Maths 165: Calculus 1

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.

"Calculus 1 was a thorough and engaging introduction, perfectly setting the stage for my further studies in engineering!" — Arjun Patel

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Our students have sent UPI transcripts to over 1,500 esteemed colleges and universities in the US, UK & Canada, earning credits up to two years of study.

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Course Curriculum

1. Ch 1.1 What Constitutes a Function: Fundamentals and Essential Vocabulary
2. What is a Function?
3. Variables of a Function
4. Domain and Range of a Function
5. Function Graphs
6. Function Examples
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 1.1
1. Introduction
2. Maps and Graphs
3. Graphing Functions
4. Lesson Summary
5. Quiz 1.2
1. Introduction
2. Functions
3. Lesson Summary
4. Quiz 1.3
1. Introduction
2. What is an Inverse Function?
3. How to Find the Inverse of a Function
4. How to Graph Inverse Functions
5. Inverse Composition Rule
6. Lesson Summary
7. Quiz 1.4
1. Introduction
2. Polynomials
3. Lesson Review
4. Quiz 1.5
1. Introduction
2. Bunnies Galore
3. x to the nth Power
4. Powers in Daily Life
5. Polynomials
6. Lesson Summary
7. Quiz 1.6
1. Introduction
2. What is an Exponential?
3. Rules of Natural Log
4. Carbon Dating Using Natural Log
5. More Rules of Logarithms
6. Lesson Summary
7. Quiz 1.7
1. Introduction
2. Plotting the slope of a line in the graph.
3. Steep Slopes vs. Gradual Slopes
4. Slope of Tangent Lines Formula
5. Lesson Summary
6. Quiz 1.8
1. Introduction
2. Road Trip to Las Vegas
3. Point-Slope Form
4. Lesson Summary
5. Quiz 1.9
1. Introduction
2. Running to the Finish Line
3. Asymptotes
4. Lesson Summary
5. Quiz 1.10
1. Introduction
2. Circles
3. Ovals
4. Implicit Functions
5. Lesson Summary
6. Quiz 1.11
1. Ch 2.1 Exploring Continuity Within Functions
2. Continuity: UFOs and Jets
3. Continuous and Discontinuous Functions
4. Lesson Summary
5. Quiz 2.1
1. Introduction
2. What are Points of Discontinuity?
3. Different Types of Discontinuity
4. Finding Points of Discontinuity
5. Lesson Summary
6. Frequently Asked Questions
7. Quiz 2.2
1. Introduction
2. Regions of Continuity
3. Regions around Jumps
4. Regions around Kinks
5. Considering Multi-Step Functions
6. Lesson Summary
7. Quiz 2.3
1. Introduction
2. Continuous vs. Discontinuous Paths
3. Intermediate Value Theorem
4. Finding a Value in a Continuous Function
5. Lesson Summary
6. Quiz 2.4
1. Introduction
2. What is the Intermediate Value Theorem (IVT)?
3. Intermediate Value Theorem Proof
4. Lesson Summary
5. Frequently Asked Questions
6. Quiz 2.5
1. Ch 3.1 Understanding the Concept of Vectors in Mathematics: Definitions and Illustrative Examples
2. What is a Vector in Geometry?
3. What is an Example of a Vector?
4. Types of Vectors in Math
5. Operations on Vectors with Examples
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 3.1
1. Introduction
2. How to Find the Magnitude of a Vector
3. How to Find the Direction of a Vector
4. Vector Direction and Magnitude
5. Direction and Magnitude Graph
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 3.2
1. Introduction
2. Vectors
3. Lesson Summary
4. Quiz 3.3
1. Introduction
2. Adding and Subtracting Vectors
3. Resolving Vectors Graphically
4. Adding Vectors Graphically
5. Subtracting Vectors Graphically
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 3.4
1. Introduction
2. Magnitude
3. Dot Products
4. Sample Problems
5. Lesson Summary
6. Frequently Asked Questions
7. Quiz 3.5
1. Ch 4.1 Analyzing and Solving Visual Geometry Problems
2. Visualization
3. Keys for Visualization Problems
4. Lesson Summary
5. Quiz 4.1
1. Introduction
2. Square Peg in a Square Hole
3. Lesson Summary
4. Quiz 4.2
1. Introduction
2. Volumes of 3-Dimensional Objects
3. Pyramids and Prisms
4. Cones and Cylinders
5. Lesson Summary
6. Quiz 4.3
1. Introduction
2. What is a Frustum?
3. Volume of a Frustum of a Pyramid
4. Volume of a Truncated Rectangular Pyramid
5. Volume of a Frustum of a Cone
6. Frustum Formula Practice
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 4.4
1. Introduction
2. Pythagorean Ice Cream
3. Pythagorean Skating
4. The Lion King Rock Problem
5. Lesson Summary
6. Quiz 4.5
1. Introduction
2. Trigonometry Functions
3. Sine Function
4. Cosine Function
5. Tangent Function
6. Examples of Trig Functions
7. Lesson Summary
8. Quiz 4.6
1. Introduction
2. SohCahToa and the Pythagorean Theorem
3. Inverse and Reciprocation
4. Using Trigonometry and Geometry
5. Lesson Summary
6. Quiz 4.7
1. Ch 5.1 Mastering Radian and Degree Conversions on a Scientific Calculator
2. Solving Triangles
3. Using Degrees
4. Switching Between Degrees And Radians
5. Using Radians
6. Lesson summary
7. Quiz 5.1
1. Introduction
2. A Lot More Buttons
3. Triangles
4. Using Exponentials
5. Lesson Summary
6. Quiz 5.2
1. Introduction
2. A Scientific Calculator
3. An Equation By Hand
4. Using the Scientific Calculator
5. Other Scientific Calculator Functions
6. Lesson Summary
7. Quiz 5.3
1. Ch 6.1 Exploring Limit Definitions Using Graphical Representation
2. The Limits of My Car
3. Limits of a Pendulum
4. Examples of Limits in Math
5. Lesson Summary
6. Quiz 6.1
1. Introduction
2. Defining Limits
3. Finding Limits
4. Quiz 6.2
1. Introduction
2. Over the Hill and Far Away
3. One-Sided Limits in Equations
4. Notation of Limits
5. Continuous and Discontinuous
6. Continuity and Limits
7. Lesson Summary
8. Quiz 6.3
1. Introduction
2. What is the Limit of a Function?
3. How to Find the Limit of a Function
4. Limit Rules
5. Evaluating Limits
6. Examples of Calculating Limits of a Function
7. Lesson Summary
8. Activities
9. FAQs
10. Quiz 6.4
1. Introduction
2. Limits of a Function:
3. Properties of Limits:
4. Lesson Summary:
5. Frequently Asked Questions
6. Quiz 6.5
1. Introduction
2. What is the Squeeze Theorem?
3. Uses of the Squeeze Theorem
4. State and Prove
5. Lesson Summary
6. Activities
7. FAQs
8. Quiz 6.6
1. Introduction
2. Genie in a Bottle
3. What is Infinity?
4. What is an Asymptote?
5. Lesson Summary
6. Quiz 6.7
1. Ch 7.1 Exploring Velocity and its Relationship with Rate of Change
2. The Velocity of My Drive to Work
3. Velocity and Inconstant Slopes
4. Lesson Summary
5. Quiz 7.1
1. Introduction
2. Rate of Change Review
3. Examples of Changes in Velocity
4. Lesson Summary
5. Quiz 7.2
1. Introduction
2. Average Rate of Change
3. Instantaneous Rate of Change
4. Average Rate of Change vs. Instantaneous Rate of Change
5. What is the Mean Value Theorem?
6. How to Use Mean Value Theorem
7. Mean Value Theorem Graph
8. Mean Value Theorem Examples
9. Lesson Summary
10. Frequently Asked Questions
11. Quiz 7.3
1. Introduction
2. What is Rolle's Theorem?
3. Understanding Rolle's Theorem through a Mean Value Theorem Graph
4. Lesson Summary
5. Activities
6. FAQs
7. Quiz 7.4
1. Introduction
2. Writing Derivatives
3. Lesson Summary
4. Quiz 7.5
1. Introduction
2. Instantaneous Rate of Change
3. Slopes as a Tangent
4. Lesson Summary
5. Quiz 7.6
1. Introduction
2. What is Differentiability?
3. How to Tell if a Function is Differentiable?
4. Differentiable vs. Continuous
5. Lesson Summary
6. Frequently Asked Questions
7. Quiz 7.7
1. Ch 8.1 Utilizing Limit Concepts to Compute Derivatives
2. Review of Derivatives
3. Derivative of a Constant Velocity
4. Derivative of a Not-So-Constant Velocity
5. Graphing the Derivative
6. Lesson Summary
7. Quiz 8.1
1. Introduction
2. Quick Review of Derivatives
3. Constant Rule of Derivatives
4. Distributive Type Rule of Derivatives
5. Lesson Summary
6. Quiz 8.2
1. Introduction
2. What are Derivatives of Trigonometric Functions?
3. Derivative of Sine
4. Derivative of Cosine
5. Derivative of Tangent
6. Derivative of Cotangent
7. Derivative of Cosecant
8. Derivative of Secant
9. Examples of Trig Derivative Rules
10. Lesson Summary
11. Frequently Asked Questions
12. Quiz 8.3
1. Introduction
2. Basic Rules
3. Finding Derivatives of Polynomials
4. The Power Rule for Derivatives
5. Calculating Vertical Velocity
6. Lesson Summary
7. Quiz 8.4
1. Introduction
2. What is an Exponential Function?
3. Derivative of Exponential Function
4. Derivative of Exponential Function Formula
5. How to Find the Derivative of an Exponential Function
6. Derivative of Exponential Function Examples
7. Lesson Summary
8. Quiz 8.5
1. Introduction
2. How to Differentiate a Function
3. Chain Rule Differentiation
4. Lesson Summary
5. Frequently Asked Questions
6. Quiz 8.6
1. Introduction to the Product Rule
2. Examples of Solving Using the Product Rule
3. Finding the Derivative
4. Lesson Summary
5. Quiz 8.7
1. Introduction of quotient rule
2. Understanding the Quotient Rule
3. Lesson Summary
4. Quiz 8.8
1. Introduction
2. The Rate of Change of Super C
3. Acceleration
4. Higher Order Derivatives
5. Second Derivatives
6. Lesson Summary
7. Quiz 8.9
1. Introduction
2. Understanding the 'Jerk'
3. Lesson Summary
4. Quiz 8.10
1. Introduction
2. Implicit Function
3. Derivatives of an Implicit Function
4. Lesson Summary
5. Quiz 8.11
1. Introduction
2. Review of Basic Trig Functions
3. Rules of Inverse Trig Functions
4. Lesson Summary
5. Quiz 8.12
1. Introduction
2. Review of Common Derivatives
3. Review of the Rules of Derivatives
4. Examples of Solving Derivatives
5. Lesson Summary
6. Quiz 8.13
1. Introduction
2. Optimization in Calculus
3. Optimization Problems in Calculus
4. How to Solve Optimization Problems
5. Lesson Summary
6. Frequently Asked Questions
7. Quiz 8.14
1. Ch 9.1 Analyzing Derivative Graphs Across Various Functions
2. Location as a Function of Time
3. The Derivatives of a Function
4. Derivative of a Single Destination
5. Rules of Derivation
6. Discontinuous Derivatives
7. Applications to Other Functions
8. Lesson Summary
9. Quiz 9.1
1. Introduction
2. The Normal Line
3. Equation of a Normal Line
4. Lesson Summary
5. Quiz 9.2
1. Introduction
2. Maximum on a Graph
3. Minimum on a Graph
4. Extrema
5. How to Find Max and Min on a Graph
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 9.3
1. Introduction
2. Extrema
3. Finding Extrema
4. Finding More Extrema
5. Lesson Summary
6. Quiz 9.4
1. Introduction
2. Understanding Concavity
3. Concave Up and Concave Down
4. Examples of Concave Up and Concave Down
5. Lesson Summary
6. Quiz 9.5
1. Introduction
2. Concavity Definition
3. How to Determine Concavity
4. How to Find Concavity from the First Derivative Graph
5. Inflection Points
6. How to Find Inflection Points
7. How to Find Inflection Points from the First Derivative Graph
8. Lesson Summary
9. Frequently Asked Questions
10. Quiz 9.6
1. Introduction
2. Review of Derivatives
3. Finding Position Using Velocity
4. Understanding Velocity
5. Velocity and Acceleration
6. Distance Based on Velocity
7. Lesson Summary
8. Quiz 9.7
1. Introduction
2. How to Find the Derivative of a Graph
3. How to Graph Derivatives
4. How to Draw the Derivative of a Graph
5. Derivative Graph Rules
6. First and Second Derivative graphs
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 9.8
1. Introduction
2. Limits
3. L'Hopital's Rule
4. L'Hopital's Rule: When Limit Approaches 0
5. L'Hopital's Rule: When Limit Approaches Infinity
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 9.9
1. Introduction
2. L'Hospital's Rule
3. What is L'Hospital's Rule?
4. General Form
5. Necessary Conditions
6. How To Do L'Hospital's Rule?
7. Why Does L'Hospital's Rule Work?
8. When to use L'Hospital's Rule
9. L'Hospital's Rule for Limits Approaching Infinity
10. L'Hospital Rule Examples
11. Counter examples
12. Lesson Summary
13. Frequently Asked Questions
14. Quiz 9.10
1. Introduction
2. Quick Review of L'Hôpital's Rule
3. Example of L'Hôpital's Rule in Complex Cases
4. Lesson Summary
5. Quiz 9.11
1. Ch 10.1 Utilizing Linearization Techniques for Function Analysis
2. Estimating Distances and Time
3. Understanding Linearization
4. Using Linearization to Estimate Travel
5. Rewriting Linearization
6. Lesson Summary
7. Quiz 10.1
1. Introduction
2. Importance of Linearization
3. Using Linearization to Estimate Speed
4. Examples of Linearization
5. Lesson Summary
6. Quiz 10.2
1. Introduction
2. Predicting the Path of a Hang Glider
3. Newton's Method
4. Linearization
5. Lesson Summary
6. Quiz 10.3
1. Introduction
2. What is Newton's Method
3. Newton's Method Formula
4. How to do Newton's Method
5. Newton's Method Examples
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 10.4
1. Introduction
2. Optimize the Problem
3. Five Steps to Optimization
4. Lesson Summary
5. Quiz 10.5
1. Introduction
2. Five Steps to Solve Optimization Problems
3. Lesson Summary
4. Quiz 10.6
1. Introduction
2. Five Steps to Solve Optimization Problems
3. Lesson Summary
4. Quiz 10.7
1. Ch 11.1 Exploring Arithmetic Series Computation Methods
2. What is an Arithmetic Series?
3. The Formula for any Arithmetic Series
4. Solving the Michigan Stadium Problem
5. Lesson Summary
6. Quiz 11.1
1. Introduction
2. Geometric Series
3. Finite Geometric Series
4. Infinite Geometric Series
5. Geometric Series Formula
6. How to Solve Geometric Series
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 11.2
1. Introduction
2. Intro to Practice Problems
3. Practice Problem #1
4. Practice Problem #2
5. Practice Problem #3
6. Practice Problem #4
7. Lesson Summary
8. Quiz 11.3
1. Introduction
2. Recommendations & Suggestions
3. Lesson Summary
4. Quiz 11.4
1. Introduction
2. P-Series
3. Harmonic Series
4. Sum of P-Series
5. P-Series Test for Convergence
6. P-Series Examples
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 11.5
1. Introduction
2. What is a Harmonic Series?
3. Harmonic Number
4. Harmonic Series Formula
5. Harmonic Series Diverges
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 11.6
1. Introduction
2. What is the Taylor Series?
3. Taylor Series Formula
4. Taylor Series Derivation
5. Exponential Taylor Series
6. Taylor Series Example
7. Lesson Summary
8. Activities
9. FAQs
10. Quiz 11.7
1. Introduction
2. The Taylor Series Expression
3. Taylor Series Steps
4. Solution
5. Quiz 11.8
1. Introduction
2. Maclaurin Series
3. How to Find Maclaurin Series
4. Taylor and Maclaurin Series
5. Derivative of Power Series
6. Series Expansion
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 11.9
1. Introduction
2. ln of 1
3. ln(x) = 1
4. Maclaurin Series for ln(1 + x)
5. Finding the Derivative
6. Evaluate at x = 0
7. Assemble the Sum of Products
8. Find the General Term
9. Find the Region of Convergence
10. Lesson Summary
11. Quiz 11.10
1. Introduction
2. What is the Ratio Test?
3. Ratio Test Formula
4. When to Use the Ratio Test
5. Ratio Test Rules
6. Ratio Test Examples
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 11.11
1. Introduction
2. Infinite Series
3. Convergent and Divergent Series
4. Convergence and Divergence Tests
5. Comparison Test for Convergence
6. How to Determine if a Series is Convergent or Divergent
7. Convergence and Divergence Tests: Examples
8. Lesson Summary
9. Frequently Asked Questions
10. Quiz 11.12
1. Ch 12.1 Exploring Summation Notation and Mathematical Series
2. Sigma Summation Notation
3. Sigma summation notation examples
4. Series to Sigma Notation
5. Sigma Notation Geometric Series
6. Lesson Summary
7. Activities
8. FAQs
9. Quiz 12.1
1. Introduction
2. Determining the Size of Your Land
3. Using Multiple Areas
4. Using Sum Notation
5. Understanding Riemann Sums
6. Lesson Summary
7. Quiz 12.2
1. Introduction
2. Riemann Sum
3. Left Riemann Sum
4. Right Riemann Sum
5. Mid-Point Riemann Sum
6. Riemann Sum Without Graph
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 12.3
1. Introduction
2. The Trapezoid & Riemann Sum
3. Trapezoids to Measure Area
4. The Trapezoid Rule
5. Lesson Summary
6. Quiz 12.4
1. Introduction
2. Determining the Size of Land
3. Using the Riemann Sum
4. Lesson Summary
5. Quiz 12.5
1. Introduction
2. Definite Integrals
3. Example of Integrals
4. Lesson Summary
5. Quiz 12.6
1. Introduction
2. When to Use a Riemann Sum
3. Riemann Sums
4. Using Two Slices
5. Calculating Multiple Slices
6. Infinite Slices
7. Lesson Summary
8. Quiz 12.7
1. Introduction
2. The Integral
3. Backward Property
4. Constant Property
5. Additive Property
6. Sums Property
7. Lesson Summary
8. Quiz 12.8
1. Introduction
2. What is Average Value?
3. Average Value of a Function
4. Average Value Formula
5. Average Value Theorem
6. How to find Average Value of a Function
7. Average Value Theorem Examples
8. Lesson Summary
9. Frequently Asked Questions
10. Quiz 12.9
1. Introduction
2. What is the Fundamental Theorem of Calculus?
3. Proving the Derivative of Definite Integral
4. Ways to Use the Fundamental Theorem of Calculus
5. Fundamental Theorem of Calculus Examples
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 12.10
1. Introduction
2. Fundamental Theorem
3. Antiderivatives
4. Indefinite Integrals as Antiderivatives
5. Lesson Summary
6. Quiz 12.11
1. Introduction
2. Curve Length
3. Example Problem
4. Lesson Summary
5. Quiz 12.12
1. Ch 13.1 Integrating Simple Shapes: Methods and Applications
2. Quick Review of the Definite Integral
3. Examples
4. Lesson Summary
5. Quiz 13.1
1. Introduction
2. Distance Traveled
3. Fundamental Theorem of Calculus
4. Anti-Derivatives of Polynomials
5. Examples
6. Lesson Summary
7. Quiz 13.2
1. Introduction
2. Trigonometry Functions
3. Integral of Functions
4. Integral of Trig Functions
5. Integral of Cosine
6. Integral of Sine
7. Integrals of Trig Functions Examples
8. Lesson Summary
9. Frequently Asked Questions
10. Quiz 13.3
1. Introduction
2. Quick Calculus Review
3. Examples
4. Lesson Summary
5. Quiz 13.4
1. Introduction
2. What is Integration by Substitution?
3. Integration with Chain Rule Importance
4. U-Substitution Formula
5. U-Substitution Method
6. U-Substitution Examples
7. U-Substitution Checking
8. Lesson Summary
9. Frequently Asked Questions
10. Quiz 13.5
1. Introduction
2. Example of a Difficult Integral
3. Solving by Substitution
4. Checking Yourself
5. Tricky U Substitutions
6. Lesson Summary
7. Quiz 13.6
1. Introduction
2. Integration by Parts
3. Integration by Parts Rule
4. How to Integrate by Parts
5. Integration by Parts Examples
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 13.7
1. Introduction
2. Linear Systems
3. Substitution Method
4. Elimination Method
5. Gauss-Jordan Elimination
6. Lesson Summary
7. Quiz 13.8
1. Introduction
2. Example of a Complicated Fraction
3. Solving for Partial Fractions
4. Solving for Partial Fractions with Factoring
5. Lesson Summary
6. Quiz 13.9
1. Introduction
2. Integration by Partial Fractions
3. Partial Fractions for Integration
4. How to Integrate Fractions
5. Lesson Summary
6. Frequently Asked Questions
7. Quiz 13.10
1. Introduction
2. What is Trig Substitution?
3. What is Integration by Trigonometric Substitution?
4. Trig Substitution Integrals
5. How to Do Trig Substitution Problems
6. Trig Substitution Examples
7. Lesson Summary
8. Activities
9. FAQs
10. Quiz 13.11
1. Introduction
2. Solving with Tables
3. Solving by Substitution
4. Solving by Parts
5. Solving by Riemann Sums
6. Example of Solving by Parts
7. Lesson Summary
8. Quiz 13.12
1. Introduction
2. How Do We Get an Improper Integral?
3. What an Improper Integral Looks Like
4. Solving an Improper Integral
5. Lesson Summary
6. Quiz 13.13
1. Ch 14.1 Analyzing Integration in Dynamic Motion Systems
2. Understanding Motion and Dynamic Motion
3. Solving Dynamic Motion with Integration
4. Calculating the Integral
5. Lesson Summary
6. Quiz 14.1
1. Introduction
2. Simple Areas
3. Calculating the Integral
4. Lesson Summary
5. Quiz 14.2
1. Introduction
2. Finding the Area Between Curves
3. Solving By Subtracting Two Areas
4. Solving for the Intersection
5. Splitting the Area into Two Parts
6. Using Inverse Functions to Find Area
7. Lesson Summary
8. Quiz 14.3
1. Introduction
2. Finding the Volume of a Cone
3. Finding the Area of a Slice
4. Example Problem
5. Lesson Summary
6. Quiz 14.4
1. Introduction
2. Understanding Generated Regions
3. The Slicing Method
4. The Disk Method
5. The Washer Method
6. Lesson Summary
7. Quiz 14.5
1. Ch 15.1 Application of Differential Notation in Physics
2. Our Changing World
3. Differential Equations
4. Lesson Summary
5. Quiz 15.1
1. Introduction
2. Separation of Variables in Differential Equations
3. Ordinary Differential Equations
4. Partial Differential Equations
5. Method of Separation of Variables
6. Lesson Summary
7. Activities
8. FAQs
9. Quiz 15.2
1. Introduction
2. Exponential Population Growth Formula
3. How to Calculate Exponential Growth
4. Exponential Population Growth Formula Practice
5. Alternative Formula for Calculating Exponential Growth
6. Lesson Summary
7. Quiz 15.3
1. Introduction
2. The Tank
3. The Draining Tank Problem
4. Lesson Summary
5. Quiz 15.4
1. Introduction
2. Related Rates
3. Importance and Uses of Related Rates
4. Related Rates Formulas
5. Related Rates Problems
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 15.5
1. Assignment
2. Final Exam Instructions
3. Final Exam

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Ch 1. Fundamentals of Graphing and Functions

Ch 1.2 Basic Functions and Their Graphs

Ch 1.3 Composition of Functions and Graphical Representation

Ch 1.4 Insight into Inverse Functions and Their Graphical Interpretation

Ch 1.5 Polynomial Functions: Characteristics and Factorization

Ch 1.6 Polynomial Functions: Exponential Elements and Simplification Techniques

Ch 1.7 Exploring Exponential and Logarithmic Functions, and the Natural Logarithm

Ch 1.8 Understanding Slopes and Tangents within Graphical Contexts

Ch 1.9 Determining Line Equations Using the Point-Slope Formula

Ch 1.10 Examination of Horizontal and Vertical Asymptotes

Ch 1.11 Unveiling Implicit Functions and Their Graphical Representations

Ch 2. Understanding Continuity in Functions

Ch 2.2 Investigating Discontinuities in Functions and Their Graphical Representations

Ch 2.3 Identifying Regions of Continuity Within Functions

Ch 2.4 Delving into the Definition of the Intermediate Value Theorem

Ch 2.5 Illustrating the Intermediate Value Theorem through Examples and Practical Applications

Ch 3. Introduction to Vector Analysis

Ch 3.2 Visual Representation of Vectors in Mathematical Context: Magnitude and Direction

Ch 3.3 Manipulating Vectors in Two-Dimensional Space: Operations and Techniques

Ch 3.4 Application of Vector Operations: Adding and Subtracting Vectors in Practice

Ch 3.5 Exploring the Dot Product of Vectors: Definitions and Real-World Applications

Ch 4. Analytical Geometry and Trigonometric Principles

Ch 4.2 Computing Volumes of Fundamental Geometric Shapes

Ch 4.3 Deriving Volume Formulas for Pyramids, Prisms, Cones, and Cylinders

Ch 4.4 Determining the Volume of Frustums of Pyramids and Cones

Ch 4.5 Utilizing the Pythagorean Theorem to Measure Distances

Ch 4.6 Exploring Trigonometric Concepts: Sine and Cosine Functions

Ch 4.7 Investigating Trigonometry in Relation to the Pythagorean Theorem

Ch 5. Advanced Techniques in Calculator Utilization

Ch 5.2 Utilizing Trigonometric Functions and Exponential Notations on a Scientific Calculator

Ch 5.3 Efficiently Solving Equations Using Advanced Calculator Functions

Ch 6. Advanced Concepts in Limit Analysis

Ch 6.2 Interpreting Limits Utilizing Mathematical Notation

Ch 6.3 Investigating One-Sided Limits and Continuity Principles

Ch 6.4 Techniques for Determining Limits of Functions

Ch 6.5 Analyzing the Fundamental Properties of Limits

Ch 6.6 Exploring the Squeeze Theorem: Definitions and Practical Examples

Ch 6.7 Examining Graphical Representations of Limits: Defining Asymptotes and Infinity

Ch 7. Advanced Concepts in Rate Analysis

Ch 7.2 Investigating Slopes as Indicators of Rate of Change

Ch 7.3 Understanding the Mean Value Theorem and its Applications

Ch 7.4 Analyzing Rolle's Theorem as a Special Case of the Mean Value Theorem

Ch 7.5 Defining Derivatives: The Formal Approach

Ch 7.6 Visualizing Derivatives through Graphical Representations

Ch 7.7 Exploring the Concept of 'Differentiability' in Calculus

Ch 8. Advanced Techniques in Calculus: Derivatives and Their Applications

Ch 8.2 Exploring the Linear Properties of Derivatives

Ch 8.3 Deriving Derivatives of Trigonometric Functions

Ch 8.4 Computing Derivatives of Polynomial Expressions

Ch 8.5 Determining Derivatives of Exponential Functions

Ch 8.6 Employing the Chain Rule for Differentiating Complex Functions

Ch 8.7 Analyzing Differentiation of Factored Polynomials: Product Rule and Expansion

Ch 8.8 Determining Appropriate Applications of the Quotient Rule for Differentiation

Ch 8.9 Interpreting Higher Order Derivatives Using Graphical Representations

Ch 8.10 Calculating Higher Order Derivatives with Precision

Ch 8.11 Investigating Techniques for Finding Derivatives of Implicit Functions

Ch 8.12 Computing Derivatives of Inverse Trigonometric Functions

Ch 8.13 Applying Various Rules of Differentiation for Accurate Derivative Calculation

Ch 8.14 Solving Optimization Problems in Calculus: Illustrations and Elucidation

Ch 9. Advanced Graphical Analysis and L'Hôpital's Theorem

Ch 9.2 Exploring Non-Differentiable Graphs and Their Characteristics

Ch 9.3 Determining Extremum Values on Graphs with Precision

Ch 9.4 Utilizing Differentiation to Locate Extremum Values Accurately

Ch 9.5 Investigating Concavity and Inflection Points in Graphical Representations

Ch 9.6 Understanding Concavity and Inflection Points through Differentiation Methods

Ch 9.7 Data Mining: Function Properties from Derivatives

Ch 9.8 Data Mining: Identifying Functions From Derivative Graphs

Ch 9.9 Unraveling the Concepts behind L'Hôpital's Rule

Ch 9.10 Applying L'Hôpital's Rule in Elementary Scenarios

Ch 9.11 Implementing L'Hôpital's Rule in Complex Problem-solving Scenarios

Ch 10. Advanced Applications of Calculus

Ch 10.2 Estimating Function Values Through Linearization Approaches

Ch 10.3 Unveiling the Concepts behind Newton's Method

Ch 10.4 Employing Newton's Method to Determine Equation Roots

Ch 10.5 Exploring Optimization Strategies Using Differentiation

Ch 10.6 Optimizing Fundamental Systems for Enhanced Performance