
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1. Introduction
1. Preview of Calculus
2. VIDEO: Derivatives and Tangent Lines
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3. VIDEO: Find the Area of an Irregular Shape
4. 1.1 Lesson PDF
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5. Check Your Knowledge
6. Quiz 1.1
1. Lines in the Plane
2. Practice Answers 1.2
3. VIDEO: Find a Slope Given Two Points
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4. VIDEO: Find the Equation of a Line Given Two Points
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5. VIDEO: Equations of Circles: Radius and Center
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6. VIDEO: How to Find the Equation of a Line from a Slope and Point
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7. VIDEO: Determine the Equation of a Line Parallel to a Line in General Form
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8. VIDEO: Determine the Equation of a Line Perpendicular to a Line in Slope-Intercept Form
9. 1.2 lesson PDF
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10. Check Your Knowledge
11. Quiz 1.2
1. Functions and Their Graphs
2. Practice Answers 1.3
3. VIDEO: Evaluate Function at a Point
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4. Check Your Knowledge
5. Quiz 1.3
1. Combinations of Functions
2. Practice Answers 1.4
3. VIDEO: More on the Composition of Functions
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4. VIDEO: Combine Functions using Algebraic Operations
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5. 1.4 lesson pdf
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6. Check Your Knowledge
7. Quiz 1.4
1. Mathematical Language
2. Practice Answers 1.5
3. VIDEO: Negating Quantified Statements
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4. VIDEO: Converse and Contrapositive
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5. 1.5 lesson PDF
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6. Check Your Knowledge
7. Quiz 1.5
1. Introduction
1. Tangent Lines, Velocities, Growth
2. Practice Answers
3. VIDEO: Slope of a Function at a Point
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4. 2.1 lesson PDF
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5. Check Your Knowledge
6. Quiz 2.1
1. The Limit of a Function
2. The Limit of Laws
3. Practice Answers 2.2
4. VIDEO: Evaluating Limits Using a Graph
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5. VIDEO: More on the Limit of a Function
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6. 2.2 LESSON pdf
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7. Check Your Knowledge
8. Quiz 2.2
1. Properties of Limits
2. Practice Answers
3. VIDEO: Solving Limits (Rationalization)
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4. VIDEO: Calculating Slope of Tangent Line Using the Definition of a Derivative
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5. 2.3 lesson PDF
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6. Check Your Knowledge
7. Quiz 2.3
1. Continuous Functions
2. Practice Answers
3. VIDEO: More on Continuous Functions
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4. VIDEO: Intermediate Value Theorem
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5. 2.4 lesson PDF
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6. Check Your Knowledge
7. Quiz 2.4
1. Definition of Limit
2. Practice Answers
3. VIDEO: Epsilon-Delta Limits
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4. 2.5 lesson PDF
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5. Check Your Knowledge
6. Quiz 2.5
1. Introduction
1. Introduction to Derivatives
2. Practice Answers
3. VIDEO: The Tangent Line
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4. 3.1 lesson PDF
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5. Check Your Knowledge
6. Quiz 3.1
1. The Definition of Derivative
2. Practice Answers
3. VIDEO: Derivatives from the Definition
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4. 3.2 lesson PDF
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5. Check Your Knowledge
6. Quiz 3.2
1. Derivatives: Properties and Formulas
2. Practice Answers
3. VIDEO: Applying the Product Rule for Derivatives
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4. 3.3 lesson PDF
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5. Check Your Knowledge
6. Quiz 3.3
1. More Differentiation Patterns
2. Practice Answers
3. VIDEO: The Power Rule for Polynomials
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4. VIDEO: Derivatives of Exponential Functions
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5. VIDEO: Derivatives of Trigonometric Functions
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6. VIDEO: Higher-Ordered Derivatives
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7. 3.4 lesson PDF
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8. Check Your Knowldege
9. Quiz 3.4
1. The Chain Rule
2. Practice Solutions
3. VIDEO: Chain Rule and Examples
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4. 3.5 lesson PDF
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5. Check Your Knowledge
6. Quiz 3.5
1. Applications of the Chain Rule
2. Practice Answers
3. VIDEO: Solving a Related Rates Problem
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4. 3.6 lesson PDF
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5. Check Your Knowledge
6. Quiz 3.6
1. Related Rates: An Application of Derivatives
2. Practice Answers
3. VIDEO: Derivatives as Rates of Change
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4. VIDEO: Differentiating Parametric Functions
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5. 3.7 Lesson PDF
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6. Check Your Knowledge
7. Quiz 3.7
1. Newton's Method for Finding Roots
2. Practice Answers
3. VIDEO: Using Newton's Method
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4. VIDEO: Determining Differentiability Graphically
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5. VIDEO: Continuity on Intervals
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6. 3.8 Lesson PDF
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7. Check Your Knowledge
8. Quiz 3.8
1. Linear Approximation and Differentials
2. Practice Answers
3. VIDEO: More on Linear Approximation
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4. VIDEO: The Properties of a Differential of a Function
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5. 3.9 Lesson PDF
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6. Check Your Knowledge
7. Quiz 3.9
1. Implicit and Logarithmic Differentiation
2. Practice Answers
3. VIDEO: Implicit Differentiation
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4. VIDEO: Implicit Differentiation with Transcendental Functions
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5. 3.10 Lesson PDF
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6. Check Your Knowledge
7. Quiz 3.10
1. Introduction
1. Finding Maximums and Minimums
2. Practice Answers
3. VIDEO: Maxima and Minima
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4. 4.1 lesson PDF
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5. Check Your Knowledge
6. Quiz 4.1
1. The Mean Value Theorem and Its Consequences
2. Practice Answers
3. VIDEO: Critical Points and the Mean Value Theorem
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4. 4.2 LESSON PDF
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5. Check Your Knowledge
6. Quiz 4.2
1. f' and the Shape of f
2. Practice Answers
3. VIDEO: First Derivative Test part(1)
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4. VIDEO: First Derivative Test part(2)
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5. 4.3 LESSON PDF
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6. Check Your Knowledge
7. Quiz 4.3
1. f'' and the Shape of f
2. Practice Answers
3. VIDEO: Concavity and the Second Derivative
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4. 4.4 LESSON PDF
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5. Check Your Knowledge
6. Quiz 4.4
1. Applied Maximum and Minimum Problems
2. Practice Answers
3. VIDEO: Max and Min Applications part(1)
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4. VIDEO: Max and Min Applications part(2)
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5. 4.5 LESSON PDF
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6. Check Your Knowledge
7. Quiz 4.5
1. Infinite Limits and Asymptotes
2. Practice Answers
3. 4.6 LESSON PDF
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4. Check Your Knowledge
5. Quiz 4.6
1. L'Hôpital's Rule
2. Practice Answers
3. VIDEO: Introduction to L'Hopital's Rule (part 1)
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4. VIDEO: Introduction to L'Hopital's Rule (part 2)
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5. Check Your Knowledge
6. Quiz 4.7
1. Introduction
1. The Integral
2. Practice Answers
3. 5.1 LESSON PDF
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4. Check Your Knowledge
5. Quiz 5.1
1. Sigma Notation and Riemann Sums
2. Practice Answers
3. VIDEO: Riemann Sums in Summation Notation
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4. 5.2 LESSON PDF
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5. Check Your Knowledge
6. Quiz 5.2
1. The Definite Integral
2. Practice Answers
3. VIDEO: Find the Area between Two Curves Using Definite Integrals
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4. 5.3 LESSON PDF
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5. Check Your Knowledge
6. Quiz 5.3
1. Properties of the Definite Integral
2. Practice Answers
3. VIDEO: Integrals and the Graph of a Function
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4. 5.4 LESSON PDF
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5. Check Your Knowledge
6. Quiz 5.4
1. Areas, Integrals, and Antiderivatives
2. Practice Answers
3. VIDEO: Integration and Antiderivatives
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4. 5.5 LESSON PDF
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5. Check Your Knowledge
6. Quiz 5.5
1. The Fundamental Theorem of Calculus
2. Practice Answers
3. VIDEO: Integrals and the Fundamental Theorem of Calculus
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4. VIDEO: Differentiating an Integral Function
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5. Check Your Knowledge
6. Quiz 5.6
1. Finding Antiderivatives
2. Practice Answers
3. VIDEO: Integration_ U-Substitution (Example 1)
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4. VIDEO: Integration_ U-Substitution (Example 2)
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5. 5.7 LESSON PDF
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6. Check Your Knowledge
7. Quiz 5.7
1. First Applications of Definite Integrals
2. Practice Answers
3. 5.8 LESSON PDF
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4. Check Your Knowledge
5. Quiz 5.8
1. Appendix 1
2. Using Tables (and Technology) to Find Antiderivatives
3. Practice Answers
4. 5.9 Lesson PDF
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5. Check Your Knowledge
6. Quiz 5.9
1. Assignment
2. Rubric for Assignment
1. Final Exam: Instructions (Important)
2. Rubrics for Final Exam
3. Written Final Exam
4. FINAL EXAM MCQ

About this course

$19.00
246 lessons
9 hours of video content

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Maths 165: Calculus 1

Chapter 1: Foundations of Contemporary Calculus

Ch 1.1: Introduction to Fundamental Concepts of Calculus: Tangents and Areas

Ch 1.2: Understanding Lines in the Plane and Their Properties

Ch 1.3: Introduction to Functions

Ch 1.4: Combinations and Compositions of Functions

Ch 1.5: Understanding Mathematical Language and Logical Statements

Chapter 2: Introduction to Functions and Graphs

Ch 2.1: Slopes and Velocities

Ch 2.2: Exploring the Concept of Limit of a function in Calculus

Ch 2.3: Exploring Properties of Limits in Calculus

Ch 2.4: Exploring Continuous Functions in Calculus

Ch 2.5: Understanding the Formal Definition of Limits

Chapter 3: Introduction to the Derivative

Ch 3.1: Understanding Tangent Lines and Derivatives in Calculus

Ch 3.2: The Definition and Interpretation of the Derivative

Ch 3.3: Properties and Rules of Derivatives

Ch 3.4: Advanced Differentiation Patterns and Applications

Ch 3.5: Mastering the Chain Rule in Calculus

Ch 3.6: Applications of the Chain Rule in Calculus

Ch 3.7: Understanding Related Rates: Advanced Applications in Calculus

Ch 3.8: Newton's Method for Finding Roots: A Detailed Examination

Ch 3.9: Linear Approximation and Differentials: Concepts and Applications

Ch 3.10: Implicit and Logarithmic Differentiation: Advanced Techniques

Chapter 4: Maxima, Minima, and Graph Shapes

Ch 4.1: Maximizing and Minimizing Functions Using Calculus

Ch 4.2: The Mean Value Theorem and Its Applications in Calculus

Ch 4.3: The First Derivative and the Shape of a Function's Graph

Ch 4.4: The Second Derivative and Concavity of Functions

Ch 4.5: Applied Maximum and Minimum Problems in Calculus

Ch 4.6: Asymptotic Behavior of Functions in Calculus

Ch 4.7: L'Hôpital's Rule in Calculus

Chapter 5: The Integral

Ch 5.1: Introduction to Integral Calculus

Ch 5.2: Summation Techniques and Area Approximations

Ch 5.3: Exploring the Definite Integral

Ch 5.4: Properties of the Definite Integral

Ch 5.5: Areas, Integrals, and Antiderivatives

Ch 5.6: Fundamental Theorem of Calculus

Ch 5.7: Finding Antiderivatives

Ch 5.8: First Application of Definite Integral

Ch 5.9: Using Tables to Find Antiderivatives

Assignment

Final Exam

About this course