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
1. Introduction
1. Preview of Calculus
2. VIDEO: Derivatives and Tangent Lines
3. VIDEO: Find the Area of an Irregular Shape
4. 1.1 Lesson PDF
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
4. VIDEO: Find the Equation of a Line Given Two Points
5. VIDEO: Equations of Circles: Radius and Center
6. VIDEO: How to Find the Equation of a Line from a Slope and Point
7. VIDEO: Determine the Equation of a Line Parallel to a Line in General Form
8. VIDEO: Determine the Equation of a Line Perpendicular to a Line in Slope-Intercept Form
9. 1.2 lesson PDF
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
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
4. VIDEO: Combine Functions using Algebraic Operations
5. 1.4 lesson pdf
6. Check Your Knowledge
7. Quiz 1.4
1. Mathematical Language
2. Practice Answers 1.5
3. VIDEO: Negating Quantified Statements
4. VIDEO: Converse and Contrapositive
5. 1.5 lesson PDF
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
4. 2.1 lesson PDF
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
5. VIDEO: More on the Limit of a Function
6. 2.2 LESSON pdf
7. Check Your Knowledge
8. Quiz 2.2
1. Properties of Limits
2. Practice Answers
3. VIDEO: Solving Limits (Rationalization)
4. VIDEO: Calculating Slope of Tangent Line Using the Definition of a Derivative
5. 2.3 lesson PDF
6. Check Your Knowledge
7. Quiz 2.3
1. Continuous Functions
2. Practice Answers
3. VIDEO: More on Continuous Functions
4. VIDEO: Intermediate Value Theorem
5. 2.4 lesson PDF
6. Check Your Knowledge
7. Quiz 2.4
1. Definition of Limit
2. Practice Answers
3. VIDEO: Epsilon-Delta Limits
4. 2.5 lesson PDF
5. Check Your Knowledge
6. Quiz 2.5
1. Introduction
1. Introduction to Derivatives
2. Practice Answers
3. VIDEO: The Tangent Line
4. 3.1 lesson PDF
5. Check Your Knowledge
6. Quiz 3.1
1. The Definition of Derivative
2. Practice Answers
3. VIDEO: Derivatives from the Definition
4. 3.2 lesson PDF
5. Check Your Knowledge
6. Quiz 3.2
1. Derivatives: Properties and Formulas
2. Practice Answers
3. VIDEO: Applying the Product Rule for Derivatives
4. 3.3 lesson PDF
5. Check Your Knowledge
6. Quiz 3.3
1. More Differentiation Patterns
2. Practice Answers
3. VIDEO: The Power Rule for Polynomials
4. VIDEO: Derivatives of Exponential Functions
5. VIDEO: Derivatives of Trigonometric Functions
6. VIDEO: Higher-Ordered Derivatives
7. 3.4 lesson PDF
8. Check Your Knowldege
9. Quiz 3.4
1. The Chain Rule
2. Practice Solutions
3. VIDEO: Chain Rule and Examples
4. 3.5 lesson PDF
5. Check Your Knowledge
6. Quiz 3.5
1. Applications of the Chain Rule
2. Practice Answers
3. VIDEO: Solving a Related Rates Problem
4. 3.6 lesson PDF
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
4. VIDEO: Differentiating Parametric Functions
5. 3.7 Lesson PDF
6. Check Your Knowledge
7. Quiz 3.7
1. Newton's Method for Finding Roots
2. Practice Answers
3. VIDEO: Using Newton's Method
4. VIDEO: Determining Differentiability Graphically
5. VIDEO: Continuity on Intervals
6. 3.8 Lesson PDF
7. Check Your Knowledge
8. Quiz 3.8
1. Linear Approximation and Differentials
2. Practice Answers
3. VIDEO: More on Linear Approximation
4. VIDEO: The Properties of a Differential of a Function
5. 3.9 Lesson PDF
6. Check Your Knowledge
7. Quiz 3.9
1. Implicit and Logarithmic Differentiation
2. Practice Answers
3. VIDEO: Implicit Differentiation
4. VIDEO: Implicit Differentiation with Transcendental Functions
5. 3.10 Lesson PDF
6. Check Your Knowledge
7. Quiz 3.10
1. Introduction
1. Finding Maximums and Minimums
2. Practice Answers
3. VIDEO: Maxima and Minima
4. 4.1 lesson PDF
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
4. 4.2 LESSON PDF
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)
4. VIDEO: First Derivative Test part(2)
5. 4.3 LESSON PDF
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
4. 4.4 LESSON PDF
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)
4. VIDEO: Max and Min Applications part(2)
5. 4.5 LESSON PDF
6. Check Your Knowledge
7. Quiz 4.5
1. Infinite Limits and Asymptotes
2. Practice Answers
3. 4.6 LESSON PDF
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)
4. VIDEO: Introduction to L'Hopital's Rule (part 2)
5. Check Your Knowledge
6. Quiz 4.7
1. Introduction
1. The Integral
2. Practice Answers
3. 5.1 LESSON PDF
4. Check Your Knowledge
5. Quiz 5.1
1. Sigma Notation and Riemann Sums
2. Practice Answers
3. VIDEO: Riemann Sums in Summation Notation
4. 5.2 LESSON PDF
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
4. 5.3 LESSON PDF
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
4. 5.4 LESSON PDF
5. Check Your Knowledge
6. Quiz 5.4
1. Areas, Integrals, and Antiderivatives
2. Practice Answers
3. VIDEO: Integration and Antiderivatives
4. 5.5 LESSON PDF
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
4. VIDEO: Differentiating an Integral Function
5. Check Your Knowledge
6. Quiz 5.6
1. Finding Antiderivatives
2. Practice Answers
3. VIDEO: Integration_ U-Substitution (Example 1)
4. VIDEO: Integration_ U-Substitution (Example 2)
5. 5.7 LESSON PDF
6. Check Your Knowledge
7. Quiz 5.7
1. First Applications of Definite Integrals
2. Practice Answers
3. 5.8 LESSON PDF
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
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

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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